Math News (Writing Personal and Private Math Journalism)

This chapter is harder for me to relate to in some instances. I think the math journalism idea is worth discussing, but I don't have the imagination to think about how a class newspaper translates into a traditional math classroom. I do however think the idea of having students look at the who, what, when, where, how, and why of topics is essential to student learning. I think the approach is very interesting, but I differ slightly on the application. I envision a classroom that uses admit/exit slips routinely as a way of capturing student thinking about many of those topics. I see a class blog used to more intentionally provide students an arena for expanding that writing. I see a classroom culture that values students questioning traditional mathematical procedures, developing and defending their own, analyzing those processes, and engaging in discourse about their findings.

Self-Discovery

Again, the am concerned with the manner in which the mathematics is presented. On page 181, the Self-Discovery discussion is an excellent example of an affective look at solving and understanding a fraction division problem. I like the approach of answering the problem, reflecting on the answer, reviewing the problem at a later time to evaluate the student's understanding. The problem is that the reflection they use as the example is procedural in nature and doesn't actually make conceptual sense. It is a student rationalizing why a procedure is correct. As much as I like the approach, I can't get over the lower-level math discussion.
"Dividing is more like cutting something into more pieces. It's okay to write the problem 1/4 ÷ 1/8 to start but then I have to turn the second fraction upside down and multiply: 1/4 x 8/1 = 2. That means there are two 1/8s in 1/4. I didn't understand before."
I still don't see the students understanding of the concept in that quote, except for the last sentence.
In my experience I would see a student approach the problem like this "1/4 ÷ 1/8 same as 2/8 ÷ 1/8 same as 2 ÷ 1 = 2" means there are two eighths in one fourth which means that one fourth can be divided into two groups of one eighth.

That answer seems to be much more in-tune with the goal of this book without holding on to the procedural approach that is represented in most American mathematics classrooms. If the authors had included more student thinking that had been developed from a conceptual approach, I would be ver pleased with this book.

Journaling

"The act of writing daiily or almost daily about a subject guarantees that the subject will become rooted in the writere's thought process."

I think this is a topic that many teachers struggle with. It is the tough balance of getting students to think about the what and why in a math class, providing students formative feedback, honoring student thinking, incorporating it into the classroom routine, and, for those students who need it, summative assessment. This book does provides an extensive amount of examples (including 101 activities/topics for journal entries). The Martinez's provide thinking about different ways of using journals, ways of keeping the writing fresh, and different types of writing and how they can be used in math journals. On page 183 figure 5.2 shows connections between learning objectives, type of learning, and things to look for, i.e. Developing confidence- Poems- lively vocabulary. It provides teachers who are willing to look for purpose but need a little help making connections between the goal and the type of writing a nice easy to use chart to jump-start their thinking.

The technology connections are limited and dated. This is one area the book is lacking. I don't see a good exploration of new online literacy technologies and the 2001 copyright makes this book dated.

## Math News (Writing Personal and Private Math Journalism)

This chapter is harder for me to relate to in some instances. I think the math journalism idea is worth discussing, but I don't have the imagination to think about how a class newspaper translates into a traditional math classroom. I do however think the idea of having students look at the who, what, when, where, how, and why of topics is essential to student learning. I think the approach is very interesting, but I differ slightly on the application. I envision a classroom that uses admit/exit slips routinely as a way of capturing student thinking about many of those topics. I see a class blog used to more intentionally provide students an arena for expanding that writing. I see a classroom culture that values students questioning traditional mathematical procedures, developing and defending their own, analyzing those processes, and engaging in discourse about their findings.

Self-DiscoveryAgain, the am concerned with the manner in which the mathematics is presented. On page 181, the

Self-Discoverydiscussion is an excellent example of an affective look at solving and understanding a fraction division problem. I like the approach of answering the problem, reflecting on the answer, reviewing the problem at a later time to evaluate the student's understanding. The problem is that the reflection they use as the example is procedural in nature and doesn't actually make conceptual sense. It is a student rationalizing why a procedure is correct. As much as I like the approach, I can't get over the lower-level math discussion."Dividing is more like cutting something into more pieces. It's okay to write the problem 1/4 ÷ 1/8 to start but then I have to turn the second fraction upside down and multiply: 1/4 x 8/1 = 2. That means there are two 1/8s in 1/4. I didn't understand before."

I still don't see the students understanding of the concept in that quote, except for the last sentence.

In my experience I would see a student approach the problem like this "1/4 ÷ 1/8 same as 2/8 ÷ 1/8 same as 2 ÷ 1 = 2" means there are two eighths in one fourth which means that one fourth can be divided into two groups of one eighth.

That answer seems to be much more in-tune with the goal of this book without holding on to the procedural approach that is represented in most American mathematics classrooms. If the authors had included more student thinking that had been developed from a conceptual approach, I would be ver pleased with this book.

Journaling"The act of writing daiily or almost daily about a subject guarantees that the subject will become rooted in the writere's thought process."

I think this is a topic that many teachers struggle with. It is the tough balance of getting students to think about the what and why in a math class, providing students formative feedback, honoring student thinking, incorporating it into the classroom routine, and, for those students who need it, summative assessment. This book does provides an extensive amount of examples (including 101 activities/topics for journal entries). The Martinez's provide thinking about different ways of using journals, ways of keeping the writing fresh, and different types of writing and how they can be used in math journals. On page 183 figure 5.2 shows connections between learning objectives, type of learning, and things to look for, i.e. Developing confidence- Poems- lively vocabulary. It provides teachers who are willing to look for purpose but need a little help making connections between the goal and the type of writing a nice easy to use chart to jump-start their thinking.

The technology connections are limited and dated. This is one area the book is lacking. I don't see a good exploration of new online literacy technologies and the 2001 copyright makes this book dated.