Assessing Mathematics Learning with Reading and Writing Assignments

Wow! This chapter on assessment is very interesting for several reasons:
  • Assessment is discussed from an alternative viewpoint
  • Procedural answers are not the primary focus of assessment- Qualitative information is as important as quantitative
  • Primary focus of assessment is formative rather than summative
  • Assessment should assess process as well as content
  • Assessment should be on-going and balanced

I enjoyed reading the chapter on assessment, but I felt like this chapter was an add-on and not as concretely connected to the rest of the book as the other five chapters were. I then looked up the authors online to find out more about their work. They have published extensively about mathematics teaching in the middle school. Joseph Martinez has more experience in middle school mathematics and Nancy Martinez has more experience in literary work.

On page 195, in the first paragraph of the chapter the authors write, "Traditional test of calculations, where just the answers to problems hold center stage, provide little more than a peep-hole into the processes going on inside our students' heads. Reading and writing expand the view, providing at least a window and at best a two-way door that makes assessment interactive and dynamic and allows for a mix of teacher evaluation and self-evaluation."

That short quote is a very succinct view of the chapter. I, again, like the sentiment of the chapter and want to voice for the last time that I agree with and appreciate the viewpoint of the authors, but wish they applied this same sentiment to the development of the mathematical thinking of the students. If a teacher took the approach that this book espouses then the teacher would provide an extensive amount of opportunities for students to develop their understanding beyond procedure. I think the piece of this that is missing or not discussed in this book is the approach to mathematics instruction.

Figure 6.1 on page 196 is a very good visual of the complex thinking and processes that must be evident for students to be able to solve complex mathematical problems underlying the need for assessment to be more than just a procedurally oriented exam. Also, the discussion that the activities in the classroom must provide the teacher a broad overview of the thinking the student has contributed in a variety of contexts. Figure 6.2 on page 202 offers another good example of how a teacher might think about capturing those opportunities. Finally, the table on page 217 contributes some great questions regarding student thinking around mathematics. "How much has the student learned?, What are the student's weaknesses?, What are the students strengths?"

The reason I particularly like the last question is that so often we focus on student weaknesses and not their strengths. In the writing process, I know one thing that we have emphasized is what are the writer's strengths and not focus on what their deficiencies are, which I think has potential for great impact on student learning and efficacy. In mathematics, I know we often have students who don't feel they are good at mathematics and if nothing else, using writing as a modality of helping students understand mathematics may provide some students the opportuntiy to be successful in mathematics! I think it is worth the time and effort of teachers to explore the possibility.