This post is by Donna Le Fever, who teaches sixth grade math and science at High Tech Middle Media Arts in San Diego.
I took a course on reading and writing across the curriculum, and the teacher posed a question:
“Why is it socially acceptable to say you are bad at math but not socially acceptable to say that you are bad at reading?” Knowing I was a math teacher, he directed the question at me, and I have thought about it ever since. Why is the subject of “math” so scary for so many people, including many of our students?
Language Arts standards are not written with the same level of detail as Math standards. This difference in detail is reflected in the kinds of curriculum available for each subject. How does the way we, as educators, follow standards and curriculum in math classrooms, impact the way society views mathematics as a whole? Does our approach allow only certain types of people to feel successful with math?
If we define mathematics as a way of inquiring, analyzing, and drawing conclusions, it may not be as easily written off as a subject that some people just don’t “get.” Throughout history, math rules and procedures have been created, but the ideas behind them were sparked from human inquiry. In school we teach students these procedures and show their application in the real world, but why is our approach so rigid? What kinds of problems can this lead to when students aren’t given the opportunity to inquire about concepts using their own powers of reason?
Here is a Common Core language arts standard for understanding literature at grade 6:
Understand Key Ideas and Details when reading literature.
Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text.
And here is an example from the math standards for number sense in grade 6:
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?.
This latter level of detail leads to curriculum offering a variety of problems with the same level of specificity, allowing little opportunity for investigating different approaches to the larger concepts at hand. Students are not given the opportunity to think about how they would process the problem or practice skills of logical reasoning. Given this level of specificity in the standards, and in curriculum packages derived from them, how do we create a classroom environment where students are engaging in each problem in a way that highlights their own analysis and conclusions, and those of others?
In a recent class project, my students shared strategies for scaling down an object by one half. As a class we reasoned through a strategy to find the ½ measurement using their ruler as a tool. However, in the process students came up with other ways they found to be more efficient, or registered past strategies for finding ½ of a fraction. They were motivated to support each other, but more importantly, students that were unsure were motivated to ask questions, e.g., “What do I do when I get 9/16 of an inch and have to find ½ because the ruler isn’t broken up into smaller parts, and I keep landing between two lines?”
This question inspired our class to look at patterns of fractions. While the task addressed the specific skill of computations with fractions, students were engaging in the larger question of number sense from multiple access points.
In curriculum designed from the grade level standards, there is very limited access, which in turn can create an issue of equity in the classroom. When a curriculum necessitates challenge options as well as accommodations for each problem, it creates the idea that there are high and low levels of math intelligence. If by sixth grade the student is to understand ratios as a comparison of two or more quantities using whole numbers, a “challenge” problem might be comparing quantities with fractional parts. An accommodation might be looking at whole number quantities less than 20. This approach assigns value to different “levels” of thinking rather than providing opportunities to analyze student questions and follow their reasoning.
In their exhaustive detail, the Common Core standards have led to a narrowly focused curriculum that reinforces the societal norm that math is only for one type of person. Schools bring together many kinds of intelligences that, in turn, can create in-depth analysis in any subject matter, given the proper framework. A deep understanding of mathematics can happen for all, when we make it socially unacceptable for people to say they are bad at math.
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