Methods of Math Teaching and Learning

This post is based on the last class session for this semester. We went out with a bang. We tackled NT with fractions. We actually started our talk about fractions the previous class session. Today was more of a review for the final. After much practice order fractions without determining alike denominators and operations with fractions using models, my PST (Pre-service Teachers) engaged in a NT involving fractions. The following is a conversation with adding fractions:   1/4 +1/2 Teacher: How did you get 3/4/ ? PST 1: I know that 1/2   is equal to 1/4 + 1/4which is 2/4.  So I used 1 /4  + 1/4 + 1/4. Therefore   it equals to 3/4.   PST 2: I just found that common denominator which is fourths. Since the first fraction already has fourth, I don’t have to change that fraction. But the second fraction is ½. The second fraction has to be changed to the new fractions that is equivalent. The equivalent fraction is 2/4 . So 1/4 + 2/4   is 3/4  .   Both student used equivalenc

Number Talks with Multiplication Drop the Zero! NOT! April 14, 2016 For Number Talks (NT) this week,  the Pre-Service Teachers (PST) were engage with multiplication using landmark numbers. PST were to mentally solve 6 x 50 and 6 x 300. This type of problem is not a real challenge. However, I wanted to see PST's approach to solving the problems. I wanted to hear thinking as relate to multiplying numbers with the multiples of 10. What approach would they choose? The following conversation took place: Teacher: How did you solve it? PST1: I multiplied 6 x5 first. That is 30. Then I dropped the zero. So the answer is 300. Teacher: What do you mean by dropping the zero at the end? PST1: I mean since the you are multiplying by 50 so I multiply 6x5 and drop the zero at the end. Teacher: So in reality what are you multiplying? Where did you get the 5? PST 1: I got the 5 from 50. 5 x 10 is 50. So I separated the 50 into 5 x 10. Then I multiplied 6 x 5 which is 30 then

This week in math methods class my Pre-service Teachers (PST) were introduced to alternative strategies for multiplication and division. According to Common Core State Standard/ College and Career Readiness Standards(CCSS/CCRS), students learn the standard US algorithm for multi digit multiplication in fifth grade.    Fluently multiply multi-digit whole numbers using the standard algorithm. [5-NBT5]        Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [5-NBT6 ]   This mean teachers use inventive strategies and strategies involving place value understanding for multidigit multiplication.   Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers