Category: Issues in Teaching Mathematics

Continue reading “Reducing the Achievement Gap”

Continue reading “The Battle Over the California Math Framework Revision”

4/5/2021 – Introduction by D. Kristofferson:

The California Department of Education publishes guideline documents for academic subject areas in K-12 education.  These documents influence teaching practices and textbook publishers and are updated on a seven year cycle.  I was alerted by the author of the following guest article, Michael Malione, that the revision for the K-12 California Mathematics Framework document is currently in progress and that public comments are being requested on the draft now.

Mr. Malione has spent considerable time studying the Framework document and has written the critique in his article entitled Draft California Mathematics Framework Shortchanges STEM.

The opinions expressed in the article are his alone, but I share his concern that the proposed 2021 revisions may have a significant and very likely negative impact on mathematics eduction in California public schools. I therefore encourage readers of this blog to consider Mr. Malione’s objections carefully and respond to the Department of Education survey via the link in his article before the April 8th deadline.

Note added 4/14/21 – The first public comment period is over. The committee working on the draft document will review the comments received, make revisions to the framework, and then put it out for a second 60 day round of public comments in June 2021.

This is a continuation of the article at The Local Math Wars Begin *Again* . The San Mateo-Foster City School District (SMFCSD) recently cited a research study by Burris, Heubert and Levin in the American Educational Research Journal, Spring 2006, Vol. 43, No. 1, pp. 105–136 which supports detracting middle school mathematics. I have devoted several hours to this paper today and posted the following comments on Nextdoor. I continue to believe that we need to consider other ideas to close the achievement gap besides detracking.

I’ve been going through the paper by Burris et al. for close to three hours today. It is a very detailed and qualified study and I am not completely finished but have read enough to relate some important notes to all of you.

First, I highly doubt that most of the people that cite this study have actually taken the time to really study it.

This does not mean that it is a bad study, but it reflects the myriad complications faced by education researchers, and the text is consequently loaded with required qualifications that make a careful study very time-consuming.

Here are a few examples.

First of all, note that the study was based on a single district in a small Long Island (Nassau County) community. They tried detracking middle school students AND placing them into an accelerated math track as Gene McKenna noted earlier.

Detracking started in 1995 for sixth graders. Six years of students were followed through high school – students from the three class years before the detracking and the first three years of students who went through the detracked program. The last of these students graduated in 2002.

Note that our country has gone through many changes since 2002…

Most of the students in the school district were white with “upper middle class incomes” and the article implies that there was a single high school with an “average enrollment of 1,100 students.” African-Americans made up 8% of the students, Latinos 12% and Asians 2%. The majority of the African-American and Latino students came from lower income families and lives in subsidized or government-owned housing. This is pretty different from our local demographics.

From the paper:

“The district developed a multiyear plan to eliminate tracking in mathematics at the middle school level (Grades 6–8). In addition, it instituted changes in teaching and learning conditions that school leaders believed would help all students succeed. These changes involved the following: (a) revision of the curriculum in Grades 6–8, (b) creation of alternate-day support classes known as mathematics workshops to assist struggling students, (c) establishment of common preparation periods for mathematics teachers, (d) integration of calculators, and (e) a revised mathematics teacher schedule consisting of four accelerated classes and two mathematics workshops.

The district decided that all tracking for instruction in the middle school would end with the sixth-grade class that would enter in 1995 and that all subsequent sixth graders would study accelerated mathematics in heterogeneously grouped classes. The superintendent and the middle school leadership team believed that the combination of (a) heterogeneous grouping, (b) a high-track curriculum, and (c) mathematics workshops would enable all learners to be successful without reducing the achievement of the most proficient students.”

So note above that the district started out with the belief that this method would work and did a lot to make it so:

“Students were placed in the alternate-day mathematics workshops according to teacher recommendations or parent requests. Workshop class sizes averaged eight students, and students were allowed to enroll in or leave the class on the basis of how they were doing in their regular class and their personal desire for support. All work in these classes supported instruction in the regular mathematics classroom, and, whenever possible, students were assigned to a workshop taught by their regular mathematics teacher. Approximately 25% of all students took a workshop class at some time during the year, including a number of high-achieving students who wanted the additional instruction.”

It is clear that this small district thought this process through carefully and devoted resources to improve the odds of success.

The researchers took the data from this district and analyzed it.

To place students into low, average, and high achievement groups, the only data that the researchers had to use was a national math competency test created in Iowa (Iowa Test of Basic Skills) and administered a single time in fifth grade.

Furthermore they had to deal with the problems of dropouts and people entering/leaving the district:

“Selection effects are possible, however, even in stable populations. For example, the inclusion of transfer students whose educational histories differ from the majority could bias a study’s results. A strategy for dealing with such effects is to include only data for the cohort members who have the most similar histories (Cook & Campbell, 1979). To reduce this possible source of bias, we included student data only for cohort members (entering high school in 1995–2000) in regular education who (a) were continuously enrolled in the school district from fifth grade to their exit from high school or completion of this study, (b) entered ninth grade between 1995 and 2000, and (c) had a permanent record folder containing all data of interest.”

This creates obvious problems with interpreting the data for the low achieving group.

The Iowa test mentioned above to define achievement levels creates an issue about interpreting data for the ill-defined high achieving group.

Overall, though, the superintendant and others in that district were happy with the results which is the most important take away.

However, the researchers note in their discussion:

“Nevertheless, it is important that further research explore the essential components of this reform. The district that implemented the reform is a suburban district that has allocated generous resources in providing support to struggling students. Fifth-grade stanine scores in mathematics indicate that students in the district earn higher scores than the national average, and the proportion of low achievers in this study was proportionally lower than the number of average and high achievers. Would the reform work in a district with fewer resources and larger numbers of struggling students?”

They do not know the answer to that question.

This study illustrates common problems with education research. The study is valuable in showing that one community attained the results that it desired. Such an outcome is not guaranteed without the desire to succeed, resources, and careful planning, and no representation is made in the paper that such a reform would necessarily succeed in areas with “larger numbers of struggling students.” This does NOT mean that we should therefore do nothing to help struggling students, but it does mean that simply detracking students in itself is not a magic bullet that will guarantee success.

I may have additional comments later, but this is about all of the time that I can spend on this today. I have not had time to go through the detailed data analysis, but am concerned from a first pass that, even though there was quite an improvement in the low performing group, the results still need detailed consideration.

For example, the “Seq II” high school math class in the paper, which is geometry, went from a 46% “low achiever” pass rate by 10th grade before the middle school curriculum change to a 64% pass rate after the change. Note that passing means a grade of >= 65%.

I don’t have the comparable “low achiever” numbers for our local high schools, but I would not be surprised if they are lower, meaning that this work might be a much heavier lift for local teachers.

3/27/2021 – A discussion began yesterday about a San Mateo-Foster City School District (SMFCSD) school Board effort “to get rid of the GATE program and all advanced math.” Nextdoor users who can access Baywood Park neighborhood posts can access the discussion entitled “The death of the San Mateo foster city school district” at https://nextdoor.com/p/Wtf3qFd5-J3w?utm_source=share&extras=Nzg3MzE3MQ%3D%3D

(Note – if this link does not work for you, please try cutting and pasting it into a new browser window. For some unknown reason WordPress is having a problem connecting to this link.).

I wrote the following response which I will quote here. Please read through to the end because the link to the slides has been made available and there is some controversy as to what was actually portrayed at the extremely long meeting. Stephen Floor on Nextdoor quoted the following from the meeting: “I want to make sure nobody walks away this evening with the idea that the district is proposing to get rid of compacted math. We understand the very important reasons that student want to accelerate in mathematics and the concern about getting to advanced math. We’re proposing to the board that due to the pandemic and related circumstances we really need to move to a heterogeneous math course and then engage with our stakeholders with what that would mean going forward for rising sixth graders in subsequent years.”

Unfortunately this comment was supposedly made at 5 hours and 28 minutes into the meeting…

Despite this comment immediately above, the concerns that I stated below remain relevant regarding reform efforts in mathematics education. There are several “progressive” influences that are currently impacting the California math curriculum.

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I have been lobbying against efforts like these for years on my blog at www.eduissues.com. I call your attention to the following article

https://eduissues.com/2018/01/29/never-believe-educational-experts-or-me/

Jo Boaler is a Stanford professor of education whose work is highly influential in California. She is a strong influence on and is part of the group who is *** currently rewriting the CA Dept. of Education Math Framework *** so expect to see much more efforts like the above as time goes on if parents don’t get organized.

Parents can comment on the CA Math Framework revision through this link (or through the link on the CA Math Framework page entitled “Mathematics Framework Online Survey” if they obsolete the link), but note that the first page of the survey makes it look like you have to be an educator to comment. This is NOT the case. Just fill in your personal info in the required fields and then click Next to move on to the second page.

*** Comments are only being received through April 8th. ***

Note that Boaler’s research work is not without its critics. This is a hot topic so I will present Boaler’s case first followed by Milgram’s and Bishop’s replies. Both sides appear to have legitimate gripes, so your “homework assignment” is to read both carefully if you want to be informed.

https://web.stanford.edu/~joboaler/

https://www.nonpartisaneducation.org/Review/Essays/v8n5.htm

https://www.nonpartisaneducation.org/Review/Essays/v8n4.pdf

As I mention in my blog article cited above “Never Believe Educational Experts – (Or Me)!”, California has a long history of educational experimentation fostered by places like the Stanford School of Education which one would think is a prestigious organization.

In Silicon Valley we like to think that bold new ideas are great. I am a scientist by training who went back to teaching late in the game after a long career in science, scientific software, and biotech. I was in on the ground floor of the Human Genome Project and managed the national gene sequence database (GenBank) for the NIH in the early 90s. I have always been open to new ideas.

Unfortunately education research has many problems as I describe in my blog article above, and the sorry history of failed educational experiments in California that have resulted in damage to children is lengthy.

I wrote my blog to try to warn younger parents of these problems so that each generation does not keep repeating the same mistakes. I hope that you will find this information useful.

*** I want to be very clear though, that the inequities that the reformers on the school board are trying to address are very real and require action too. Please be respectful of this fact. We need to act in a way such that we raise the general level of our society; not just fight for our own children. ***

My concern remains though that we can hopefully achieve that goal without injuring our most talented students.

My experience working with local high school students is that better students who are put in mixed math classes are bored and feel held back. This is largely because our society has become so divided by income levels that there is a chasm in education levels among students of the same age.

At the same time, the opposite happens for students who are put into accelerated classes that are beyond their capabilities as the blurb cited at the top of this conversation indicates. I have addressed this problem at length in other articles on my blog.

Please get organized and speak up TOGETHER now, but PLEASE also heed my other concerns mentioned immediately above.

In general I favor evolutionary change in educational practice. Abrupt changes affect too many kids and can not be undone. Kids should NOT be guinea pigs in educational experiments done to enhance the publication records of academics.

I’ve been told that Jo Boaler, originally from England, likes to end some of her writings with the phrase, “Viva la Revolution.” referring to shaking things up in math education. Proceed with caution…

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This is a later comment that I made on Nextdoor.  Note that the slides for the meeting are available here: 7_2_MiddleSchoolMathProgramUpdate032521_0.

I skimmed through the slide deck (43 slides !!!). I am not surprised that this meeting went on till late at night. Slides 11-29 appear to be a “lesson” in Common Core Math, for example, probably intended to illustrate its “richness.”

This is another example of the problem that I often see at school board meetings. Administrators make up massive slide decks that people can not take in at a single sitting and then proceed to lose their audience. As a result, all kinds of misperceptions can occur. This is not my idea of good teaching technique.

I agree with Stephen Floor above that the slides do appear to show that there is still a path to Calculus in High School, but, not having heard the actual discussion, I do not know how much this was emphasized during the meeting. I have often seen slides skipped over quickly as time grows short and the Board and audience grows restless.

I DO know that Common Core has always tried to slow things down and delve more deeply into topics, and this has led to this exact same debate in years past. Common Core itself is a subject of massive controversy which has also been discussed in articles on my blog.

I will add a link to the slides in my blog article and add the qualifications above, but I don’t have the time to watch yet another five hour board meeting. Something is clearly wrong with this method of decision making.

NOTE – for those of you who are so motivated, the link to the Board meeting video is here: https://www.youtube.com/watch?v=EOKVK5VFzrQ. The meeting went on for SEVEN hours apparently.

NOTE added 3/27/21 at 9:30 PM: Gene McKenna has provided notes/comments on the Board meeting video on this topic at

https://docs.google.com/document/d/1R41a3drvVVszgN7YQ4tsyKMj3tYz5YgAzHTyziS2pls/edit#heading=h.x4a5kbnpgepe

The San Francisco Chronicle has a podcast entitled “Fifth & Mission.”  On Feb. 15th, 2020 the topic was “Chaos upends San Francisco’s Aptos Middle School.”  The podcast is a discussion of Heather Knight’s column of the same date entitled “‘Lord of the Flies’: Fights, bullying, chaos upend San Francisco middle school.”

Aptos Middle School is near the well-to-do St. Francis Wood and Monterey Heights neighborhoods several blocks east of Stonetown Galleria, but has students bussed in from other parts of the City including the poorer Bayview and Portrero Hill neighborhoods.  Somewhere between only 5-20 students between the ages of 11-14 years old at the school

managed to wrest control of the school from the adults.

And everybody agrees these kids, just 11 to 14 years old, need far more support to cope with the horrifying trauma they’ve experienced in their short lives and get them engaged in school. Where families and teachers disagree with administrators, however, is whether the school district — which is big on talk about social justice — is actually providing that support.

The district says it is. But the mayhem — physical fights, bullying, chaotic hallways and vile language — shows that’s clearly not the case.

In fact, for the 1,000 students at Aptos, there’s just one social worker. And the only real concession the district has made after complaints about safety has been allowing Principal Nicole Trickett to use money tagged for new technology to hire a temporary security guard for more protection in the hallways.

Why should this concern us here in the suburbs??

In the course of my tutoring work, I talk to students every day about their classes.  While we may not have problems locally that are quite this severe, this is not isolated to Aptos Middle School.  I taught for a year at one of the better high schools in San Francisco where a female teacher was beaten up by two female students who were subsequently suspended.  I constantly saw kids roaming the halls when they should be in class and at times deciding to barge in to other classrooms to talk to their friends in the middle of lessons.

The disrespect shown to teachers and the constant barrage of foul language in the halls between periods was shocking enough to me at the time, and I would not be surprised if it has become worse since then.

I generally work with more serious SMUHSD students in precalculus, calculus, physics and chemistry, but have some students in the regular math stream.  I often hear that about half the regular math classes are filled with students who come in to high school with very weak math backgrounds, have basically given up on the subject, and cause disruptions in class.  This clearly impacts the learning of the better students in the class.  I have no quantitative data on how frequently this happens, but I suggest that parents reading this article talk to their own kids and try to get a sense of the occurrences from them.

In the past I have written many times with a degree of disapproval about the frantic rush to accelerate kids in math, and said that the regular stream should be considered.  However, I have also argued for an honors stream that presented the material at a level in between the regular and AP classes.  There seems to me to be a significant number of students who would benefit from this intermediate stream which would save them the stress and expense of the AP exams.  Possibly due to lack of resources this has never gone anywhere despite a similar attempt by Aragon parents several years ago to request an honors stream from the administration.

When I first started tutoring eight years ago, I had several regular stream students and was fairly satisfied with the regular math classes at that time.  However, as my reputation grew, I increasingly focussed on the higher level math classes.  Since I have worked with some families for as long as 6-7 years, I have accepted some siblings in regular stream math classes in the last few years and am now concerned about the pace of the regular curriculum.  These students are competent in math but are bored in the regular math classes.  Textbooks have been abandoned in favor of worksheets, and the level of difficulty seems to have decreased.  One Algebra 1 class this school year spent the first 10 to 11 weeks on simplifying algebraic expressions and the slope-intercept, point-slope and standard formats for the equation of a line.  Most work was completed in class and a weekly homework worksheet took the student only about 20 minutes to finish.

Possibly because teachers have to deal with such a wide variety of math skills (and this problem may have been exacerbated by aborted curriculum experiments such as Everyday Math in the local K-8 district), this slowdown may have been necessary.

However, combining a slower curriculum with kids that are bored with or given up on math is a recipe for problems.

Public school teachers are in a tough position with disruptive kids.  Serra High School, a local Catholic school, had a staffed after-school detention center for discipline problems which gave Serra teachers an acceptable disciplinary option.

Many public high schools require the teacher who assigns detention to stay after school to monitor the student themselves!  This clearly does not encourage teachers to use detention as a disciplinary tool.  Instead, for example, when I taught in SFUSD, the helpful classroom management advice that I was given by a vice principal was simply, “Don’t let them see you smile until after Christmas!”, i.e., the teacher is expected to control the classroom by giving stern looks and emulating a prison guard persona!  Whatever happened to parental responsibility for teaching their kids proper behavior?  When I tried to call home to talk to parents, I frequently found that the parents were not available because they were working two minimum wage jobs to make ends meet and older children were taking care of younger kids!

Stern looks will clearly not work with disruptive kids from traumatized family backgrounds, some of whom have no hesitation to yell, “FU, I don’t have to listen to you!” and storm out of a classroom.  A relative of mine worked as a school security officer in southern California and has told me stories of veteran teachers coming to him in tears telling him that they can no longer control these kids.

Various ACLU lawsuits have enhanced student “rights” over the years, to the detriment of teachers in my opinion, and I have also heard of cases where teachers have been threatened with lawsuits by parents to halt disciplinary measures against their children.

Public schools also have to accept and teach all students, and, instead of the “old school” method of streaming kids into advanced, regular, and remedial classes, the tendency now is to “mainstream” the slower students and have them work in groups with some of the better students, in the hope that they will learn from their peers as well as from teachers / “authority figures.”  While this may work to some extent, it has also led to interesting incidents like a student being criticized by their group for being out sick, thereby resulting in a lower grade for others in the group!!

Our society can no longer afford to ignore the trauma in the poorer segments of society if for no other reason than the cynical one that it negatively impacts the rest of us.  Drug addiction, homelessness, joblessness, single-mother families –  the list goes on.

If children emerge from school without a decent education, their odds of becoming productive members of society are clearly lowered significantly.  Even worse, if they leave school with the idea that they can engage in antisocial behavior with impunity, do not be surprised if you can’t leave your cars at night with anything visible inside of them or that people brazenly snatch iPhones and iPads in broad daylight from Apple Stores.

San Francisco is not that far from San Mateo…

For some thoughtful perspectives and possible solutions for these problems I recommend the following:

Hope and despair in the American city – Why there are no bad schools in Raleigh by Gerald Grant

and chapter 6 entitled “The Only Valid Passport from Poverty” in the book

The Teacher Wars – A History of America’s Most Embattled Profession by Dana Goldstein.

I only hope that we have not let this situation fester until it is too late to act.

 

Continue reading “Why a “Sage on the Stage” in a Classroom is not always a Bad Thing”