September's comments.
30 September. In Wednesday's class, we discussed Sections 2.2 and 2.3, in which the idea of a teacher's solution to a word problem is developed and explicated.
Students are reminded that they must do the reading assigned for a given class before that class. The lecture and the quizzes will both assume that they have done so, so the former may confuse them and they may lose points on the latter.
For Monday's class, students should read Sections 3.1--3.3 of the text.
Homework for Wednesday's class was Homework Sets 8 and 9, from the text.
26 September. In Monday's class, we finished our initial discussion of division by discussing division with remainder. Until students learn about fractions or decimals, the appropriate setting for division with remainder is measurement division, not partitive division. Also, word problems for division with remainder must be carefully crafted so that they have a clear answer. (We will explore this more in our discussion of Sections 2.2 and 2.3 on Wednesday.)
For Wednesday's class, students should read Sections 2.2 and 2.3 (which we will cover very quickly) and do Exercise 3.2 on p. 53 of the text. Students should also bring the workbook and the textbook for Primary Mathematics 5A with them to class.
Homework for Monday was Homework Set 7, on p. 47 of the text.
20 September (4 PM). In today's class, we discussed how to use the rectangular array model of multiplication to illustrate the principles of associativity, commutativity, and distributivity, as well as the multiplicative identity. We then moved on to division, discussing it abstractly (as the inverse operation to multiplication) and concretely (in terms of partitive and measurement division).
Homework for today is Homework Sets 5 and 6, on paes 30 and 36, respectively, of the text. It is also specially emphasised that students should read Section 1.7 on their own, since this will not be discussed in class.
Students should read Sections 2.1 and 2.2 for Monday's class.
20 September (12:30 PM). In Monday's class, we moved on to subtraction. There are several models of subtraction as a concrete problem: the take-away, part--whole, and comparison models. Also important is the abstract idea that subtraction is the inverse, or opposite, operation to addition. We discussed the strategies of counting up and counting down, and when each was appropriate, as well as the idea of compensation. Students should be sure to read the discussion of four-fact families on page 22 of the text.
Next we moved on to multiplication. When one thinks of multiplication as counting the total number of objects in some collection of groups of objects (the set model), or as repeated addition (the measurement model, essentially), it can be difficult to see why important facts like commutativity and distributivity are valid. The rectangular array model provides a more suggestive picture.
Homework set 4, on page 24 of the text, was assigned today. Students may omit problem 8(a).
For today's class, students should read Sections 1.5 and 1.6.
13 September. In today's class, we discussed how associativity allows us to sum long lists of numbers, even though we can only ever add two numbers at a time. We also considered what it means to sum infinitely many numbers. At the end of a class, we started to discuss the methods and techniques by which elementary-school students learn to add.
No new homework was assigned today.
12 September. In yesterday's class, we discussed place value notation (or positional numbering). Place value has its roots in the idea of bundling (grouping ten pennies together into a dime, ten dimes into a dollar, &c.). Sometimes, adding two bundled collections can be done just by grouping the bundles. If the bundles get too big, we must rebundle.
We also began to discuss addition, and its interpretation in the set and measurement models. Addition is commutative and associative (taking these together, we say it has the any-order property), and the number 0 is the additive identity.
For Wednesday's class, students should read Section 1.4. Remember that there will be a quiz tomorrow, on which questions may appear covering both what we have done so far and what is discussed in today's reading.
Homework for today is Homework Sets 2 and 3, on pages 13 and 18, respectively, of the text. (Note that this homework is not due until next Monday, the 18th.) Although students are encouraged to read the workbooks as directed, you need not solve problems 1(a, b, e), 2(e), or 3(a) in Homework Set 2.
6 September. In today's class, we discussed counting; in particular, the set ("how many things in this collection?") and measurement ("how wide is the blackboard?") models of numbers. We discussed some historical numbering systems: tallies, Egyptian hieroglyphics, and Roman numerals. We also saw how complicated multiplication is in Roman numerals, if one is not allowed to use Arabic numerals to help. Today's class corresponds to most of Section 1.1 of the text.
For Monday's class, students should read Sections 1.2 and 1.3 of the text.
Homework for today is Homework Set 1, on page 6 of the text.
Permanent version of this page created on 3 October 2006.