Understanding CRT

 I'm seeing many articles that make some pretty nasty claims about Critical Race Theory. It's a legal theory, stating that people are not inherently more criminal or less intelligent based on their skin color or any other biological factor. However, we see a disparity of incarceration and educational achievement correlated to those factors. The theory then, is that there is something in our laws and our culture that is causing these disparities. I find this non-controversial. Many do not. 

Here is a recent article that was linked to me to make the anti-CRT case. 

https://bariweiss.substack.com/p/should-public-schools-ban-critical?fbclid=IwAR2-hejN6gyQXvCFZKYFDQLFnjq75n5cxNR9JJHfgjRmgtOY2tKENH-tqc0

I could take it on face value, accepting the half dozen or so anecdotes as evidence. My experience is that information presented like this usually misses much of the data behind it. I'll drill down on one of them to demonstrate this.

This article gave examples, claiming they made up a case against CRT. Here’s one:

·  California’s Department of Education is proposing to eliminate opportunities for accelerated math in the name of “equity.” That means discouraging algebra for eighth graders and calculus for high schoolers. 

 The "eliminate opportunities" goes to Reason magazine. I would call this a "polemic". If I accepted the opinion of the author, I could have stopped there. This research was fairly easy because it had the report in this article. Although, it is long. I haven't read the whole thing, but if anyone would like to point out something in it, I'd be glad to respond. I'll respond to one of the quotes in Reason magazine below.

https://www.cde.ca.gov/ci/ma/cf/

https://reason.com/2021/05/04/california-math-framework-woke-equity-calculus/

This one reminded me of The National Enquirer, repeating the words in the title in a subheading, then again in the first paragraph. It quoted a report, and picked out some of the evidence for how it made it’s case. I’ll give them credit that they linked to the full report. It claimed the “entire second chapter is about connecting math to social justice concepts”. I downloaded that chapter and could not confirm that. I was hard pressed to find mention of social justice, let alone a theme.

The Reason article quotes the report, "To encourage truly equitable and engaging mathematics classrooms we need to broaden perceptions of mathematics beyond methods and answers so that students come to view mathematics as a connected, multi-dimensional subject that is about sense making and reasoning, to which they can contribute and belong."

Robby Soave, the Reason author, follows up with the comment, “This approach is very bad.” He makes some general statements about people having natural abilities to excel at math and how we should encourage them. He cites no data, no studies. In the next paragraph, he says, “young people who aren't particularly adept at any academic discipline might pick up art, music, computers, or even trade skills.” I have a computer degree. Calculus was required because of the way it teaches you to think about problem solving. I have trouble trusting Robby after this comment.

There is still a lot of that report to read, but so far, I’m seeing how it encourages a method of engaging young people in reasons for using math and working with others to solve a problem. The “discouraging” that is mentioned in the Bariweiss article is probably one of many possible recommendations to consider, not a main theme.

 

Here's one of the vignettes in Chapter 2 of the report. Not sure how farming is a social justice issue.

Vignette–36 Fences

Lori, a high school geometry teacher, introduces a problem to students. Lori explains that a farmer has 36 individual fences, each measuring one meter in length, and that the farmer wants to put them together to make the biggest possible area. Lori takes time to ask her students about their knowledge of farming, making reference to California’s role in the production of fruit, vegetables, and livestock. The students engage in an animated discussion about farms and the reasons a farmer may want a fenced area. While some of Lori’s long-term English learners show fluency with social/conversational English, she knows some will be challenged by forthcoming disciplinary literacy tasks. To support meaningful engagement in increasingly rigorous course work, she ensures images of all regular and irregular shapes are posted and labeled on the board, along with an optional sentence frame, “The fence should be arranged in a [blank] shape because [blank].” These support instruction when Lori asks students what shapes they think the fences could be arranged to form. Students suggest a rectangle, triangle, or square. With each response, Lori reinforces the word with the shape by pointing at the image of the shapes. When she asks, “How about a pentagon?” she reminds students of the optional sentence frame as they craft their response. Lori asks, the students think about this and talk about it as mathematicians. Lori asked them whether they want to make irregular shapes allowable or not.

After some discussion, Lori asks the students to think about the biggest possible area that the fences can make. Some students begin by investigating different sizes of rectangles and squares, some plot graphs to investigate how areas change with different side lengths.

Susan works alone, investigating hexagons––she works out the area of a regular hexagon by dividing it into six triangles and she has drawn one of the triangles separately. She tells Lori that she knew that the angle at the top of each triangle must be 60 degrees, so she could draw the triangles exactly to scale using compasses and find the area by measuring the height.

Niko has found that the biggest area for a rectangle with perimeter 36 is a 9 x 9 square—which gave him the idea that shapes with equal sides may give bigger areas and he started to think about equilateral triangles. Niko was about to draw an equilateral triangle when he was distracted by Jaden who told him to forget triangles, he had found that the shape with the largest area made of 36 fences was a 36-sided shape. Jaden suggested to Niko that he find the area of a 36-sided shape too and he leant across the table excitedly, explaining how to do this. He explained that you divide the 36-sided shape into triangles and all of the triangles must have a one-meter base, Niko joined in saying, “Yes, and their angles must be 10 degrees!” Jaden said, “Yes, and to work it out we need tangent ratios which Lori has just explained to me.”

Jaden and Niko move closer together, incorporating ideas from trigonometry, to calculate the area.

As the class progressed many students started using trigonometry, some students were shown the ideas by Lori, some by other students. The students were excited to learn about trig ratios as they enabled them to go further in their investigations, they made sense to them in the context of a real problem, and the methods were useful to them. In later activities the students revisited their knowledge of trigonometry and used them to solve other problems.