CD listing Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School Thomas P. Carpenter...

Classroom videos included on CD that accompanied:

Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School
Thomas P. Carpenter, Megan Loef Franke, and Linda Levi, Heinemann:Portsmout. 2003

EDU 614 directory

Movie title on CD	Section and Time	Topic	Notes
Kevin	2.1 - 1:40	Equality: Solving the a number sentence 4+5=__+3	Read number sentence and tell me what to put in the box; Reads says "same as" for = ; Can you tell ... __ ; counts on fingers ...
David	2.2 - 3:02	Equality: Using Relationships to solve number sentences 6+2=__+3 57+38=56+39	First grade Why 5? Didn't knowif 5 or 7 ... Same as the 6+2, because 57&56 are related like 38&39
Lillian	2.3 - 10:19	Equality: Developing Children's Conceptions of Equality 8+4=___+5 7=3+4 3+4=7 7=7 ... 15+4=__ + 11	Fourth grade Class discussion fourth grade Think about number fit in box...; 12; How many think 12?; All Backwards... Misconception... ... 6=6; 5=5; 10=10; 5=4+1... Same on both sides (teacher asks at 5:00) ... Goes back to 5+4=__12__+5 ; talk to partner.... should we leave the 12 there? How many people?; ... So what need to do?; ... Put 19 in box? ... need to be very careful what you mean...
Emma	3.1 - 17:45	Relational Thinking Learning to Think Relationally 7+6=__+5 14+6=__+13 43+28=__+42 15+16=15+__ 28+32=27+__ 67+83=__+82	Second grade Add 7+6 and count; knew this was 13 so... Think 7; why; 14+6=20 so something +.. Those are 71; How know? left to right; Think what... count up... help if use blocks? 42... then used ones to 71; then group to get 29 ... ; how get that?; another way to get that answer? ... How do that so quickly? look at numbers... No... Asked how do 15+16... could do something like that? no; want to do it the other way? yes...; so what goes in box?... 30 something... 33; why? one more...; One more? tell me again what is so exciting? What about this? 60; why? it's kinda of like this one. Which one? 68; why pick 68? ... ; Learn something from all of thes?; What did you figure out? ....
Megan	3.2 - 6:11	Relational Thinking Children Generating Number Sentences 7+6=__+5 14+6=__+13 43+28=__+42 15+16=15+__ 28+32=27+__ 67+83=__+82	Second grade Write true false; How did you know that was true so fast?; say again, I am not sure I am hearing it...; How know without ever adding the numbers?; ... ; Prove to me; They are in a different order of adding them; Have to have two numbers can't switch them around in the number... (((Why didn't teacher explore this?))) What am I doing with switching?... A lot of conjectures... Need to write down to keep track of.... ............................
Kenzie	3.3 - 4:59	Relational Thinking Using Relationships to Generate Number Facts 37=7+7+7 46=12+12 37 = 14+7 46 = 12+12 4*7=__	Third Grade How many sevens did I say?; Why don't you read it?; True because * is same True, can we go back up here?; yes; ... True; ?; 4 sixes; 32; have a way to check it? Oh 10+10... Tell me what you would put in the box. 28; How know? used 37 = 7+7+7; 47=14+7; 46=12+12; 47=28
KF111400	4.1 - 4:10	Conjectures: Generating a Conjecture Using Number Sentences 98+0=98 841+0=__	First/second combination Class discussion 10+0=__; Student demonstrates with 10 blocks; Think we have a conjecture going here; Writes, If you add 0 to a number, then ... Maybe any number minus zero...
Susie	4.2 - 8:01	Conjectures A Conjecture Comes Up in Class Discussion Conjecture, read out loud, is it true? a+b-b=a	Second grade Try numbers, regular, super high, super low... Work with different types; Not completely, because can't do infinity; 1/2+11-11=1/2; 5+5-5=5; 5+ -5 --5 =5; rewrite the conjectures; b-b is always 0 ; other conjecture is a+0=a; If you put two conjectures together and they are always true, then it would prove the third is true. Which is better way to prove? this way would take your hole life...
Allison16	5.1 - 2:41	Open Number Sentences Solving the Equation b+b+b-20=16	Fourth grade Add, then put into three groups (10,10,10; \|\|,\|\|,\|\|) prove by adding; then prove by plugging into equation. How do you know that adding wouild give what all these were?
Cody	5.2 - 1:52	Open Number Sentences Solving the Equation k+k+13 = k +20	Fourth grade What would k have to equal for that to be a true number sentence? What made you think to try 7? Why did you know that k+13=20?
Allison	7.1 - 1:29	Justification Justifying a Conjecture About Even and Odd Odd + odd = even	Conjecture - proves by drawing lines on white board and pairing.
Thad	7.2 - 3:08	Justification Developing an Understanding Numbers (chapter 7) 05=510 5+5+5=10+5 1+1+1+1+1=5+0	Second grade Class discussion Can you say that this is true? I think that is true; Why? How id you know that?;...; What happens whenever add zero?;...
Mike	8.1 - 3:28	Further Justification Using Symbols in Proof If you add odd to odd you get even	Fourth grade m + m + 1; Matter what m is? No it is the mathematician's role. What if m = 3 1/2? Can't be a fraction.; Then I will add another b+b+1 and if add both of them, get m + m + 1 + b+b+1 = 2m + 2b + 2 ... Can never do every sample that's out there.