Talk:Good Math Lesson Plans





Comment by David Moursund 8/24/08 Plus Updates
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Comment by Stickler for Details 5/7/08
I have read that time on task is one of the best predictors of learning in schools. It seems to me that an important part of planning a lesson is to think carefully about how to keep students on task.

Response by Dave Moursund 5/7/08. There is lots of research to support the importance of time on task. My elementary school classroom observations suggest, however, that some teachers spend so much effort trying to keep the class quiet and on task, that the net result is way too much time is spent off task. That is an interesting dilemma!

Comment by Melanie Baggett May 2, 2008
I read the article about calculators in mathematics education. The author of the article mentioned that although calculators were important tools in education, the benefits of calculators had a negative tone. The author also mentioned that elementary school aged students should learn how to use them. However, as a teacher I would fear that using calculators would teach my students to depend on a 'computer' to do the thinking instead of themselves. I can think of many reasons that a student should be taught to think independently of a calculator. For example, when going to the grocery store, I add up the cost of the items so I will know about how much money I will need to spend. I also take into consideration the mileage it takes to get to places and how much gasoline it will take to get me there. In the evenings when I cook, I often double recipes depending on how many people I will be feeding. All of these daily computations are done without a calculator. I see value in being able to compute numbers withouth depending on a calculator. I think if children were taught with a calculator to compute numbers, then they would not be able to make sense of number in the real world. The goal of teaching is for my students to be able to think for themselves. I want my students to be productive citizens.

Comment by Anonymous # 1
It would be nice if someone would condense the article to a length that a typical teacher would be willing to read. Right now, few teachers would be willing to work their way through the somewhat weighty (but good) material.

Comment by Anonymous # 2
I recently read the 2006 article "Our Impoverished View of Educational Reform" written by David C. Berliner. This article discusses the role of poverty in poor school performance. It seems to me that poverty should be taken into consideration in lesson planning. It comes in as one looks at prerequisites. On average, children raised in poverty lack many of the across the curriculum prerequisites that are assumed in teaching any topic, whether it be math or any other subject area.

Quoting from the article:


 * As educators and scholars we continually talk about school reform as if it must take place inside the schools. We advocate, for the most part, for adequacy in funding, high quality teachers, professional development, greater subject matter preparation, cooperative learning, technologically enhanced instruction, community involvement, and lots of other ideas and methods I also promote. Some of the most lauded of our school reform programs in our most distressed schools do show some success, but success often means bringing the students who are at the 20th percentile in reading and mathematics skills up to the 30th percentile in those skills. Statistical significance and a respectable effect size for a school reform effort is certainly worthy of our admiration, but it just doesn’t get as much accomplished as needs to be done.

Comment on Teacher-Centered Math Education
Here is some support of the assertion that math is taught using a teacher-centered, oral tradition approach.

Ellis, Mark W. (2008). Leaving No Child Behind Yet Allowing None Too Far Ahead: Ensuring (In)Equity in Mathematics Education Through the Science of Measurement and Instruction. TC Record. Retrieved 12/15/07: http://www.tcrecord.org/Content.asp?ContentID=14757. For other articles by Ellis, see http://faculty.fullerton.edu/mellis/.

Quoting from this article:


 * Mathematics education in the United States, as it was played out within schools (and with/in children), changed little during the 20th century (Cobb, Wood, Yackel, & McNeal, 1992; Fey, 1979; Stodolsky, 1988). Representative is Susan Stodolsky’s description generated from her study of mathematics teaching across 39 fifth-grade classrooms in the 1980s: “Math instruction places all but the exceptional student in a position of almost total dependence on the teacher for progress through a course. In essence, the traditional math classes contain only one route to learning: teacher presentation of concepts followed by independent student practice” (pp. 122–123).


 * The persistent image of mathematics teaching and learning involved the teacher at the front of the class dispensing knowledge while students sat quietly copying notes, working on practice problems and, later, being assessed on their ability to reproduce the facts and manipulations exhibited by the teacher. This approach “situates mathematics as a priori knowledge, based on objective reason alone, without taking into account the experiences students bring to mathematics or the meaning they make of what is learned . . . [and] allows students’ mathematics achievement to be discretely measured, quantified, and stratified” (Ellis & Berry, 2005, p. 8).3 As Tate (1994) observed, “traditional mathematics classrooms are structured to rank students’ understanding of a body of static ideas and procedures” (p. 481). Access to higher levels of mathematics had historically been available only to those few deemed to possess sufficient ability.

Comment: The Concept of Proof
It seems to me that many students never understand the concept of a proof in math. This leads me to think about the overall process of solving math problem and then presenting arguments that will convince other people that both your solution process and answer(s) are correct. A math proof can be thought of as an argument that a particular type of math assertion (a theorem) is correct. Thus, it seems to me that problem solving and theorem proving should be more carefully intertwined in teaching math.

Comment by David Moursund
The article is long and sometimes not as well organized as it could be. However, it is a start.

I strongly believe that our use of comptuers in math education is dismal. Surely we want students to learn to learn in a computer environment, and learn to make effective use of resources provided by the Web. Why is this not a regular part of the curriculum for all students?