Knowing and Learning Mathematics for Teaching Proceedings of a Workshop (2001) / Chapter Skim
Currently Skimming:
Promising Approaches for Helping Prospective Elementary Teachers Learn Mathematics for Teaching
Promising Approaches for Helping Prospective Elementary Teachers Learn Mathematics for Teaching
Pages 105-126
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 105... ...
The moderator concluded the session by presenting an argument for why sites of teaching practice might provide opportunities for teacher learning and broadened the list of sites of practices beyond those considered in the Workshop. PANELISTS Looking et textbooks Richard Ask ey, University of Wisconsin-Madison The Professional Growth of a Classroom Teacher Carol Midgett, Southport Elementary School The Importance of Mathematical Content Alice Gill, American Federation of Teachers NSF and Teacher Preparation Programs James Lighthourne, National Science Foundation Where Are We?
|
From page 106... ...
Ma claimed that one of the main ways in which the Chinese teachers she interviewed developed their deep understanding of elementary mathematics was by serious study of their texts. Here is an example of a problem that appears in a Chinese fifth-grade book and also in a Japanese elementary school text.
|
From page 107... ...
in their work on the mathematical knowIedge of elementary school teachers was to divide ~ 4 by 2' and make up a story problem with this division being the operation leading to a solution. The topic of division of fractions is treated very well by White.
|
From page 108... ...
~ think this material could be used as Ma says the Chinese teachers she interviewed used their texts, to develop a deeper understanding of the mathematics they teach. SQUARE ROOTS An even more impressive treatment is .
|
From page 109... ...
This is used as background material for taking square roots and cube roots. The section on square roots starts by listing the squares of I, 10, 100, and 1,000 and the squares of 9, 99, 999, and 9,999.
|
From page 110... ...
52 Figure 3. Geometrical Explanation of the Process of Extracting the Cube Root \ 253 US x a CM \~ 20 x 52 Figure 4.
|
From page 111... ...
The resulting approximation is the old Babylonian method for extracting square roots. To see that you understand this method, work out the corresponding formula for cube roots.
|
From page 112... ...
If the general case of a parallelogram has not been done, the general case of a triangle wall also not have been done. In a Singapore series of elementary school math books, area is introduced in the second half of third grade (Primary Mathematics Project Team, 1993-1995, 3B)
|
From page 113... ...
Some wall, and many more wall if the teachers know what to look for and what questions to ask. The teacher's guide (Primary Mathematics Project Team, 1994-1996, Figure 7.
|
From page 114... ...
Figure 8. Decomposing Triangles into Right Triangles / 10m 4m (a)
|
From page 115... ...
Mahwah, NJ: Lawrence Erlbaum. Primary Mathematics Project Team.
|
From page 116... ...
Although ~ had taught my students to recognize, create patterns using multiple media, extend and correct patterns, ~ failed to see the pervasive value of patterns in all strands of mathematics and their multiple foundations in algebra. The Standards also gave me a view of the development of mathematical ideas across the K-12 continuum and where my grade level contributed to that continuum.
|
From page 117... ...
The tasks required that ~ analyze my instructional practice and its impact on student learning. ~ had to provide evidence, as well as artifacts, proving that ~ thoughtfully planned, intentionally taught to a learning objective, and reflected upon the impact of my practice on student achievement.
|
From page 118... ...
Just think, as teachers and all of us are we have unlimited possibilities and we have unending challenges. Whether we are · ~ ass~shng · six-year-ol(ls in understanding mathematics, · preservice teachers to recognize the inadequacies of their own mathematics instruction, · planning professional (levelopment to extend the learning of veteran teachers, · shructuring university classes to retool professors, we are identifying the common practices that lead to learning and the shructures that support their teaching.
|
From page 119... ...
how to (levelop a concept, as oppose(1 to just throwing something out for students to learn as "the way it is." We know there are teachers who really (lon't even have a goo(1 grasp of the procedures anti aigorithms for mathematics in gra(les above the ones they expect to teach in elementary school. The sa(1 thing is that the way our licensure system works anti the way teachers in school districts are assigned, teachers may think they're going to teach first or secon(1 gra(le anti en(1 up in sixth or seventh because they hol(1 a K-8 license.
|
From page 120... ...
Later, they can share their own videos or exchange classroom visits with peers and talk about teaching and lessons without feeling personally threatened. Analyzing student work is very important, but you can't analyze it until you know the math behind the work.
|
From page 121... ...
The development of excellent math teachers is a complex process. No single idea or tool will accomplish what is needed, including requiring deeper knowledge of mathematical content.
|
From page 122... ...
developed a classroom observation instrument for evaluating reforme(1 teaching K-20 classrooms across all science and mathematics disciplines. Findings indicate a strong correlation between the use of reformed teaching strategies and students' achievement pre/ post test gains.
|
From page 123... ...
was instrumental in influencing changes in state policy regarding certification of elementary and middle schools teachers. Whereas previously the state did not require prospective elementary teachers to study any science or mathematics, new licensure requirements include 12 hours of mathematics and 12 hours of science for a NSF AND TEACHER PREPARATION K-6 license and 21 hours of mathematics for a middle school license to teach mathematics.
|
From page 124... ...
A comparison of students in the reform college algebra class with students in a traditionally taught class indicated the students in the reform class scored significantly higher than traditionally taught students in three dimensions: conceptual understanding, ability to employ multiple approaches, and communication skills. At San Francisco State University, one of the San Francisco Bay Area CEI`P institutions, Mathematics 301, a course required for future mathematics teachers, was revised to increase the hours and revise the materials and processes used during the class.
|
From page 125... ...
Otherconversationssuggested other promising sites of practice, and it seemed that a reasonable way to focus our discussion was to begin to make a list about tasks of teaching that serve as places where teachers have an opportunity to learn some mathematics. Such a list might include the following potential sites of practice: · Learning to use and adapt student curriculum materials and teachers' guides , , ~ ~ 1 ~ ~ ~ · Critiquing and reviewing instructional materials · Studying cases of mathematics teaching · Analyzing cases of student thinking · Analyzing videotapes of teaching, including an analysis of questions and answers · Analyzing student work · Remo(leling mathematical tasks and analyzing the nature of tasks · Managing classroom~iscussion · Implementing assessments · Looking at standards As we think about this perspective on developing teacher knowledge, we might make some conjectures about why sites of practice seem promising as contexts through which teachers can learn mathematics, in particular the mathematics it takes to teach well.
|
From page 126... ...
We need to begin in a (liscipline(1 way, using what we know about (loin" research, the task of studying outcome as we build coherence anti language, anti groun(le(1 arguments about using sites of practice to help preservice students come to know the mathematics they will need to teach well.
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.