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2.1 Read the following word problem:

Leticia has 8 Pokemon cards. She gets some more for her birthday. Now she has 13 Pokemon cards. How many Pokemon cards did Leticia get for her birthday?

Do you think that a typical first grader could solve this problem? NOTE. The problem could be read to the child

.
Yes

No
 

2.2

If a friend of yours disagreed with you, what would you say to support your position?

2.3 Here is another word problem.  Again, read it and then determine whether a typical first grader could solve it.

Miguel has 3 packs of gum. There are 5 sticks of gum in each pack. How many sticks of gum does Miguel have?

Do you think that a typical first grader could solve this problem? NOTE. The problem could be read to the child.

Yes
No

If a friend of yours disagreed with you, what would you say to support your position?

 
 
 

 3.1 Teachers often ask children to share their strategies for solving problems with the class.  Read the following student answers and indicate whether each makes sense to you. Then, click on the button at the bottom of the page to continue.

Carlos 149 + 286  Written on paper	Henry 149 + 286  Henry says, "I know that 40 and 80 is 120, and one hundred and two hundred makes 300, and 120 and 300 is 420, and 9 and 6 is 14, so 420 and 10 is 430, and 4 more is 434."	Elliott 149 + 286  Written on paper	Sarah 149 + 286  Sarah says, "Well, 149 is only 1 away from 150, so 150 and 200 is 350, and 80 more is 430, and 6 more is 436. Then I have to subtract the 1, so it is 435."
Does Carlos's reasoning make sense to you? Yes No	Does Henry's reasoning make sense to you? Yes No	Does Elliott's reasoning make sense to you? Yes No   Would you like to see a further explanation? Click here  to see a further explanation.	Does Sarah's reasoning make sense to you? Yes No

= 100 Called a flat	= 10 Called a long	= 1 Called a single

Maria Manipulatives Maria uses manipulatives (base-ten blocks) to solve the problem. Maria says, "I took one flat for the 100 in 149 and 2 flats for the 200 in 286.  I took 12 longs: 4 for the 40 in 149 and 8 for the 80 in 286.  I took 15 singles for the 9 in 149 and the 6 in 286.  Then I counted like this, '100, 200, 300'; then for the longs, '310, 320, 330, 340, 350, 360, 370, 380, 390, 400, 410, 420'; then the singles, '421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435.'  So the answer is 435." Does Maria's reasoning make sense to you? Yes No

Carlos 149 + 286 Written on paper

Henry 149 + 286 Henry says, "I know that 40 and 80 is 120, and one hundred and two hundred makes 300, and 120 and 300 is 420, and 9 and 6 is 14, so 420 and 10 is 430, and 4 more is 434."

Elliott 149 + 286 Written on paper

Sarah 149 + 286 Sarah says, "Well, 149 is only 1 away from 150, so 150 and 200 is 350, and 80 more is 430, and 6 more is 436. Then I have to subtract the 1, so it is 435."

Maria Manipulatives = 100 Called a flat = 10 Called a long = 1 Called a single Maria uses manipulatives (base-ten blocks) to solve the problem. Maria says, "I took one flat for the 100 in 149 and 2 flats for the 200 in 286.  I took 12 longs: 4 for the 40 in 149 and 8 for the 80 in 286.  I took 15 singles for the 9 in 149 and the 6 in 286.  Then I counted like this, '100, 200, 300'; then for the longs, '310, 320, 330, 340, 350, 360, 370, 380, 390, 400, 410, 420'; then the singles, '421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435.'  So the answer is 435."

3.2. If you were a teacher, which of the approaches would you like to see children share? Select "yes" or "no" next to each student and then explain why or why not. Carlos Yes No Henry Yes No Elliott Yes No Sarah Yes No Maria Yes No 3.3 Consider just the strategies on which you would focus in a unit on multidigit addition.  Over a several-weeks unit, in which order would you focus on these strategies?  First: no preference  Carlos  Henry  Elliott  Sarah  Maria  I don't want to share any others  Second:  no preference  Carlos  Henry  Elliott  Sarah  Maria  I don't want to share any others  Third:  no preference  Carlos  Henry  Elliott  Sarah  Maria  I don't want to share any others  Fourth: no preference  Carlos  Henry  Elliott  Sarah  Maria  I don't want to share any others Fifth: no preference  Carlos  Henry  Elliott  Sarah  Maria  I don't want to share any others  Please explain your answer for the rankings in 3.3 above.     3.4.  Do you think that Carlos could make sense of and explain Sarah's strategy?  Why or why not?   3.5. Do you think that Carlos could make sense of and explain Elliott's strategy?  Why or why not?

4.   Here are two approaches that children used to solve the problem 635 - 482.

Lexi                                  5613 5                -  4 8 2                    1 5 3     Lexi says, "First I subtracted 2 from 5 and got 3. Then I couldn't subtract 8 from 3, so I borrowed. I crossed out the 6, wrote a 5, then put a 1 next to the 3. Now it's 13 minus 8 is 5. And then 5 minus 4 is 1, so my answer is 153."	Ariana   635 -  400  =  235 235 -   30 =   205 205 -    50 =   155 155 -      2 =   153            482         Ariana says, "First I subtracted 400 and got 235. Then I subtracted 30 and got 205, and I subtracted 50 more and got 155. I needed to subtract 2 more and ended up with 153."
4.1 Does Lexi's reasoning make sense to you? Yes    No	4.2 Does Ariana's reasoning make sense to you?   Yes    No

4.3. Which child (Lexi or Ariana) shows the greater mathematical understanding?  

Lexi    Ariana

Why?

4.4  Describe how Lexi would solve this item:  700 - 573.

4.5 Describe how Ariana would solve this item:  700 - 573.

Question 4 (continued)

Here are those two approaches again so that you can refer to them to finish this section.

Lexi                                  5613 5                -  4 8 2                    1 5 3     Lexi says, "First I subtracted 2 from 5 and got 3. Then I couldn't subtract 8 from 3, so I borrowed. I crossed out the 6, wrote a 5, then put a 1 next to the 3. Now it's 13 minus 8 is 5. And then 5 minus 4 is 1, so my answer is 153."

Ariana   635 -  400  =  235 235 -    30 =   205 205 -    50 =   155 155 -      2 =   153            482         Ariana says, "First I subtracted 400 and got 235. Then I subtracted 30 and got 205, and I subtracted 50 more and got 155. I needed to subtract 2 more and ended up with 153."

For the remaining questions, assume that students have been exposed to both approaches.  

4.6  Out of 10 students, how many do you think would choose Lexi's approach? out of 10 students would choose Lexi's approach. 4.7  If 10 students used Lexi's approach, how many do you think would be successful in solving the problem 700 - 573?   out of 10 students would be successful.   Explain your thinking.

4.8  Out of 10 students, how many do you think would choose Ariana's approach? out of 10 students would choose Ariana's approach. 4.9  If 10 students used Ariana's approach, how many do you think would be successful in solving the problem 700 - 573?   out of 10 students would be successful. Explain your thinking.

4.10 If you were the teacher, which approach would you prefer that your students use? 

      Choose one of the following Lexi's Ariana's Both

  Please explain your choice.

5. What were your reactions when you were asked to solve a new kind of problem without the teacher's showing you how to solve it?

5.1  When you are a teacher, will you ever ask your students to solve a new kind of problem without first showing them how to solve it?     

Yes   

No

If you answered that you would ask your students to solve a new kind of problem without first showing them how to solve it.  Please elaborate on your reasons:

5.2  If you answered that you would ask your students to solve a new kind of problem without first showing them how to solve it. How often will you ask your students to do this?

I am sure that I want to become a teacher.
I think that I want to become a teacher.
I am not sure that I want to become a teacher.
I am leaning against becoming a teacher.
I am sure that I do not want to become a teacher.