Gideon’s Math Homework   6 comments

Reposted with permission from Alan Singer of Hofstra University, Hempstead, NY

Gideon, my grandson, is almost nine-years old and starting fourth grade this year. He loves soccer, baseball, online videos, hip-hop, and school because that is where his friends are during the day. His attitude toward homework, and I suspect any school assignment, is to get it done fast so he can move on to more important and interesting things.

On last year’s New York State 3rd grade common core aligned math assessment Gideon scored in the proficient range, not the highest level, but not bad on a test where 70% of the students failed. I have been doing math homework with Gideon since school started and I noticed a couple of things that concern me about how math is being taught. I am not blaming his teachers or the school. I am certainly not blaming Gideon. But I worry that the problems he is having in math reflect the push for test prep for standardized tests.

The first problem is that Gideon seems to be convinced that there is only one right way to solve a problem and if he does not solve it that way he will be marked wrong. This problem he will get over either as he learns more about how the world works or becomes less interested in pleasing his teachers.

The second problem is a bit more serious to me as a teacher and grandparent. Instead of trying to understand a math problem and being willing to play with the numbers, Gideon is committed to remembering a long, complicated sequence of steps to finding a solution. If he makes a mistake somewhere in the sequence he gets the answer incorrect, but he does not recognize it as incorrect, because his goal was following the prescribed steps, not coming up with a result that makes sense.

Kids are supposed to be learning to estimate from the start of elementary school so they can stop and say this cannot possibly be the answer, but estimation requires both feeling comfortable with the relationships between numbers and a willingness to experiment and speculate, qualities that appear to be neglected in the test prep math curriculum.

One night recently Gideon had to figure out how many tens are in 540. He set up number groups. There are 10 tens in one hundred so he had five groups of 10 tens each. There are 4 tens in forty. He then added 10+10+10+10+10+4=54. I did not have a problem so far. But then he had to figure out how many tens were in 370 and he started to set up his number groups again instead of just saying if there are 54 tens in 540, there must be 37 tens in 370. He did not see or even look for the relationship between the two problems. They were separate entities.

The third question was how many twenties are in 640 and again he started by setting up his number groups. I asked him how many tens were in 640 and if there were more tens or twenties, but his response was “That’s not the way we are supposed to do it.”

Maybe that was what he was told, maybe he was misinterpreting instructions, but in either case, he would not play with the numbers and try to figure out a solution on his own. He was memorizing rules, not learning math.

Initially I thought the problem here might just be Gideon’s stubbornness and anxiousness to be finished, after all there were other more rewarding things to be done. But email exchanges on the Long Island “Middle School Principals” listserv ( point towards much more serious problems with the way math is being taught and assessed in the New World of Common Core and high-stakes assessments.

A principal at one affluent Nassau County middle school reported that in his school 235 eighth grade students took accelerated ninth grade math and 190 of them, 78.6% of the students, earned a grade of 80% or better. But inexplicably, 82 out of the 190 high scorers, 43%, scored less than proficient on the 8th-grade common math assessment. Three other middle school principals from similar districts reported the same phenomenon.

A fifth principal from another affluent high-performing Nassau County school district described the state math assessments as a “Kafkaesque system” that “does not make sense,” as a “fake testing system” that “hurts kids” and their teachers. He has middle school students who passed high school math examines with mastery level scores but who failed the common core standardized test and now must be assigned to remedial classes. He also cannot figure out how when his school had the highest seventh grade English and math assessment results in the state on the common core test, only one out of six of his seventh grade ELA and math teachers was rated highly effective.

He charged that the current instructional and testing system “only enriched consultants, textbook companies and service corporations.” He called it a “fiasco” that “only ensures further unfunded mandates, pushes schools to become test-prep centers, further institutionalizes an over-testing system that terribly hurts kids, and enshrines an unfair evaluation system that actually makes it harder to terminate unsatisfactory teachers.”

Actually, I do not find the lack of correlation between the 9th-grade algebra test scores and the 8th-grade common core assessments inexplicable. I think the same phenomenon is at work that I saw in Gideon’s homework. Students are not learning math, they are being prepped for tests to maximize test scores.

When you put different types of questions on the math test they are stymied because the procedures they were taught to follow do quite line up with the problems and they either do not know how, or are afraid to, adjust. They do not estimate, they do not hypothesize, they do not “do the math,” they just get lost in the steps and get the answers incorrect.

I remember learning math the old-fashioned way, my friends and I had fun figuring out things we actually wanted to know and were very competitive at it. Back in the days before calculators and computers, the newspapers only updated baseball batting averages on Sundays, except for the league leaders. My friends and I were big baseball fans, our elementary and middle schools were about a mile from Yankee Stadium, and we needed to know the latest batting averages for Mickey Mantle, Roger Maris, Yogi Berra, Elston Howard, and “The Moose” Bill Skowron, so we calculated them every day during lunch (and sometimes when we were not paying attention in classes). It was not that we liked math –we loved baseball. Math was just a tool.

I walked into my high school 10th grade statewide geometry math test without having paid attention for most of the year (Bill Cosby used to tell the joke that when he was a kid his family was so poor he couldn’t afford to pay attention). But I was comfortable with math, numbers and problem solving and actually figured out geometry while taking the test itself.

I like finding patterns in math, I enjoy problem solving, and I appreciate the way it helps me to think systematically and provide evidence to support my conclusions. But I am convinced my comfort level is rooted in my love of baseball and the Yankees.

The other night I asked a group of college students if Robbie Cano is batting .310 and goes one for three with a sharp single, two fly outs, and a base on balls, what happens to his batting average. Some of the students had no idea, some of them started to calculate, but I knew his batting average went up, by just a little bit, because I know the relationships between numbers. That is what I am trying to teach Gideon.

Alan Singer, Director, Secondary Education Social Studies
Department of Teaching, Literacy and Leadership
128 Hagedorn Hall / 119 Hofstra University / Hempstead, NY 11549


Thanks to Professor Singer for this article which is also published at Huffington Post.

6 responses to “Gideon’s Math Homework

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  1. This is a letter I wrote to the English Department atLehi High School in Lehi, UT, about the book “The Bluest Eye” which is on the AP English suggested reading list. Thought you might be interested in the response I got .

    My name is Annalese Evans and I am writing you concerning a book you have listed on your suggested reading list. I am not sure if you have read The Bluest Eye but I have read excerpts from it and I feel it is very inappropriate for high school reading. This book talks about pedophilia, incest and graphic sex, and I feel it needs to be removed from your list. I am wondering if you could give me a reason it is on the list and any redeeming qualities that it may possess. If you are questioning what I am talking about try reading pages 84-85, 130-131, 148-149, and 162-163 just to start. If this is the type of literature you feel is appropriate for our youth than I am afraid you are not the teacher I want teaching my kids. I also feel that there are other questionable books on the list as well. Have you read Wicked? Not at all like the musical, I assure you. It also contains sexual content. With all the great literature we have I am sure we can do without books that contain this content. I would very much appreciate hearing back from you concerning this matter. A Very Concerned Parent, Annalese Evans

    > Date: Mon, 9 Sep 2013 14:30:52 -0600
    Subject: AP English Reading List
    Dear Mrs. Evans,

    Thank you for your feedback to Ms. Rhodehouse concerning her AP reading list. Students are told at the beginning of the year that they can choose not to read something that they find offensive. In the case of The Bluest Eye, she does not require the novel to be read nor does she teach it in her AP class. Students are given a “suggested” list of resources to better aid them in understanding possible novels that might appear on the AP test. Students do not have to read The Bluest Eye, but should be aware that the College Board has included Toni Morrison’s novels as an option on the essay section in the past. Including the novel is a way to allow students to have the knowledge and the choice to include it in their AP test preparation.

    Please feel free to contact me should you have any more questions.


    Christian Smith
    Assistant Principal, Lehi High School

    Here is my response
    6:41 PM
    To: Christian Smith_lhs

    So basically what you are telling me is that regardless of content, we are teaching kids that they need to read filth to be able to pass a test. This is the wonderful world of Common Core for you! Thanks for letting me know where you at Lehi High School stand on the welfare of my children. I will make sure I continue to be as vigilant as ever concerning their education there. I am very concerned for the children whose parents are not as aware as I am but you can rest assured I will do everything in my power to alert them. Thank You for your response. Annalese

  2. Wow, very strange… I have a 9 yr. old son named Gideon who is also in the fourth grade!!!! We are however, in Florida and are only beginning to “introduce” Common Core in the schools. It is already becoming a problem for my Gideon.He is in the gifted program and loved school until this year. The math drives him insane as it makes no sense to him. To him, math is an absolute (which he is correct there are rules in math, 4 times 3 will always equal 12 no matter what). The english is way below his level (he reads at a 7th grade level) and he is bored out of his mind. I have heard when we finally implement CC there will be no letter grades… Is this true???? my Gideon strives for all A’s, without grades what do the children strive for? I have so many concerns about this CC and would love to learn more about it from someone who has a child in it.

  3. Hello, can please someone clear my confusion. I have postgraduate degree in math. I looked at SBAC tests for math for 6th grade and it look to me like a set of puzzles, but mathcounts or matholympiads are easier than SBAC, because on SBAC the main problem you can’t figure out what question means most of the time. They call it rigor. Ok, suppose now the kids will be really trained to solve puzzles, they will become very smart as a result of Common Core lessons taught in school. But the Common Core lessons in school mean actually relaxing the requirements – group work, 3×4=11, explanation matters more than right answer. On test however wrong answer will be scored wrong, and no group work there. So there is a very big disconnect. I just attended Common Core presentation meeting in Cupertino, CA where kids could try SBAC for the first time in the back of the room on small laptops while the presentation was going on. My nieces (very good diligent students) were horrified after trying the math and ELA tests on the laptops in the back of the room. In English SBAC exam there are long passages and then they have to type in the evidence – all questions we saw are same type. My niece was saying this questions in English exam give her feelings that she is the criminal in a court and she had to present evidence that she did not do the crime so she doesn’t have to go to jail. She also cannot type fast. Here Common Core is not implemented yet and these are first meetings selling the common core. The parents got to see SBAC as their kids were trying it on laptops in the back of room. The parents felt they could not solve anything either. Since that was open question answer session somebody asked that we don’t understand how to solve these problem ourselves. So the answer was that even though you might be well educated and have a nice job, you were not exposed to this rigor in your childhood, so you cannot solve these problems. However the 21st century demands this kind of “rigor” so our kids need to be trained in this. Cupertino is one of top performing school districts in SF bay area and parents were told common core is great and it will make the kids step up to the demands of 21st century. This was the very first presentation and nobody saw the new stuff in classrooms yet. So all questions from parents were mostly how to help children to achieve the rigor. The district officials told that they have this new method called teamwork in class where kids will explain each other and that will magically make everyone be able to solve SBAC. Can you please tell me what to do. My sister was really upset she was about to cry, and her kids said please take us out of school for those days when these tests are given, we don’t want to break our heads. Can you please tell me for CA what is consequences of not taking SBAC next year. Will the kids get failing grade? Will they be thrown out of school? Will they have to repeat their grade? My nieces don’t want to homeschool. They love their public school, their friends, their teachers. They come happy from school every day (Common Core in not yet implemented). They wait whole summer for the school to start again. What should we do in this situation? My sister is thinking about private school but can’t really afford it, and her daughters don’t even want to go to any other school than the public school they are enrolled in right now.
    In CA SBAC will be given in 2014-2015 school year they will be in 7th and 8th grades that time.
    Also do you know when kids can enroll in Community College full time if they drop school, only in 10th grade? And then hey will have to take GED which is also common core aligned now

    Thank you so much

    • Contact California United Against Common Core for California-specific information. Here in Utah, consequences for opting out of the Common Core S.A.G.E. test varies from no punishment at all to students (in my school district) to serious academic penalty (according to a parent in a Southern Utah school district.) My feeling is that grades are less important that protecting student privacy, protecting students from invasive and stressful standardized testing, and protecting students from taking tests based on experimental, untested Common Core standards. I would opt out, but that is a personal decision. Good Luck.

  4. Thank you Christel, I want to ask if others also feel SBAC math is strange and group work in class will not help to pass it? Utah is also in SBAC, so what is the experience there?

  5. Pingback: Here to There » Blog Archive » Gideon’s Math Homework

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