Preservice Teachers’ Learning to Respond on the Basis of Children’s Mathematical Understanding

Table 7

Nature of tasks selected during the Inquiry into Student Thinking assignment.

Problem type

# of tasks

PSTs example

Number choices

Join Change Unknown

5

“Joshua collects rocks. He likes to keep them in bags of ten. Last week he had a total of ____ bags. After finding some more this week, he now has ____ bags. How many rocks did Joshua find this week?”

Number Choices: 5, 6) (5, 8) (8, 12) (9, 15)

Join Result Unknown

8

I would create Joint-Result-Unknown (JRU) or Separate-Result-Unknown (SRU) problems for the students. A JRU example would be “Sunny has ____ fish, and then she buys ____ more. How many fish does she have now?” Number choices would include

Number Choices: {(10, 50) (20, 30) (10, 41) (15, 25)}.

Compare change unknown

1

Emilio had 64 soccer cards. Sunny had 28 soccer cards. How many more soccer cards does Emilio have than sunny?

Separate result unknown

4

Emilio has __soccer balls. __ Soccer balls roll away. How many Soccer balls are left?

Number Choices: (15, 5) (26, 16) (57, 27) (81, 51)

Group size unknown

2

Jack has 65 pencils. He wants his 5 classmates to each have an equal amount of pencils. How many would each classmate get?”

No number Choices

Number of groups unknown

3

Sunny has 94 chocolate chips. She needs 10 chocolate chips to make a cookie. How many cookies can Sunny make?

No number Choices

Both product unknown & Joint Result Unknown

4

Sunny has 8 rolls of candy. Each package has 11 candies in it. She also has 12 extra candies. How many candies does she have in all?

No number Choices

Product unknown and compare result unknown

1

Mary had __ bags of cookies with __ cookies in each bag and Amy had __ bags of cookies with __ cookies in each bag. Which one had more cookies?