Reducing the Achievement Gap

A different and hopefully somewhat novel approach to addressing this perennial problem.

11/26/2021 – Our local education leaders (not to mention those on the national scene) have talked for years about closing the “achievement gap” in learning between historically disadvantaged groups such as African-Americans and Hispanic-Americans versus white Americans and Asian-Americans.  Solutions are still elusive after all of this time, and our local San Mateo-Foster City School District (K-8) is currently reevaluating mathematics instruction in light of pandemic learning loss (see also Part 2 of the previous linked article).  6th grade students began this school year without an accelerated math option and plans are still under discussion on a curriculum pathway to Algebra by 8th grade for these 6th graders that will also address the needs of students who are behind in math.

The sides to date have tended to focus on either eliminating accelerated math options entirely in middle school (influenced by Professor Jo Boaler at Stanford who is a co-author of the California Math Framework revisions) versus keeping the previous accelerated pathway but providing additional resources to help struggling students.

I think that unfortunately both of these solutions are likely to fail.

Despite the noble goal of having the more advanced math students work in groups with students who are not at grade level in a so-called “homogeneous” class, I am concerned that the gap by middle school already has become too wide.  At a recent parent meeting at Borel Middle School with our new superintendent Diego Ochoa, one parent mentioned that her son, who is a capable math student, came home in tears.  He was bored by the pace of the middle school math class but at the same time wanted badly to help a fellow student who was struggling with 3rd grade math topics.  Her son was frustrated about math and also felt guilty that he could not provide adequate assistance to his friend.

Here’s another example.  Over my last decade of tutoring, I have encountered students in pre-calculus and even AP Calculus who surprisingly do not completely understand fractions, and this comes back to haunt them when they study rational functions (essentially fractions containing variables instead of just numbers).  I have also had local high school math teachers acknowledge that they too encounter problems with math preparation of students in supposedly advanced math classes.  Finally one time when discussing this issue with a local high school principal I was told candidly that “we have to deal with what we are given.”  I expand on this issue a few paragraphs below.

If we are to address the achievement gap problem, we need to put our resources to excellent use in the early years of elementary school and prevent or at least minimize the problem from occurring in the first place.  If we do not address the issue early, we will continue to fail.   Once the gap becomes blatantly obvious, the chance of successfully helping students on the lower side of the gap is markedly reduced.

  1. –  The Need for Math Specialists

I have read (and written about here before) that teacher math anxieties can affect the progress of their students.  I stated in my article

When I returned to teaching, I frequently collected high school teachers’ opinions on why so many students were struggling with math. High school teachers were often frustrated because, by the time the students were their responsibility, their math foundations were already shot. As in other professions, teachers are hesitant to criticize their colleagues, but, the opinion that I heard most often (usually expressed in hushed tones) was that they thought too many elementary school teachers did not have adequate training to teach mathematics properly.

Should we be surprised? I would think that most elementary school teachers choose the profession primarily because they enjoy working with young children, not because their passion is math and they have a burning desire to teach it to six year olds.

 This research paper begins with a review of papers in the literature about elementary teacher math anxieties and their effect on students’ education.  It attempts to extend the study to adolescents in 9th grade mathematics.

To address the problem, in my article quoted above I suggested the following:

So how do we resolve this issue? I moved from Massachusetts to California in 1963 in 5th grade. In Massachusetts, we studied French, but Spanish was the foreign language taught in California’s elementary schools. Our 5th grade teacher did not know Spanish, so we had a daily lesson that we watched on TV (I still remember this lesson being interrupted by a news flash that President Kennedy had been shot in Dallas). There was also a roving native Spanish-speaking teacher who came to our classes every few weeks.

If we have trouble training all of our elementary teachers in mathematics education, why can’t we train roving math specialists who go into each class daily for the math lesson of the day?

Clearly this would be a major effort and require significant training resources.  It would NOT solve the problem of middle school students who are already behind.  However, if we do not take steps to improve elementary math education from the beginning, we will continue to produce children who require later intervention at even greater expense.

Several years ago, after serious problems that led to the abandonment of the Everyday Mathematics program used by SMFCSD,  I met with a SMFCSD Assistant Superintendent and volunteered time to assist elementary school teachers with math lesson development.  I was essentially told that the District already had excellent professional development.  I am currently trying to resume these discussions with our new Superintendent and Assistant Superintendent Chambliss.

2. –  Actively Recruit non-White / non-Asian Candidates as Math Specialists

It became very obvious to me when I was a Peace Corps teacher in Malaysia years ago that children need successful role models who look like themselves.  Peace Corps volunteers go into developing countries to provide teaching resources often where none are available.  However, the volunteers are obviously foreigners from a wealthy country.  The children may find them interesting curiosities, but usually do not see them as role models that they can possibly emulate in their own lives plagued by poverty.

In this country we run into a similar, though less extreme, problem in our public schools.  The majority of our teachers are white females, and many are tasked with educating students of color and English language learner immigrants.  Some do so very successfully, but there are also notable failures.  If  students had passionate math teachers from a background similar to theirs (the motion picture Stand and Deliver comes to mind), math results might improve significantly.

When I have discussed this possibility with people in education, one argument raised against this proposal was that this solution advocates the very “separate but equal” segregation that Brown v. Board of Education banned with the 1954 Supreme Court ruling.

I disagree strongly with this objection.  No one is advocating the return to racially segregated schools; instead the point is to have a faculty that represents  all parts of our society, i.e., a diverse teaching staff.  Sadly there is a tendency in our society to classify some subjects like math as “white” or “Asian.”  I know from direct experience that this classification is often being made by the students themselves.  Having teachers of color in these areas is a big first step in breaking these harmful stereotypes.

In her book “The Teacher Wars“, Dana Goldstien in chapter 6 relates the history of racial issues in American schools going back to before Brown v. Board of Education.  She describes an interesting, unintended consequence of the desegregation in the South brought about by that Supreme Court ruling.   When black students were integrated into white schools, many black teachers at previously segregated black schools lost their jobs.  Furthermore, the white teachers in the schools where black students  were sent harmed these students by holding them to lower expectations than demanded by their former, now unemployed, black teachers.  This  clearly illustrates the often overlooked thorny issues that can arise when people tiptoe around these complex problems.

I realize that some school districts are trying to pursue the hiring of African-American and Hispanic-American teachers with varying degrees of success.  Perhaps we need more state and federal funding for teacher training/scholarships, signing bonuses for new teachers, or (gasp) higher pay for these math specialist positions.  The latter unfortunately sometimes runs into union opposition to higher pay scales for certain specialties.

This is an area where I think that teacher unions may need to take a hard look in the mirror.  We clearly have an achievement gap and an equity problem that all unions espouse a willingness to address.  If higher pay is required to recruit math specialists to solve this problem, then unions should not reject this option without excellent justification.  Merely having more advanced students train students who are behind in their math groups places a burden on students with no/limited teaching experience and risks losing them from the public school system.  This can eventually lead to a downward spiral of the entire system.

3.  –  Train Math Specialists in real “real world” applications

The people who train children in mathematics need to have the opportunity to interact with people who are actively employed in fields that utilize mathematics.  Too often “real world” applications used in classrooms are divorced from teachers’ direct experiences (and sometimes from “reality” itself !)

These three suggestions above are not quick fixes, will take a long time and significant resources to implement, and will not solve the immediate problem of students who are already far behind in math compared to their current grade level.  These students need intensive educational resources and often one-on-one help or at least very small class sizes to help them catch up.  Otherwise they will be excluded from fields that require this knowledge – the “easy and cheap” default solution.

Middle school students who are advanced in math such not be held accountable for earlier failings of the educational system by being recruited to raise up students who are behind in their education (though it would be admirable if they volunteered their time for such purposes).

At the same time parents can not use this excuse to avoid addressing the equity issue.  As I mentioned at the recent Borel meeting with the Superintendent, we frequently see posts on social media like Nextdoor of concerns about crime in our neighborhoods.  Well-to-do people ignore addressing these equity issues at their own peril.  If one has to make a crass appeal to self-interest as opposed to simply doing the right thing by all of our citizens, please note that it is much cheaper to educate our children and make them productive citizens than to pay for housing them in over-crowded prisons when they rob stores and houses after failing to find decent work.

If we continue to focus solely on intensive remedial remedies in middle school and later instead of taking measures to prevent or at least minimize the development of the achievement gap in the first place, we will continue to lament this problem for decades to come.

In the meantime I await a chance to discuss this problem with Mr Ochoa and Chambliss and explore ways in which I might assist in at least some small manner.

Note to readers: On an issue as complex as this one, I frequently add additional thoughts to the article at later times, so please feel free to check back here if this topic interests you.

Also please note that you can post comments following this article below.  Scroll all the way down to the “Leave a Reply” box to reply to the main article or click the Reply link following a particular comment to respond primarily to that comment.  Comments are moderated and will appear here after they are reviewed and approved.

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Thanks as always for your participation!

Author: David Kristofferson

Retired Ph.D. scientist, teacher (after retiring from industry, taught in private and public high schools and then worked a decade in my own private tutoring business), bioinformatician (managed both the NIH-funded GenBank National Nucleic Acid Sequence Databank and the BIONET National Computer Resource for Molecular Biology), IT director at Eos and Raven Biotechnologies, software product manager, AAAS Fellow, avid cyclist, and backpacker!

13 thoughts on “Reducing the Achievement Gap”

  1. Thank you for your updates and nuanced analysis. Keep them coming! I’m wondering what is the difference between students who do “completely understand fractions” and those who do not? Why are some kids getting the education, and how can other students emulate them?

    I recall a probably apocryphal story of schools in China where students attend special seminars are led by the top students to learn best practices they use to excel in school.


    1. That is the $64 million question in your first paragraph. When doing problems with rational functions, I frequently have to remind students that one needs a common denominator to add two fractions and that division by a rational function is equivalent to multiplication by its inverse.


  2. David, this is an excellent article on all levels. Your astute observations and knowledge of the subject matter of the state of affairs in our math education in K-12 system is right on. Your recommendations for changes are terrific. We have reading specialists in the elementary schools- why not math specialists? I applaud your efforts to get involved in the earlier years of our math education. The math gaps my children experienced in high school definitely resulted from prior math teaching in elementary and middle school.


  3. Great article, David. I agree we need to start much sooner than 6, the grade. I didn’t know schools can’t pay math teachers more than other subjects. Did I read that right? Seems very counter productive. And I agree it will take apt to fix the problem. Simply shifting the deck chairs around and accelerating in grade X instead of grade Y is not going to solve anything.


    1. Thanks, Gene. I can’t make a general statement for all school districts regarding pay, but, in my personal experience, public school teachers get compensated based on years of experience with a bump up for a masters degree or a Ph.D. (not a tremendously big bump either). I have not seen differentiation by subject area, though I have been told that schools can use one-time signing bonuses.


  4. This is an interesting idea. My son in 6th grade is bored out of his mind in Math class. He is not very advanced by any means, but we worked outside of the classroom in Elementary to learn the fundamentals. If the advanced Math was offered in 6th grade, he probably would have made the class (not a guarantee).
    The current problem is this: his current Math teacher at Bowditch forces him to solve the very easy problems in certain way, that everyone has to follow. He is not just challenged to learn, he is being forced to follow the basic way of solving problems that beginners have to do. This is becoming very frustrating for him as he knows how to solve fractions and decimals, showing his steps, but still doing it in ways that don’t force you to draw charts, tables and pictures. The teacher however is singling him out and after him saying things like – “this way of solving problems is not going to get you anywhere”. Very frustrating, but not much we can do…..


    1. I should also add that I sympathize with both parties here. I recall being in a similar situation to your son years ago when telling my high school analytical geometry class about a different solution method and getting rebuffed. At the same time the teacher is trying to deal with some students who are undoubtedly behind where your son is in math, and undoubtedly does not like their lesson being confused with additional material when those kids may be having a hard enough time “getting” the lesson being taught. The teacher should treat your son respectfully, but it is also a two-way street. You might want to encourage your son to talk to the teacher one-on-one instead of making his comments to the entire class.


      1. Completely understand. He isn’t making any comments to the entire class. I understand that the teacher can’t possible assign different levels of work to the class, but some freedom in solving the problems in an individual way may be OK. I am not a teacher, so just thinking out loud. Why not just realize that he’s got the concepts and is solving the problems in an acceptable way? Not sure that forcing to solve ALL the problems in the same way is a good approach.


  5. I have received the following comment from a retired local teacher who wishes to remain anonymous but gave me permission to post the following text:

    I have been following your posts and updates regarding the Math Framework for a while now and could not agree with you more.  Here are couple of points I would like to add:
    — Unless the district makes an effort to fix the elementary level, very little will change, if anything at all.
    — Elementary schools need to departmentalize their math program.  Actually, this might provide a much needed relief for some teachers and allow them to use their talents in areas they have more expertise in.
    — People who make the all important decisions about the math curriculum at any level, MUST have applied math experience.  
    Thank you again for the work you do in shining the light on Math Education in SMFCSD and beyond.”


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