BERJAYA

Success Academy Teaching Algebra To 2nd Graders: rigor or torture?

Posted on December 27, 2023 by garyrubinstein

Success Academy is the infamous charter network of New York. Founded in 2006, and featured in Waiting For Superman, its growth was fueled by high standardized test scores. But as people, like me, looked more closely at the publicly available datapproa we found that there are some shady ways to achieve high standardized test scores.

The biggest factor inflating their test scores is student attrition. By putting pressure on the families of struggling students and by threatening to force those students to repeat a grade or two, Success Academy ends up only graduating about 25% of the students who begin there. And though they do take some students off the waitlist to replace some of the students who leave there, many of those ‘backfill’ students struggle there and are also forced to repeat a grade or have to transfer out.

With all the research I have done about Success Academy over the years, it is always strange for me when I find myself in the presence of an actual Success Academy student. It’s like being a paleontologist and seeing a live dinosaur. But a few weeks ago I got the chance to meet a child and his mother while taking my own son for a haircut.

I was waiting on the bench they have at the barber where my son was getting his haircut in the back of the shop when I overheard another boy at the front of the store talking about math with his barber. ”Ask me to count by 5s,” he said. ”Now ask me to count by 10s.” His barber started quizzing him, “How many 5s do you think are in 100?” and when the boy figured out that it was 20, the barber asked “How many 20s do you think are in 100?,” which was quite a good follow up question, I was impressed.

The boy’s mother was seated next to me and she told the barber that he was excited because he had just come back from math tutoring. She said that the extra tutoring was $60 an hour and she already paid up for a session a week until June. The barber said, “I’m in the wrong business.” She said that it was a lot of money but he needed it because his new school is really hard. I already suspected the answer but I had to ask what school is was and she told me Success Academy. Her son transferred in this year as a second grader and was not doing well, especially considering he has a learning disability.

“They teach some crazy math over there,” she said and then proceeded to take out her phone to show me some pictures she took of some of his assignments.

You don’t hear much about what they actually teach at Success Academy. I know about the test prep in the spring but it seems like it would be to their advantage to have a good, developmentally appropriate curriculum, or would it?

Looking at the phone, I had to take a second to process what I was looking at. While second grade is a time to get familiar with numbers and learn ways to add and subtract and to get some ‘number sense’ and do some basic problem solving involving adding and subtracting and even some informal multiplication (counting by 5s for example), what I was looking at was, without doubt, Algebra.

The question on the phone was to solve for c in the equation:

17+10+c+2=19+30

Algebra is when you solve for a variable by adding or subtracting equal things to both sides of an equation. In 6th or 7th grade, you would solve this by turning it into c+29=49 and then subtracting 29 from both sides of the equation to get c=20.

For this second grade class, they made the question so that a student might notice that you could put the 17 and 2 together on the right and turn this into 19+10+c=19+30 and then you can get rid of the 19s and turn it into 10+c=30 which would mean that c=20. It still is Algebra and not something that I’d advise teaching to second graders. It’s too abstract for kids that young who are just getting comfortable with numbers and adding and subtracting. So why does Success Academy think this is a good thing for second graders to learn?

The mother said that even though Success Academy is hard for her son, she wants to keep him there because “They get their students into Ivy League schools. And they help them get scholarships too.” I did not have the heart to tell her that only a very small percent of Success Academy students even make it to 12th grade there and the students who get into the Ivy Leagues are generally not the ones who transfer in during second grade.

“I heard they sometimes make students repeat a grade?” I felt bad about saying it, but I knew how she was going to respond. ”They already told us he may have to repeat,” she said and then said “You ever hear of a kindergartener having to repeat?”

“No,” I lied and she said “My friend’s son had to repeat kindergarten there.”

I didn’t pry anymore. I’m hoping that maybe her son can catch up and can thrive there and maybe be one of those 25% who graduate from there and get a scholarship to an Ivy League school. Which brings me back to the question: Why are they making second graders do Algebra?

That math is so developmentally inappropriate, there can’t be a good pedagogical rationale. It can’t be that students rise to meet the ‘rigor’ of the 6th or 7th grade math. The only reason I can speculate is that this math is designed to break kids like this boy, to use as a weapon to weed him out. If you want to make struggling second graders and their families miserable, there is no more sinister way to do this while simultaneously saying that you are doing them a favor by keeping your expectations high.

My son’s haircut ended and I said goodbye to the mother and wished her and her son good luck. It felt a little strange knowing so much about what they are likely going to suffer in the coming years but not really being able to warn them. Maybe it will work out for them, I hope so.

Posted in Uncategorized | 12 Comments

Will KIPP NYC Be Disqualified (Again) From U.S. News & World Report Best High School Rankings?

Posted on September 25, 2023 by garyrubinstein

There is exactly one KIPP high school in New York City.

KIPP NYC College Prep High School was started in 2009 to serve students graduating from KIPP middle schools. In 2013 they moved into a new facility that was part of a $100 million project.

While KIPP was once the ‘gold standard’ of charter schools, they do seem to have lost their luster. Once featured in the Waiting For Superman ‘documentary,’ KIPP does seem to have failed to live up to the original expectations. Between 1995 and 2010 they grew steadily but over the years there have been so many KIPPs that have not performed well and have closed down. Though occasionally there is some report, like recently, about how minority students who attend KIPP high schools have a higher college graduation rate than minority students who don’t, the reports seem to have a lot of flaws.

Every year, U.S. News & World Report ranks the high schools in this country. Based mostly on A.P. results, the national rankings and the state by state rankings can be important, especially for charter schools who can use a high ranking as something to put into a report for funders.

According to the latest 2023-2024 rankings, the top two charter high schools in New York City are Success Academy Charter at #12 and KIPP Academy Charter at #20.

In my most recent post I explained how Success Academy’s standing is inflated by their use of the ‘fifth year of high school’ lowering their less important graduation rate statistic while raising their college readiness statistic.

Now for KIPP, there are some notable things just based on this abbreviated view of their results on the U.S. News site. For one thing, the name of the KIPP high school is not ‘KIPP Academy Charter School’ but ‘KIPP NYC College Prep.’ The other thing is that their Enrollment is listed as 276 instead of the 1000 students they actually have. And, yes, they have the all important College Readiness score of 100 which means that all of their seniors take and get a 3 on at least one AP exam.

The mystery gets stranger when you search for KIPP high schools in New York and two schools come up, KIPP Academy and KIPP Infinity.

So there is the other KIPP high school in NYC according to U.S. News and that school has 4 times the number of students and in that under performing sibling of the 20th ranked school they don’t have any students passing the AP test. How can this be?

The answer is that there are not two KIPP high schools but only one. These schools, KIPP Academy and KIPP Infinity are actually middle schools. Even in the New York State data, there is not an official KIPP NYC College Prep school but these middle schools have as part of their enrollment the high school students. I don’t know why New York State allows them to do this and why they can assign all the students and only the students who pass an AP exam to KIPP Academy middle school and the students who don’t pass an AP to KIPP Academy Infinity middle school.

According to the KIPP website, over 90% of the over 1000 students at the (one and only) KIPP High School take an A.P. course.

If 90% of the students take the test but only 25% of those get a 3 and are put into the KIPP Academy middle school numbers, that means that 75% of those students (which is about 70% of the students at the actual KIPP high school) take an A.P. but don’t get a 3 on it. So if the two schools were accurately listed as one school in the U.S. News rankings, the combined college readiness score would be around a 25 which would put them not at #20 in New York State but more like #300.

Now one way to defend KIPP on this is to say that this is New York State’s fault. They are the ones that allow KIPP to assign the students from their one high school into two middle schools depending on whether or not they pass their AP tests and that New York State reports the data to U.S. News who have no way of knowing that these are really just the students from one high school. But certainly it would be ethical of KIPP to let U.S. News know about this.

But I’m not going to put the blame on New York State entirely. Because U.S. News should have been aware of this as the same thing happened six years ago. Back then they had four different middle schools categorized as high schools. I discovered this scheme back then and blogged about it and a few months later KIPP was disqualified from the list, possibly because word of my post got back to them. But not before the ‘school’ was celebrated in places like The74 for being, at that time, the fourth ranked high school.

For sure they should be disqualified again like they were in 2017. Then this loophole should be closed by New York State. There is just no reason why a high school in its own $100 million building has students assigned to two different middle schools depending on how they did on the AP test. If New York State won’t fix the loophole then U.S. News can check for this with the KIPP NYC schools especially since they have done this before. And KIPP could do more than just hope nobody will notice what happened again.

Posted in Uncategorized | 4 Comments

Success Academy Games U.S. News & World Report Best High School Ranking

Posted on September 17, 2023 by garyrubinstein

In the latest U.S. News & World Report Best High School Ranking 2023-2024, the Success Academy High School was ranked the 102nd best high school in the country and the 12th best high school in New York State.

Here is the list of the top 13 New York High schools on the list:

1	High School Math Science and Engineering at CCNY
2	Townsend Harris High School
3	Queens High School for the Sciences at York College
4	Stuyvesant High School
5	Staten Island Technical High School
6	Bronx High School of Science
7	High School of American Studies at Lehman College
8	Brooklyn Technical High School
9	Brooklyn Latin School
10	Eleanor Roosevelt High School
11	Manhattan/Hunter Science High School
12	Success Academy Charter School-Harlem 1
13	Jericho Senior High School

Over the years, U.S. News has tweaked the way they weigh certain categories, but the primary component has always been what they call the ‘College Readiness’ index, which counts for 30% of the overall score. The way the College Readiness index is calculated is that they take the percent of students at the school who took at least one AP test and that counts for 1/4 of that score while 3/4 of the score is the percent of students at the school who took and got at least a 3 on at least one AP test.

The AP test is graded out of 5 and colleges often give credit for a score of 3 or better. But this ranking does not do anything to distinguish between schools where students take multiple AP tests and where they get 4s and 5s on them. So a school that has 100% of the students take exactly one AP and they all get 3s on it would be ranked higher than a schools where 98% of the students take an average of four APs each and they get an average of a 4 on them. But still, the ranking system does seem to put schools where graduating students are successful in college nearer to the top of the list. In the New York list, the schools in the top 13 are mainly the specialized New York City high schools.

When you go to the top schools list, they feature three statistics on the main view: Graduation rate, college readiness, and enrollment. Enrollment isn’t part of the ranking calculation but Graduation Rate, which they define as the number of students who enter 9th grade and graduate 4 years later, is 10% of the ranking.

For all the schools in the top 80 in New York state, the second lowest graduation rate was 92%. The first lowest was Success Academy with a 75% graduation rate.

On this graduation rate statistic, Success Academy is actually in the bottom 10% in the state and also in the bottom 10% in the country. Nationally it is number 16,468 out of 17,680.

As I’ve written about before, only about 25% of the students who start Success Academy as Kindergarteners end up graduating from the school in 12th grade. More amazing is that only about half of the students who make it to 9th grade also stay to graduate from there in the 12th grade. And among those who do graduate, at least 25% of those take five years to graduate. So this 75% graduation rate is somewhat misleading if you think it meant that the students drop out since the other 25% likely graduate the next year.

Success Academy explains that this is a feature of the school. In their family handbook they explain that they ‘holdover’ students who they think need to repeat a grade and they also ‘skip’ students (skip a grade) who they think are advanced. You would think that most of the holdovers would happen before 9th grade and that once a student completes 9 years (or 10) of school there that they should be in pretty good shape to do the last four years without needing to be a ‘holdover’ either again or for the first time.

But it seems that Success Academy often has students take the fifth year of high school after they have finished 12th grade. On their site they describe it as ‘a fifth year of high school.’

Reading into this explanation there are some things I notice. One is that some ‘previously skipped’ students get eventually left back which must be a kind of strange thing for them. Also notice that one of the benefits of the fifth year of high school is that those fifth year students can now take AP courses. In other words, the 75% four year graduation is directly related to their 100% college readiness index. So if they were not to have the 5th year of high school maybe their 75% four year graduation rate would turn into a near 100% four year graduation rate but their college readiness index might go from 100% to 75% and since the readiness index is 30% of the ranking and the graduation rate is just 10% of the ranking, that change would move the school way down on the overall ranking.

My feeling is that this fifth year of high school, like most things that Success Academy does, is something that benefits the organization more than it benefits the kids. It helps the school get 100% of their students into colleges, it helps the school get some of those students into better colleges than they might have gotten into if they didn’t do that ‘fifth year of high school.’ And, in this case, those extra AP tests help them inflate their position on the U.S. News & World Report rankings.

Posted in Uncategorized | 5 Comments

What (The Heck) Am I Doing On The Citizen Stewart Podcast?

Posted on August 16, 2023 by garyrubinstein

Life is short.

Over the past 11 years, since I entered the education reform debate on social media, I have had a lot of ‘debate opponents.’ The first was actually business tycoon Whitney Tilson, but others have come and gone, they are a blur to me. Joel Klein, John White, Cami Anderson, the list goes on. There was once even a TFA communications director named Juice Fong, if I remember correctly. Generally these opponents run out of steam or interest and they fade away. The thing that causes them to run out of energy is also the reason that I’ve been able to basically destroy them in all the debates — they are not fully invested in their cause the way I am.

One aspect of Twitter that is hard to avoid is ‘trolling,’ which is when someone responds to a tweet with some kind of pointed comment. It is a bit of an art form to do this sometimes in 140 characters, the ‘classic’ Twitter limit. I have actually done my share of trolling, sometimes I can’t resist. It’s just part of the medium. And if you can dish it out you should be able to take it in, so I expect to get trolled sometimes myself. In a strange way, it’s a kind of complement when you get trolled since it means that you are perceived as somehow important enough to attack.

Of all the Twitter opponents I have ever sparred with, there is no doubt that the relationship that had the most energy in it was my experience with Chris ‘Citizen’ Stewart. Now I know that many of my blog readers have a very negative impression of him, and maybe by now you’re blocked him on Twitter and maybe he has blocked you too.

Chris Stewart is a parent of five children. He was an elected school board member in Minnesota. Over the years he has been a blogger, a podcaster, and, yes, a Twitter troll. I don’t remember when I first interacted with him, but it was likely around 2015 during the height of the ed reform movement. At that time, the influence of Waiting For Superman and rock star reformers like Michelle Rhee caused an anti-teacher’s union, pro charter, mania. I joined in on the ed reform skeptic side and helped use data to combat ed reform propaganda. So Chris would sometimes comment on my Tweets and we would go back and forth. Back in those days I found it fun to do the Twitter debates though sometimes things would get personal. I did try to be careful what I would say, you can go through the archives and check if you want, I never deleted any of my Tweets. Though I sometimes did not like his style on Twitter, I had a sense that unlike the Whitney Tilsons and the Joel Kleins, Chris Stewart’s passion for what he was doing stemmed from a genuine place. I felt like maybe he was naive because he wanted to believe some of the ed reform propaganda, but it wasn’t because he had to be right and everyone else had to be wrong but because he truly wanted education to improve in this country, particularly for Black children.

Though the education wars continue on so many fronts, my area of expertise — using data to combat charter school propaganda — isn’t needed as much as it used to be so you may have noticed that I don’t blog as often as I used to and I haven’t been involved in a lot of Twitter fights either. It’s actually nice to not have ‘nemeses’ that I have to worry about challenging my tweets.

But I’m still a public school advocate and public school teacher advocate and as part of that, I’m going to the NPE conference in October and participating in a few panel discussions. One of them is about how the ed reform debate has changed and what the new sorts of arguments and messages might be coming from the reformers. So a few weeks ago I listened to a few episodes of Chris Stewart’s new podcast and was pleasantly surprised by what I had heard. In the past year and a half, it seems, Chris Stewart has evolved in his thinking. And I know some people who have endured some Stewart barbs on Twitter are not going to buy it, but I listened to these podcasts and from my perspective I was hearing thoughtful nuanced analysis of big education issues. And the cohost Ravi Gupta, who I had not known much about before, is also someone who sounded reasonable to me even though he once was in charge of a ‘no-excuses’ charter chain in Tennessee about 10 years ago. So I listened and wrote up a positive review, which included a correction about something inaccurate they said about me, personally.

A few days after I posted the review, Chris Stewart reached out to me to invite me to be a guest on the podcast. A few years ago he had invited me on another podcast but I did not really trust him at that time. But this time, my gut told me that ‘yes’ I want to do this. So I did.

I was pretty nervous, like maybe this was a trap and it was going to be two against one and maybe they had found some things I have written or Tweeted and were going to take them out of context, I didn’t know what was going to happen. But we talked for almost an hour and their team edited it into a very accurate 40 minutes of what we talked about and the tone and sentiment of why it was important for us to do this. The two hosts were very welcoming to me and treated me like a valued guest. I’m pretty happy with the way it came out. I did not ‘win’ all the points I might have wanted to if this were a few years ago. Maybe not needing to prove I’m so correct or so smart is good for my blood pressure anyway.

So while this was a good thing for me to do, and I think for Chris Stewart also, I’m not certain that it translated into riveting podcast entertainment. I hope it did. You’ll have to judge for yourself. You can listen to it here. It is also on Apple Podcasts and on Spotify.

Maybe some people will think that I’ve ‘sold out’ and was fraternizing with ‘the enemy’ and by ending the feud I’ve somehow given up the fight. Don’t worry about that. There are still plenty of fights to be fought, like what’s going on in Houston with the state takeover and there are still crazy ed research reports that convert the 50th vs the 51st percentile into so many ‘days of learning’ or even ‘weeks of learning’ and I’ll be around to examine the issues and interpret the numbers when needed just like before.

As far as other former Twitter opponents, this does not indicate I’m doing a blanket reconciliation with all of them, so don’t get any ideas Campbell Brown.

Posted in Uncategorized | 4 Comments

A New Low For TFA: Some trainees only get about 11 hours of student teaching.

Posted on August 15, 2023 by garyrubinstein

Teach For America’s teacher training has always been the weakest spot of an organization that has no shortage of weak spots.

Ask any teacher what the most useful part of their training was and they will tell you that it was their student teaching experience. You can read about and discuss the theory of teaching and about how what students do and don’t respond to, but until you are standing in front of an actual class, it is all just theory.

Back in the early 1990s when TFA was a new organization, they had the sense to know the value of student teaching so in the seven weeks of training, they tried to make it so each teacher got to do five weeks of student teaching for three hours a day, a total of 75 hours of student teaching. Yes, this wasn’t enough, but it was at least a good faith effort to maximize the institute time.

When TFA nearly ran out of money in the mid 1990s they moved the institute from Los Angeles to Houston. In Los Angeles there was year round schooling so there were many opportunities to do student teaching in an actual school. But in Houston all they could do is the limited enrollment summer schools. The institute was shortened, I think to five weeks, so there were just four weeks of student teaching. To make matters worse, there were so few students at these summer schools that instead of trainees getting their own class, you would have four teachers teaching a class, sometimes of about 12 students. Each corps member would get only one fourth of the time to be the ‘lead teacher’ so the number of hours as lead teacher was reduced from 75 in the early 1990s to then about 15 hours (4 weeks=20 days, 20 days * 3 hours = 60 hours, 60 hours / 4 = 15 hours). And this is how it was from about 1994 until 2019, so for 25 years. I was annoyed by this reduction of student teaching and spoke up about this a lot over the years.

But according to a new article in Education Week called Once a Big Player, Teach For America Tries to Regain Its Footing, the student teaching in some regions has been reduced from 4 weeks to 3 weeks. So for teachers that have 3 weeks, they likely only get 11.25 hours of in-person student teaching.

From the article:

And the organization has adjusted its training and onboarding process. TFA spokesperson Natalie Laukitis said in an email that corps members now receive three weeks of virtual training focused on teaching content, classroom management, and how to create an equitable and inclusive learning environment. Then, corps members undergo at least three weeks of practicum, in which they work directly with students under the supervision of a TFA employee.
https://www.edweek.org/teaching-learning/once-a-big-player-teach-for-america-tries-to-regain-its-footing/2023/08?utm_source=nl&utm_medium=eml&utm_campaign=eu&M=7413480&UUID=467c6649b307288df0a5e38c12a64c52&T=9876685

Also ironic that TFA has adopted a hybrid training model where three weeks of the institute is done virtually. Especially with all the ‘learning loss’ hysteria as a result of pandemic remote school, you would think that TFA would want to avoid virtual training as much as possible.

When TFA corps members only get 11.25 hours of student teaching, their chances of being effective teachers is quite low. And when a corps member is an ineffective teacher, there are two main categories of people who suffer. The students of that corps members are complete innocent bystanders in this dynamic. They have to suffer through a teacher who does not know how to properly manage a class. But the other one who suffers is the TFA corps member themselves. They are the ones who will go through the trauma and the guilt of failure and the regret of trusting that TFA cared enough about them and about their students to at least attempt to help them prepare to be in charge of the learning for dozens, if not hundreds, of children.

One thing I wonder is if TFA is not, in some way, violating the contracts they signed with school districts who they provide corps members. In some of those district, they pay TFA a hefty finders fee for the privilege of hiring untrained teachers who only have about an 80% chance of making it through the first year and a much lower chance of having a positive impact on their students.

Posted in Uncategorized | Leave a comment

HISD Suffers With ‘New Education System’ Turnaround Plan

Posted on August 10, 2023 by garyrubinstein

With around 200,000 students, Houston Independent School District (HISD) is the 8th largest school district in the United States. For years there was talk about the state possibly taking over the district and this finally happened on June 1, 2023. The board was fired and replaced by Texas Education Agency (TEA) appointees. Mike Miles, who founded a charter school network called Third Future Schools and was previously the head of Dallas Schools for three years, was hired as the new HISD superintendent. While most people new to a job like this would take some time to get the ‘lay of the land,’ Miles instantly proposed some radical, and in my estimation, terrible, reforms which I will outline in this post.

He identified the three lowest performing high schools in HISD: Wheatley, Kashmere, and North Forest. Those three schools together with the 26 middle and elementary schools that feed into those high schools were to become part of a new ‘New Education System’ known as NES. This NES is the latest ‘turnaround’ district. Over the past 20 years there have been several of these, the most prominent are the Recovery School District (RSD) in New Orleans, set up after Hurricane Katrina in 2003 and the Achievement School District (ASD) in Tennessee, created in 2011 with Race To The Top money. There was also Michigan’s Education Achievement Authority (EAA) in 2011 as well as a few more that have popped up around the country. To my knowledge, there has never been a successful takeover of this sort in the history of this country. The EAA has been shut down, the RSD has been merged back into the New Orleans school system and the ASD has floundered, never having any success at all in improving the test scores of the schools it took over. It is funny/sad to see this hopeful panel discussion by the leaders of these districts before it was known how badly they would fail. (I’ve written a lot about the ASD, but here is something I wrote summarizing the history of these turnaround efforts.)

These turnaround efforts sometimes have school closures or staffs at schools having to reapply for their jobs and often have the schools converted into charters. For the HISD NES model, the schools are not getting taken over by charters but teachers do have to reapply for their jobs. Teachers at these schools will get raises and opportunities for bonuses with test score based merit pay. Other changes that will happen at these 29 schools are a restructuring of the teacher role where the teacher is like a ‘surgeon’ doing the most important part of the job while other tasks like grading, lesson planning, and discipline are done by others. Also, you may have read about elsewhere, libraries at these schools are converted into discipline centers where students are sent to watch a live streamed version of the lesson on a computer screen.

The reason that no turnaround effort like this has ever worked is that it is based on faulty assumptions about what the cause of the low test scores are at those schools so any solution based on those assumptions is doomed to fail. It is like trying to treat a broken leg by giving a patient a complete blood transfusion.

As someone who has been teaching since 1991 – and my first four years were in HISD actually, looking at the list of changes makes me shudder. Anyone who ever taught can see how most of these changes will make the schools worse but I want to summarize some of them here.

All teachers have to reapply for their jobs – When students come back and learn that many of their favorite teachers were not hired back, this can be very traumatic. There is no guarantee that the teachers who replace those who weren’t hired back, even if those teachers have been successful at a different school, will necessarily be a good fit at this school. This uncertain improvement coupled with guaranteed disruption is a pretty big risk. Why not first see how the current staff does with these new supports?

Discipline handled by administrators – In every school the most competent teachers handle their own discipline problems and at these schools it will be no different. When the teacher, building on the relationships they formed with the student and the families, handles discipline in class it is a lot more effective. When administrators do the discipline, it involves a student having to leave the class and fall behind. So in a way this is like every school where the administrator handling discipline is the last resort. But I think they are implying that the administrators are going to be so tough on the students, sending them to a detention center (in the room that used to be the school library) to watch the lesson on a live feed, so the discipline will be so much more efficient that teachers will choose to go right to that rather than ‘waste time’ doing discipline by building relationships with the students. So when the students are all in the former library watching a lesson on a video that they were struggling to concentrate on in the actual classroom, they will have even more trouble watching it on the video where they can’t even ask questions if they have them. These detention centers will surely be places where students suffer and don’t learn much and I just don’t see this model working. It will depend on whether or not teachers really believe that they don’t have to deal with discipline anymore since they can just send the kids out right away as it is no longer their jobs to do the discipline. If that is the case, those former libraries could get really full really quickly and they might have to find another room, maybe the band or art room, to convert to an overflow room.

Lesson plans and materials provided by curriculum developers – It sounds like teachers at these schools will be mandated to follow scripted lessons and pacing schedules. It is so unlikely that these scripted lessons will be good enough and the pacing schedule so perfect for all classes. There are times where a concept takes more time than you thought it would and especially if the next topic builds on that one, you cannot just go on until you finish the first topic. If you are forced to stay at a pace produced by someone who does not know your classes, it can be a very miserable experience for students and for the teacher. Creating your own lessons based on standards maybe, is one of the most important parts of teaching. There is no way a scripted lesson can be as good as a teacher made lesson tailored specifically to their student. I wonder how much flexibility teachers will have in adapting the lessons, at least, to make them more appropriate for their students. In my experience, bad lesson plans lead to discipline problems. And even if administrators are handling those discipline problems, it still is frustrating if you are forced to use bad lesson plans that are almost guaranteed to result in this.

Differentiated assignments copies made by support personnel – Yes it would be nice to have someone make copies for me, but I’ve been at schools where the materials have to be submitted a week in advance and teachers cannot touch the copy machine. I’d be concerned that with all the copies made by the support staff, the copy machines might be off limit and potentially if you want to make copies of something that is not part of the scripted curriculum, maybe you will not be able to.

Papers graded by support personnel – Grading is a time consuming process. And, yes, there are times where my ‘grading’ is little more than glancing and seeing if any effort was put into the assignment. But grading is also an integral part of the teaching process. It is where you see what the students produce and get to assess if they learned the concepts. With math, the end result of grading is not just what percent of the final answers did the student get correct, but what are the common errors that I’m seeing. So if someone else is being paid to do my grading for me and I don’t even have the time to do the grading myself because under this model maybe my day is filled with the other teacher responsibilities, then I’m not able to teach as effectively since I don’t have all the information I need. Logistically speaking, I can’t see how this would work. What is the ratio of people whose job it is to ‘grade’ to the number of teachers. I think that one ‘grader’ could probably only help about four teachers a day so this would be a pretty big staffing issue. And who would ever want to be a full time grader? The thing that makes grading a tolerable task for teachers is that the teacher is invested in the results. The teacher wants to know how the students are progressing and how the lessons were received. Just grading a stack of papers from kids that you don’t know anything about would be extremely tedious to do all day. Are these graders expected to write feedback on the papers? Or is the net result of the grading merely to get a numerical grade on the assignment. This is one of those that sounds good on paper but doesn’t work so well in reality. It’s like saying that assistants will eat lunch for the teachers.

Four periods of duty in a month (75 minutes each time) – Once a week doing something for the school seems reasonable, it happens in a lot of schools. But I’d want more details about what they have in mind, what if you are manning the library/discipline room?

$10,000 stipend – For sure they have to offer something to compensate for the frustration teachers are going to experience in these schools. I suspect that many of them will find that it wasn’t enough money to make it worth it.

$3,500 incentive pay – Usually these are based on some very opaque ‘Value Added’ algorithms leaving some of the most talented teachers not getting the bonuses. There is not evidence of this kind of merit pay having any impact on student achievement..

A bizarre recent development is that in addition to the 29 NES schools in the Wheatley, Kashmere, North Forest feeder pattern, a whopping 57 schools have volunteered to become NES ‘aligned’ schools (NESA) where they will get some of the financial incentives if they agree to follow the NES blueprint. I was sad to see the school I used to teach at, Furr High School, on this list, especially as it was so recently reformed by the XQ superschool program and was featured in the three network simulcast funded by Laurene Powell-Jobs. I am not sure why any school would voluntarily apply for this. I don’t know that those schools get the $10K stipends, probably not. Maybe they like the idea of other staff members planning lessons and grading papers, I can’t say what motivated them, but I expect that many of the staffs at those schools are going to regret this being foisted on them when they weren’t even targeted for it.

Turnaround efforts like this have never worked and they have even gone out of style in recent years since there have been so many failures. I would like to do some updates with anecdotes from actual teachers at these schools throughout this turnaround process. If you have any information, go to this form if you want me to write about it. I will keep your names anonymous and even which school you are at can be suppressed if you are worried that you will get in trouble for reporting this stuff to me.

Here is the link to the form.

Posted in Uncategorized | 3 Comments

Is Most School Math Useless? Part 5: What should the math curriculum be?

Posted on August 7, 2023 by garyrubinstein

If you’ve read parts 1 to 4 of this series, you may be confused. I the first part I said that not much of the school math is useful. In the second part I listed a few of those useful topics. In the third part I listed some topics that I don’t consider so useful. If I ended it there, it would seem like the best course of action would be to cut the amount of math we teach by at least half. But in the fourth part I wrote about something that seems to negate the point of the first three posts. I said that some of that ‘useless’ math was just as important as the useful math because it is engaging in the way that art or music can be useless but engaging. So this fourth part could be used to defend the position that no math topics should be put on the chopping block and we should just leave the math curriculum exactly how it is, maybe cutting the topics that are deemed ‘useless’ and not thought provoking but maybe expanding the remaining topics so those can be learned to more depth.

If you’re worried that that’s where I am going with this series, you can relax because in this post I will suggest a radical change to the K-12 math curriculum. But before I can do that, there are three really important questions that have to be answered: 1) What is the current K-12 math curriculum? 2) What is the current K-12 math curriculum trying to achieve? and 3) What is the current K-12 math curriculum actually achieving?

I think I should answer question 3 first. What the current K-12 math curriculum is actually achieving is traumatizing the vast majority of students. We know this because the moment that math becomes optional for the vast majority of students, they never take it again. And they forget most of the math they learned and are left with a vague memory of how much they hated math.

For question 2, the current K-12 math curriculum is pretty easy to describe. From kindergarten to 8th grade has your basic math operations, adding, subtracting, multiplying, and dividing with whole numbers then fractions and decimals and then negative numbers. Proportion and percents lead to various word problems. Some basic Geometry with area and perimeter of different shapes ranging from squares to circles and even some 3 dimensional objects. Eighth grade is usually ‘pre-Algebra’ where students start solving for missing variables and learning how to solve simple ‘systems of equations’, really there is no such thing as ‘pre-Algebra’ — if they are using variables and doing operations to both sides of an equation to solve for a missing variable, then that is ‘Algebra.’ Some students get through this pre Algebra course by the end of 7th grade. 9th, 10th, 11th, and 12th grade are Algebra 1, Geometry, Algebra 2, and pre-Calculus. Pre-Calculus is basically Algebra III. Students who got through pre Algebra in 7th grade can take Algebra 1 in 8th grade so that they take pre-Calculus in 11th grade so that in 12th grade they can take ‘Calculus’ (which is like Algebra IV). Some students take statistics instead of Calculus. It’s not clear if colleges ‘like’ Calculus better than statistics. In New York State students have to take Algebra 1, Geometry, and Algebra 2, and pass the Algebra 1 state final (known as ‘The Regents’) to get a ‘Regents diploma. To get an ‘advanced Regents’ diploma they have to pass all three Regents. A passing score on these math Regents is a 30% which is curved up to a 65. 1/3 of the students who take the Algebra 1 Regents get under a 30% and they fail. 1/3 of the students get between a 30% and a 60%. A 30% gets curved to a passing 65. A 60% gets curved to a passing 80. 1/3 of the students get between a 60% and a 100%. A 100% does not get curved, it is a 100. The students who ‘passed’ with a pre-curve score of 30% to 60% will be forced go on to Geometry and Algebra 2 but will not take the Regents exam since for the Regents diploma you have to take 6 credits of math but you only have to pass the Algebra 1 Regents.

Question 1 is the hardest to answer. You know how I feel about what this curriculum actually accomplishes from my answer to question 3. But what was this trying to accomplish? Keep in mind that this curriculum was built over a 200 year period from the early 1700s to the early 1900s. Harvard wanted students to come in knowing Algebra so Algebra was added to high school. Then Harvard wanted them to know Geometry so Geometry was added to high school. Calculus was a big deal since it was invented in the 1600s and if students studied Algebra 2 and pre-Calculus they would be more prepared for that in colleges. A lot of colleges require one semester of Calculus for many majors. So maybe the purpose of the K-12 curriculum is to get as many students as possible to eventually master Calculus. But taking Calculus does not really mean that you mastered it since even Calculus with its great name is just a subtle collection of tools for studying curves and finding the area of unusual 2D and even 3D shapes. Yes, Calculus is used in physics but those applications are not prominent in the first year of Calculus (though there are some questions about studying a particle that moves left and right along a straight line and speeds up and slows down and acts pretty crazy.) I don’t think the goal of the current K-12 math has anything to do with the intrinsic beauty of math, for its own sake, as a feat of human imagination that I waxed about in part 4. That’s just something that I try to empathize when I teach since I’ve found it to be more motivational and fun for students and then they are willing to endure the more boring stuff since they know I will give them something to puzzle over as much as I possibly can.

OK, now that you know all the issues, you have a context for considering what I think the K-12 math curriculum should be. The first and most important thing is something that many people have been saying for many years. There are too many topics taught in those K-8 years. I’d say there are about 400 ‘things’ that are taught so the curriculum is too packed and teachers have to do they best they can with the topics but they often have to go on to the next topic before every student has mastered the last one. With too many topics, there isn’t enough opportunity for students to do meaningful activities where they can figure out the insights themselves. For early math education the master of this is the great Marilyn Burns. Marilyn Burns is now 82 years old and she is still active in math education. Her 1975 book ‘The I Hate Mathematics! Book’ is a classic. What is so great about her math activities is that they are not just open ended things where the kids meander and hopefully figure out the thing, as some ‘discovery’ approaches devolve into. There are other places where good math activities exist. During the pandemic I had my son, who was in 3rd grade at the time, do The Art Of Problem Solving’s ‘Beast Academy’ program and it was great. Before you accuse me of loving ‘fuzzy’ common core math, I’d better say that students do need to learn their times tables. And I feel pretty strongly that calculators are over used in the younger math grades. In order to do the math well (and it is not so easy to teach this way, which is another issue I will get to some other time), some topics in the early grades will have to be cut. Who gets to decide what to cut? Unfortunately nobody is asking me to do it because I could do it, no committee, just me, in about 3 days.

The 9th grade year (or the 8th grade for students who get through the K-8 by 7th grade) is where things would really change. I would make the 9th grade year a selection of topics from Algebra 1, Geometry, Basic Statistics, Data Science, even some computer science and, yes, some useless but mind blowing math. This 9th grade would need to be good and students would have to like it because (and here’s where I might shock you) after 9th grade I believe math should be completely optional. I envision the 10th grade year (9th grade for accelerated students) to be the best parts of Geometry, Algebra 2, and more computer science, stats, data science, and, yes, some fun ‘useless’ stuff. 11th and 12th grade can be more advanced topics similar to the 10th grade content. Accelerated students can still take Calculus in 12th grade, but there would be no shame in taking statistics or whatever else we want to offer them.

So when you ask me what the goal of my K-9 math plan is, it is very easy to answer: The goal is that students will voluntarily take the 10th, 11th, and 12th grade courses. The K-9 is going to have to be engaging or kids will not choose to take those optional courses and there won’t need to be as many math classes at that school (or math teachers, gulp). The funny thing about my plan is that I believe it would also achieve the goal of the original program to maximize the number of students learning Calculus. At least that’s what I think. Maybe I’m wrong and it will just mean that most high school students stop taking math after 9th grade. If that’s what happens, we’d have to just keep improving the K-9 courses until students elect to keep learning math. And if that still doesn’t work, at least math will no longer be remembered as 13 years of torture — just 10.

Resources:

Here’s an article from USA Today from 2020 that has other people with similar ideas. I don’t like the emphasis on international test scores, but it is good to see that I’m not the only person who thinks this way.

In the introduction to the disastrous common core math standards, they actually say something wise:

“For over a decade, research studies of mathematics education in high-performing
countries have pointed to the conclusion that the mathematics curriculum in the
United States must become substantially more focused and coherent in order to
improve mathematics achievement in this country. To deliver on the promise of
common standards, the standards must address the problem of a curriculum that
is “a mile wide and an inch deep.” These Standards are a substantial answer to that
challenge.
It is important to recognize that “fewer standards” are no substitute for focused
standards. Achieving “fewer standards” would be easy to do by resorting to broad,
general statements. Instead, these Standards aim for clarity and specificity.”

Such a missed opportunity.

Click here for the other parts of this series.

Posted in Math, math reform | 9 Comments

Is Most School Math Useless? Part 4: The usefulness of useless math

Posted on August 5, 2023 by garyrubinstein

Some of the most ancient math texts found on clay tablets from 1800 BCE in Mesopotamia are filled not with ledgers and bookkeeping but utterly ‘useless’ questions like “If you subtract the side length of a square from its area you get 870. What is the side length?” (BM 13901.2) along with lengthy algorithms for calculating the solution. Fast forward to 300 BCE in ancient Greece where they studied Euclid’s Elements, a Geometry book based mainly on using a compass and a straight edge to produce various Geometric shapes and then proving that the shapes created are what they were supposed to be like “Construct an isosceles triangle having each of the angles at the base double the remaining one. (In modern terminology to make a triangle whose three angles are 36, 72, and 72 degrees)” (Euclid IV. 10) Why the Babylonians cared to answer a question like this is not known though for the Greeks we do know that for them, at that time, Mathematics was a search for ideal truths.

In the 1700s and 1800s in this country, the only math topics taught were things that were ‘useful’ in life, like converting units of measurement and other things related to commerce. But over the past 300 years the math curriculum has grown so it has some topics that are useful (or potentially useful) and some that are more abstract and theoretical and certainly less useful than the others if not totally useless. In earlier posts I estimated that about 1/3 of the topics are useful while the rest are not.

In this post I want to examine the ‘useless’ topics and show why at least some of them have a value that transcends whether or not students will ever have an opportunity to use them in their adult lives.

In part 2 of this series I listed six topics that I felt were so useful that every student should master them before graduating high school. And if learning math that is useful is the only thing that matters, we could strip the curriculum down to just these things and the World would likely not end. As the parent of two kids who are now 15 and 12, I would be unhappy, though, if the only math my kids learned were these useful topics.

There are plenty of useless things that I want my kids to learn. When I was in school my favorite part of the day was actually not my math class but my band class. I loved playing the trumpet and took pride that I was first chair and I enjoyed practicing at home (though my family didn’t as much). I looked forward to the band concerts and band competitions we went on. But as much as I loved band and how it made me feel and challenged my determination and endurance sometime, is there anything more ‘useless’ than playing a trumpet? I suppose that some people go on to become professional trumpet players but not many. And I stopped playing the trumpet when I moved into a New York City apartment and now I dabble with another ‘useless’ instrument, the piano. The same could be said about Art. Aside from someone who becomes a professional housepainter, very few people will ever ‘use’ what they learn in Art class. What about poetry? If poetry just ceased to exist, would it really matter?

But of course the ‘use’ of poetry, art, and music isn’t that we are going to use them as adults but because they engage our minds. These creative fields offer us a type of challenge. Some people find these challenges fun. It causes our brains to release dopamine which is like a free drug.

For me, Math is a lot like playing a musical instrument. I like using my mind to discover some kind of pattern and then to see if I can prove that the pattern wasn’t just a coincidence. When I figure something out I get such a feeling of satisfaction. Often when something is too difficult for me to figure out myself I have to cheat and see how someone else figured something out and when I’m reading it it is, for me, like a page turner mystery novel. I’m getting near the end but not quite there yet and suddenly I can see where its going and even if I don’t, when I get to the end I think “Wow, how did I not figure that out myself, it seems so easy now.” And often the math topics that provide the most enjoyable adventure in trying to figure them out or just to understand why they work are the topics that are about as ‘useful’ as playing the trumpet.

In this post I’m going to briefly describe nine topics that are not particularly ‘useful’ but that I think all students should have the opportunity to experience. These topics, by the way, are already in the K-12 curriculum but they are mixed in with so many other less fruitful topics that they might get lost in the crowd. I’ll list these in order from earliest learned to latest learned

#1 The Distributive Property. Though a cousin of the maligned ‘commutative property’ I mentioned in the last post, the distributive proper says that if you have a question like (2+4) * 5, you will get the same answer if you do 6 * 5 = 30 or if you do 5*2 + 5*4 = 10 + 20 = 30.

The distributive property lets you do something like 27 * 6 = (20+7)*6 = 20*6 + 7*6 = 120+42=162. You could even do a double distributive property 27 * 46 = 27*(40+6)=27 * 40 + 27 * 6 = (20+7)*40 + (20+7)*6 = 20*40 + 7*40 + 20*6 + 7*6 = 800 + 280 + 120 + 42 = 1242 which is the basis of the standard multiplication algorithm.

The distributive property also works for subtraction so if you wanted to do 19 * 43 you could do (20-1)*43 = 20*43-1*43=860-43=817.

#2 Pi (𝛑). A circle that has a diameter of 10 turns out to have a circumference of about 30. More precisely it is closer to 31.4159. Long ago they realized that the circumference of a circle was slightly more than three times the diameter, somewhere between 3 1/8 and 3 1/7.

What we now call Pi is very close to 3 1/7 and we usually just memorize 𝛑 is approximately 3.14 which is good enough for the formulas Circumference = 𝛑 * diameter and Area = 𝛑 * radius * radius.

If you give students a bunch of circles they can estimate Pi themselves. Especially if you make it a mystery that the students figure out, it is less likely that they will have no idea what Pi means when they become adults even if they never have to use it in life.

More advanced students can learn how Pi was cleverly calculated in ancient cultures and computer science students can write programs for computers to calculate Pi to millions of decimal places (After 3.14 the other places are ‘useless’ unless you consider solving one of the great mysteries of humankind a worthy challenge).

#3 The Pythagorean Theorem. Maybe the most famous formula in math, a²+b²=c², which you can use to find the third side of a right triangle if the other two sides are known.

For example, if the two legs of the triangle are 5 and 12, then the third side can be calculated by doing 5²+12²=c², 25+144=c², 169=c², 13=c

But what makes The Pythagorean Theorem so thought provoking is the over 200 different proofs of it, many of them visually intriguing like this one.

The Pythagorean Theorem is also the basis of the distance formula in coordinate Geometry and the basis of the entire subject of Trigonometry. Plus it can help you if you ever have a 13 foot ladder and a 12 foot ceiling and you want to know how far to put the foot of the ladder from the base of the wall.

#4 Geometric Constructions. What was once the main theme of the ancient Euclid’s Elements book is still a part of the curriculum but has been relegated to a small unit at the end of the course. But mastering the two tools of the compass and the straight edge and seeing how far you can go with just using these is a two thousand year old game that is both fun and challenging. Even Honest Abe Lincoln loved carrying around his Euclid’s Elements. I particularly like teaching my students how to make a perfect pentagon with these tools though it does take a lot of steps. It’s hard to look at this and not marvel at the ingenuity of how they came up with this.

#5 Completing The Square. The ancient Babylonians answered questions we now would phrase as x²+10x=39 (though they might say ‘Ten times the side length of a square is added to its area and the result is 39. What is the side length?’). In 820 CE an Arab mathematician called al-Khwarizmi (the word ‘algorithm’ came from his name) devised a clever way of finding the missing value.

Imagine a rectangle that represents x²+10x

Now the area of this rectangle has to be 39 but a lot of rectangles have area 39. So he splits the 10x into two halves and slides one half over so now the ‘L’ shaped thing has area 39. The sides of the ‘L’ are x+5.

But a lot of ‘L’ shaped things could have area 39. So the ingenious step is to ‘complete the square’ to fill in the missing piece that turns the ‘L’ into a square.

So now the square does not have area 39, but 39+25=64 because the filled in square had area 25. Well 8*8=64 so x+5=8 and x=3 which is the answer.

When this process is done more generally, it turns into the infamous quadratic formula!

#6 The Golden Ratio. Hidden in the regular pentagon is the number Phi (𝜑) which is approximately 1.618. This ratio is found in nature and some conspiracy theorists claim that it is also hidden in The Mona Lisa.

#7 Coordinate Geometry. In the 1600s the famous philosopher Rene Descartes completed a process that was in the works since Greet times. He showed that Geometric shapes can be converted into mathematical equations and vice versa. Without this, we would never have had Calculus.

#8 Permutations and Combinations. If you go to a Baskin Robbins and get a 3 scoop cone using 3 of the 31 flavors, how many ways can you do that? What if you prefer a cup? Getting the answers to these two questions (26970 and 4495) is the start of a branch of math that can tell you the odds of winning the power ball and the likelihood that someone is cheating with weighted dice when you gamble with them.

#9 Infinite Geometric Series. If you walk halfway to the wall and then half the remaining amount and then keep doing that, will you ever reach the wall? Well, if you stop and pause for a second after each segment then ‘no.’ But if you don’t, then yes because 1/2+1/4+1/8+1/16+… can be shown to equal (or ‘converge to’ if you want to get technical) 1. But what about other series like 1/4+1/16+1/64+… or 1/3+1/9+1/27+…? These pictures give hints.

I hope I’ve succeeded in at least giving you a taste of how math can be something that students could enjoy learning even if it isn’t for something directly applicable to their adult lives.

If the powers that be were to ever find themselves reading this blog post and they got fully convinced that the only redeeming value of 2/3 of the math we learn in school is that it can give us the kind of thrill that we get from poetry, art, or music, they would instantly cut the funding for math the way they have done for those other subjects.

Resources:

There are hundreds of books out there where a math expert gives a survey of intriguing math topics that can spark interest in the subject. They all have most of these ‘greatest hits’ I listed above.

Here are some that I’ve liked.

The Joy Of X: A Guided Tour of Math, from One to Infinity by Steven Strogatz, professor at Cornell wrote much of this for a viral New York Times series.

Beyond Numeracy by John Allen Paulos, the sequel to ‘Innumeracy’, this book is great.

The Magic of Math: Solving for x and Figuring Out Why by Arthur Benjamin, professor at Harvey Mudd and creator of the viral ‘Why Statistics Is Better Than Calculus’ TED talk.

Click here for the other parts of this series.

Posted in Math, math reform | 4 Comments

Is Most School Math Useless? Part 3: What are the most useless math topics?

Posted on August 4, 2023 by garyrubinstein

I’d estimate that about 15% to 20% of school time in K-12 is spent on math. Elementary and middle schools often have their students do 90 minutes of math a day. And it is common for students to take a math class every year throughout high school.

In my last post I listed a meager six math topics that I consider ‘useful’ and by that I mean that those math skills are really needed by adult consumers and also, to some degree, in a lot of professions. And if you believe me about this and you think that any math that is not useful should not be taught in school you might wonder how much time should be dedicated to those topics throughout a students schooling. Now I’m not saying that I think that we should cut all topics besides these few but if I had to answer how long it could take to teach those, I’d say that we could do it in about 1/3 the amount of time. Math would be a thing like music, art, or physical education.

It’s still an interesting thing to think about, though, because it gets to the fundamental question of ‘what is the purpose of learning math?’ or ‘what is the purpose of learning anything for that matter?’ or ‘what makes this thing better to learn than that thing?.’ I will eventually provide my opinions on these questions.

But before we cut 2/3 of the time that we dedicate to math, we should take a look at what sorts of things would we be depriving the students of and whether there would be negative side effects of these discarded topics.

In Part 2, I mentioned a topic that I said was not ‘useful’ of finding the prime factorization of composite numbers. While it is true that hardly anyone in their adult lives are ever asked to break 555 into 5*3*37, maybe the ‘use’ of this skill is not so direct. The ‘use’ of some ‘useless’ topics is that they are prerequisite skills to more complicated topics in future years and those more complicated topics might be ‘useful’ in some science applications. So some ‘useless’ topics might have some utility as scaffolding to other topics.

Another reason that something like factoring has more ‘use’ than it at first seemed is that prime numbers are really important in more advanced math. They are the building blocks of all other numbers. Maybe someone who loves factoring eventually becomes a math major and they use advanced factoring to create a new cryptography method based on it.

And one more argument in favor of keeping the topic of factoring is that fun puzzles are a way to motivate students to be interested in math. So after studying multiplying and dividing and first doing some questions like without using the number 1, what are the possible answers to 15=?*? (3*5, 5*3) and 12=?*? (4*3, 3*4, 6*2, 2*6) you could put a ‘challenge problem’ on the board 555=?*?*? and this gives an opportunity for students to problem solve and to make theories and test them, like they might suspect that 5 is one of the factors and then they have 555=5*111 but 111 looks kind of like a prime number, but apparently it isn’t, and so forth. In this way the ‘use’ of the factoring topic is to make math interesting and provide challenging problems that lead students to think deeply about problems and get the satisfaction of making progress on these problems.

Using this reasoning, I could probably justify keeping every ‘useless’ topic since as a teacher this is what I try to do. No matter how boring a topic might seem, I do my best to find some way to make it into a thought provoking experience. For some topics this is more difficult to do but with enough imagination it usually can be done.

But even though I can maybe find a way to make every topic into something that engages my students and in that way restore the 2/3 of time that I took away from math earlier, I don’t think that we would need to keep every topic so that every student takes 13 years of math. It’s just too much of a good thing and it takes time away from some other meaningful things kids can be learning about.

Here is a sampling of some topics that I would cut if I could. It’s not that these topics can’t be made meaningful, but it just isn’t worth saving them all.

#1 Knowing the names of the some of the properties of mathematical ‘groups’ in elementary school. In the 1960s there was a math education reform plan famously known as ‘new math.’ Though they actually did a decent job on the high school curriculum, the elementary school curriculum was too abstract and was universally mocked and eventually abandoned. But one vestige of it that still endures today is that 3rd graders across the country have to know not just that 2+3=3+2 but to memorize that this is called ‘The commutative property of addition’ and they get tested on state tests about knowing this vocabulary word. Now I’m not saying that this can’t be made into a meaningful topic with some thought provoking challenges (Off the top of my head: What if I invent a new math symbol ‘@’ so that 2@3=2+2+3 and 4@6=4+4+6, would it be true that 2@3=3@2? Make up two of your own symbols and your own definitions for them so that for one of them the commutative property holds and for the other one it doesn’t, and so on — so yes, it is possible to make ‘the commutative property’ interesting, but in my mind, this would be one of the first topics to go.

#2 Absolute value. When a number has two bars around it like | 5 | it means the distance the number is from 0, which in this case is 5 so | 5 | = 5 but also | -5 | = 5 since it is also 5 away from 0. Then, in Algebra 1 they do questions like | x | = 5 so there are two answers 5 and -5 and then they do things like | x+2 | = 5 which has two answers of 3 and -7. Still in Algebra 1 they learn to ‘graph’ absolute value functions which look like the letter ‘V’. Then in Algebra 2 they do absolute value inequalities. Altogether, this takes about a month of math class. Absolute value? More like absolute bore.

#3 At least half of the standard Geometry curriculum. Before math teachers get too mad at me, let me say that it’s probably true that I love Geometry more than you do. I read Euclid’s Elements like it is the Bible. Over the past 15 years I’ve mastered nearly all of the geometric Archimedes treatises. But when I look at the standard Geometry curriculum that my own daughter just completed last school year, I get depressed. And yes, Geometry can be taught in a way that is meaningful, just like pretty much every topic (even Absolute value!) can be made meaningful. But it is really hard to get 9th or 10th graders excited about abstract Geometric shapes. Here’s an example of a typical thing from Geometry:

So you have this circle and the two lines and you are told the length of the segments ID, GD,and KD and you are asked to find the length of HD. There turns out to be a rule that has a very clever proof but that most students eventually just memorize that if you multiply ID*GD and you also multiply KD*HD they will always have the same product. So since ID*GD=21.79, KD*HD=21.79 and since KD=2.6, HD=21.79/2.6=8.39.

Not that I don’t like that theorem but if something has to go, this and about 20 other theorems kind of like this would be on my list. As I said, this theorem is kind of a surprising relationship of lines in a circle and it does have an ingenious proof but is it something that students really ‘need’ to know? It just becomes a thing to memorize and forget after the final exam. Yes, back in 300 BC in Euclid’s Elements this was a really big deal. And maybe there is a place for a Euclidean Geometry elective in a high school for students who really wants to get into the abstract world of triangles, quadrilaterals, and circles and all their obscure properties.

#4 Least Common Multiple and Greatest Common Factor. The multiples of the number 20 are 20, 40, 60, 80, etc. The factors of the number 20 are 1, 2, 4, 5, 10, and 20. The multiples of the number 15 are 15, 30, 45, 60, etc. The factors of the number 15 are 1, 3, 5, and 15. So the least common multiple of 20 and 15 is 60 since that is the smallest number that is a multiple of each. The greatest common factor is 5 since that is the largest number that is a factor of each. These topics are sometimes justified because they can be used to simplify problems involving fractions. Like if you wanted to add 1/15 to 1/20 you could turn them into 20/300 + 15/300 = 35/300 but then you would have to reduce at the end. It is better to use as the common denominator the least common multiple so 4/60 + 3/60 = 7/60. The other concept can get used in reducing fractions so 35/300 can be reduced by dividing the top and bottom of the fraction by the greatest common factor which is 5. But what would be so bad if you reduced with a common factor that was not the greatest. So if you had 24/60 and you didn’t realize that 12 was a common factor and you only noticed that they are both even and instead reduced to 12/30 and then noticed again they are both even so you reduced to 6/15 and then you noticed the common factor of 3 to get 2/5. So the person who used 12 originally reduced the fraction in just one step. Do you get an award for that? My children spent a lot of time learning various methods for LCM and GCF. There was even one that was called ‘The Birthday Cake Method’ because the steps resembled the layers of a big cake.

#5 Radian measure. In the real world the unit we measure angles in is degrees. So a 90 degree angle is a quarter of a circle and 180 degrees is half a circle and a 60 degree angle is a small angle you might use to describe how big a pizza slice is. Well in Calculus it is sometimes better to use a different unit of measurement called a radian where one radian is about 57.3 degrees. And now a 90 degree angle is 1.57 radians approximately and pi/2 radians exactly. It can get pretty confusing but students who are in Calculus can handle it. But in New York state the concept of the radian measure is introduced in the Geometry curriculum in 9th or 10th grade and the next two years Algebra 2 and Precalculus use radians also. The extra layer of confusion prevents students from being able to understand the more important concepts in trigonometry that are in the course.

So I could do this type of description for at least half the topics studied in math. But to add complication to this, I could also make descriptions for each of these topics that would make them sound like they are really important. And I could take a topic that I consider to be really important and could, for arguments sake, describe it in a way that would make it seem useless. If you were to ask a different math teacher what their top ten most expendable and least expendable topics are, the lists would be very different from mine. Of course I think that I’m the ultimate arbiter but so do they.

I guess it is like a reading list in a literature class. There are near infinite number of good works of literature but there is not enough time to do them all. So you can cram too many and cover some, if not most, superficially. Or you can pick a smaller subset and do those in depth. How many you do will depend on how much time you’re given. For math it seems like we have 13 years to fill and even with that we try to cram 15 years of stuff into it. If we were told that you’re only going to get to fill 9 years and you should limit your topics so that they can all be done in a meaningful way, you’re going to have to choose your topics wisely.

In the previous post I listed six concepts in math that are very practical, and if taught well, can be very thought provoking. In the next post I’m going to list some topics that aren’t ‘useful’ in the traditional sense but that I think are essential to be learned in math class for other reasons. Making a list like this forces one to answer the big question ‘What is our goal in teaching math?’.

Click here for the other parts of this series.

Posted in Math, math reform | 12 Comments

Is Most School Math Useless? Part 2: What is the most ‘useful’ math?

Posted on August 3, 2023 by garyrubinstein

What if your house was burning down and you could only save one box of your things? What would you save? Fortunately most people will never have to make this decision but it is still an interesting exercise where you think about what it is in your life that really matters.

As a math educator I sometimes think what if I could only choose a small collection of the most ‘useful’ math topics to save from the entire K-12 curriculum. As I argued in the previous post, I think that at least half of the school math topics are not really ‘useful’ in the sense that you will ever actually ‘use’ them in your life. With this narrow definition of ‘useful’ and ‘useless’ an example of something that is pretty useless is to find what’s called the ‘prime factorization’ of a number like 555 and write it as 3*5*37. There might be some uses of prime factorization in some other math topics but certainly on its own it isn’t a very useful skill.

But some math topics are very ‘useful’ and I think that all students should learn them at some point throughout their schooling. In this post I’m going to make an annotated list of what those topics are. These are like the box I’m saving of ‘useful’ math. The list isn’t going to be very long which leads to the question about whether the math curriculum could be compressed so that it doesn’t take 13 years or if some of the less ‘useful’ topics should still be taught for other reasons.

In the old days, like the 1700s, a big thing that math was used for was converting different units of measurement for commerce. So converting ounces to pounds and things like that were very important and you practiced with difference currencies and things like that. Well here in the 21st century we aren’t doing those sorts of conversions very much but in this new world there are different kinds of calculations we have to do. In the news all the time we see different statistics and sometimes two different news sources interpret data in different ways so an informed citizen should have some basic ‘numeracy.’

#1: Basic adding, subtracting, multiplying, and some division. With all the options we have as consumers, it is important for us to be able to look at two competing options and decide which one is better for you. There are different ways to teach these things and I’ll address those later, but these things should be mastered by everyone.

#2: Percentages. Though percentages are really just an application of division and multiplication, I think everyone should have an understanding that 50% of something is the same as half of it while 10% of something is one tenth of it. So 50% of 400 is 200 and 10% of 400 is 40. And once you know about 10%, you can easily calculate or estimate other percentages, like 30% of 400 will be 3 times 10% of 400 which is 3*40=120. Also see how that is a little more than 25% of 400 which is one fourth of 400 or 100. Calculating tips and understanding when businesses offer 30% off or a loan that has a 2.75% interest rate and things like that are really important so consumers can make informed decisions.

#3: Basic Geometry. Knowing how to find the area of a rectangular or triangular floor is something that everyone should know. Put that skill together with multiplying and dividing and you can figure out how much carpet to order and how much it will cost.

#4: Basic statistics and probability. When you make an investment, including whether or not to play the lottery, you are taking a risk. So having some ability to measure this risk will help citizens make the right choices and not get taken advantage of.

#5: Basic ‘data science’. Nowadays we hear so many numbers on the news, but people can’t interpret these numbers without knowing how to think about them. Like we hear that crime has ‘doubled’ from last year and it sounds pretty bad. But someone who has studied this kind of data science knows what the other relevant information is. Like in this case, if crime went up from 1 incident to 2 incidents, that’s a lot different than if crime went up from 10,000 incidents to 20,000 incidents even though they are both ‘double.’ In the education research that I have done, I’ve come across papers that claim that an educational strategy resulted in ‘110 additional days of learning’ which can really mislead a reader who is not aware of the assumptions that go into these sorts of calculations.

#6: Interpreting graphs. So often, especially nowadays, data is presented in a visual form. There are scatter plots and pie charts and so many ways to use pictures to represent information. An educated citizen should be able to look at these and understand them.

There are a few more things I could add but not many. The amazing thing is that most students are exposed to these 6 things but because it was mixed in with so much clutter they may not master these most ‘useful’ skills. If readers want to write what they would add (or subtract) from this list, please write a comment.

And I’m not saying that I think these six things should be the entire math curriculum. There is more to math, in my mind, than whether or not it is ‘useful’ in the traditional sense. So if these are the most ‘useful’ things, why not just teach these and save all that time and money by getting rid of the ‘useless’ things? Well I think that there are two types of ‘useless’ math: There’s ‘useless’ math that is mentally stimulating and for many people, if it is taught properly, fun. And there’s ‘useless’ math that isn’t so fun or interesting. So of course I would want to purge the ‘useless’ stuff that isn’t very fun and keep and even expand the ‘useless’ stuff that is fun. I will try to distinguish between these two categories in the next post.

Resources:

Here are three books that will make you wonder “Why didn’t I learn that in school?” The fact that you didn’t is the point I’m trying to make in this post.

When it comes to ‘numeracy’ the classic book that I think should be required reading for every adult is the 1988 classic ‘Innumeracy: Mathematical illiteracy and its consequences’ by John Allen Paulos.

A more recent book that I loved so much is ‘Humble Pi: When Math Goes Wrong In The Real World’ by Matt Parker. In this book he shows how various math mistakes and assumptions have led to disasters of varying degrees.

‘Weapons Of Math Destruction: How Big Data Increases Inequality and Threatens Democracy’ by Cathy O’Neil explains the danger of trusting computer algorithms too blindly because there are sometimes faulty assumptions baked into the algorithms.

Click here for the other parts of this series.

Posted in Math, math reform | 16 Comments

Gary Rubinstein's Blog

Success Academy Teaching Algebra To 2nd Graders: rigor or torture?

Will KIPP NYC Be Disqualified (Again) From U.S. News & World Report Best High School Rankings?

Success Academy Games U.S. News & World Report Best High School Ranking

What (The Heck) Am I Doing On The Citizen Stewart Podcast?

A New Low For TFA: Some trainees only get about 11 hours of student teaching.

HISD Suffers With ‘New Education System’ Turnaround Plan

Is Most School Math Useless? Part 5: What should the math curriculum be?

Is Most School Math Useless? Part 4: The usefulness of useless math

Is Most School Math Useless? Part 3: What are the most useless math topics?

Is Most School Math Useless? Part 2: What is the most ‘useful’ math?

Follow Blog via Email

Archives

Categories