Being a social studies teacher with a passion for all things writing, I was struck by how much writing is required of students on the math assessments. Interestingly, it was often the writing that prevented students from receiving full credit on some of the answers. Many of the teachers complained about this, particularly as we moved onto the middle grade levels. Often, I heard comments like these:
"These kids clearly knew the answer - I don't know why we can't just give them full credit."
"These scoring guides penalize the students who can 'do math' in their heads and don't need to show their work."
I understand their arguments but I also know that NYS is trying to emphasize (through the standards as well as the assessments) the power of communicating in math. And in order to communicate well in math - they must do so using the very technical language of math. While these teachers found the issue to be one of math (and sometimes of reading), I really saw these as the students not being able to express themselves in the mathematical language. A few examples:
When asked to express their answer in exponential form, several students would provide the correct answer when writing "three to the sixth power" but could not receive full credit because they did not write it in correct form.
Some students would write to explain how they found a particular answer, but in a somewhat vague manner such as "because you have to find the straight 180 so you would subtract." Teachers would argue that it is evident that the students understood the notion of complementary angles, but in reality there is not enough detail in this statement. The straight 180 what? Subtract what? From what?
Writing in the disciplines is very content specific. I have long held the belief that each content area has its own literacy that goes beyond merely teaching students to use the English language. In social studies, students need to be able to read and communicate about maps using correct terms. They need to understand the symbolism in political cartoons and the trends in charts/graphs. In science, they need to understand scientific notation, the symbols in chemistry and how to write a chemical equation. I could go on and on but you get the picture. Each discipline requires a highly technical language and one that we must explicitly teach our students. Each of us truly is a teacher of literacy.
For my math friends, it didn't seem the appropriate time to share my thoughts about the difference between having students muscle through the math to come up with a correct answer and having them share their understandings of the process and relationship between numbers in written form. But you can bet that I will be learning more about the technical writing in other subjects so that I can help them teach writing there as well.
Cross-posted on Grand Rounds.
4 comments:
As an eighth grade NYS math teacher, I agree with your posting wholeheartedly. Its not about being able to calculate the answer, its about being able to express and share your process with those who don't understand the math. (Many of my own colleagues will disagree with me here.)
When we think about the "real world" and what mathematics most of our students will be working with, many of them will be using a computer application or program which will do most of the calculations. They in turn then need to express these calculations and how they were arrived with members of management and others who will need to apply the data. Similarly, those who are creating these very same programs will need to be able to share with the "rest of the world" how and why their process works, in a clear and concise manner. Simply stating that they had to subtract 135 from 180 (or as most 8th graders in our area said "subtract 180 from 135" which is false) is not enough to demonostrate a full understanding of the concept of parallel lines, transversals, supplementary angles, etc.
I scored the second question you used as an example! It was frustrating reading answers where I knew the student knew what they were trying to say, but it just didn't come out right. If they would have just used the right vocabulary (and a little proper grammar) they could have received full credit. It makes me think of all the times as teachers we say, "if you can teach it to someone else, you really know it." That's what they need to do in their explaination, write it like their teaching it to someone. I'm thinking more journal writing, vocabulary instruction and cooperative learning in math!
Sheri's got it exactly right.
We assess to determine a student's understanding of the concept taught. We can't infer that; they must demonstrate it. An effective demonstration requires control of the vocabulary, a grasp of the grammar, and, of course, the underlying understanding of the concept.
Subtracting 135 from 180 is not the same as subtracting 180 from 135, any more than "eats, shoots and leaves" is the same as " eats shoots and leaves" (from Lynne Truss's book).
Language matters.
As a high school math teacher, scoring the tests has been a real eye-opener for me as a mathematician first and then as a teacher. In the past I would use "cutsey" words to help (or what I thought was to help) students remember mathematical terms/definitions. For example, I would refer to the hypotenuse of a triangle as the "hippopotamus" of a triangle. Scoring these exams made me realize that using "cutsey" words like this is really incorrect modeling of how to communicate mathematically. I should be the model for my students.
Scoring the exams is great professional development for teachers of math. I wish we were able to provide all of the secondary math teachers the opportunity to score the 3-8 exams...I think it would be a real shock to some of them what the state expects of students with regards to communicating mathematically.
Post a Comment