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.
- – 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.
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