Research Article

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

## Table 8

Nature of tasks selected and/or generated during the tutoring assignment.
 Type N Example Number choices CGI-word problems 17 Student 1(use their names in the real setting) has ___race cars. Student 2 gave student 1___more race cars. How many race cars does student 1 have in total? Student 1 adding to 10_(5, 5) 7, 3) (4, 6) (15, 5) student 2 adding to 100 (50, 50) (80, 20) (35, 65) (42, 58) True or false sentences 3 The student will be presented with these problems one at a time and they determine whether the problem is true or not.4 + 2 = 63 + 3 = 64 + 2 = 3 + 3 Those numbers are chosen because they are within the range of 1–10 and they are familiar 10s fact for the student. The values of the equations are slightly higher but the sum allows for more differing equations to be used. I chose this equations and numbers using low numbers in value while presenting anew concept in to make her more comfortable and confident in the use of those numbers … Number sentences and/or equations 3 5 + 8 = 8 + 54+3 = hmm + 2 5 + 8 = 8 + 5-I chose this number because I want to see if my students understand that the number to the right is the same with the number to the left4 + 3 = hmmm + 2-I chose this number sentence because I wanted to see if the students understand that the equal sign means the same as and that both sides of the equation should add up to the same number. Counting 5 After the students complete the number 10 worksheet the teacher will pass out the dot-to-dot worksheet. Students will need to complete both worksheets by drawing lines from the numbers 1–30 and 5–500 first by counting up by ones and then by 5’s. This will give the students the bases for counting so that they will be able to count the “how many objects” worksheet. No number choices Place value 2 I will start by writing a two digit number on my scratch paper for both students to see e.g., 76.I will ask them to say the number and then I will point at the different digits and then ask them what this number represents (prompting students to point out the place). After discussing the two-digit number, I will add to digit to the end of the number making it a 3 digit three digit number. I chose some two digit and three digits because at this grade level students know three digit numbers and breaking them into place values is a good task, but I also choose two digits so that they can see the difference …
Note. N = number of problems.