Knowing and Learning Mathematics for Teaching Proceedings of a Workshop (2001) / Chapter Skim
Currently Skimming:
Teachers' Understanding of Fundamental Mathematics
Teachers' Understanding of Fundamental Mathematics
Pages 11-22
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 11... ...
PANELISTS Knowledge of Fundamental Mathematics for Teaching Liping Ma, Stanford University Elementary Teachers and Essential Mathematical Knowledge Mark Saabs, Bronxville High School What Is Fundamental Mathematics? Genevieve Knight, Coppin State College
|
From page 12... ...
Her memories of elementary teaching in China suggested that Chinese teachers would react quite differently. She investigated this suspicion in her dissertation research, asking Chinese elementary teachers the same questions that had been asked of U.S.
|
From page 13... ...
Like basic attitudes, basic principles may play a role in teaching, as well as knowing, mathematics. They may appear as parts of what Chinese teachers call a "knowledge package" for a given topic a network of conceptual anti proce(lural topics that support anti are supporte(1 by This perception of what it means to know elementary mathematics has been challenged by many in the U.S., in particular by the writers of the various National Council of Teachers of Mathematics Standards.
|
From page 14... ...
When Chinese teachers were asked the same question, about 20% made comments such as This reflects a general principle in the organization of knowledge packages: Not all topics receive equal emphasis. Some are considered key pieces, and teachers take particular care that students un(lerThis mistake should have happened when students learn multiplication by two-digit numbers.
|
From page 15... ...
Instea(l, students' learning of curriculum topics supports anti is supporte(1 by knowle(lge of basic principles: composing anti (1ecomposing a higher value unit, the rate for composing a higher value unit, anti a(l(lition anti subtraction as inverse operations. How do teachers help students focus on these basic principles?
|
From page 16... ...
The two aspects are often considered as separate content and pedagogy and taught to prospective teachers as separate subjects mathematics and methods. But, just as a mathematical attitude toward elementary mathematics makes it more than a collection of disconnected procedures, the "knowledge package" way of thinking about teaching elementary mathematics makes knowledge for teaching more than content plus pedagogy.
|
From page 17... ...
The facile answer is: as much as possible, and the more, the better. Liping Ma's book gives a more sober view of the situation.
|
From page 18... ...
notes that much of the "deep knowledge" of the Chinese teachers she interviewed was acquired during their own elementary and middle school education. Our problem is that we need to start this cycle in motion.
|
From page 19... ...
Ma, L (1999~. Knowing and teaching elementary mathematics: Teachers' understanding offundamental mathematics in China and the United States.
|
From page 20... ...
In Liping Ma's work, she refers to the mathematics for elementary teachers that is really conceptual un(lerstan(ling, fundamental to shaping the foundation for young learners to mentally assemble (liscrete units of knowledge to form units of units that eventually generate complex structures in abstract mathematics. Teachers recall their own early experiences that gave meaning to mathematics for them.
|
From page 21... ...
a well-designed system that allows us to determine when a teacher or student "un(lerstan(ls." As a community, we need to examine what is fundamental mathematics and collectively promote research that wall enable us to prepare elementary teachers to teach for student understanding. As we engage in conversations over the next few days, let us attempt to share best thoughts W H AT I S F U N D AM E N TA L M AT H E M AT I C S ?
|
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.