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
Movie title on CD |
Section and Time |
Topic |
Notes |
Kevin |
2.1 - 1:40 |
Equality: |
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: |
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: 8+4=___+5 |
Fourth grade |
Emma |
3.1 - 17:45 |
Relational Thinking 7+6=__+5 |
Second grade |
Megan |
3.2 - 6:11 |
Relational Thinking 7+6=__+5 |
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 3*7=7+7+7 |
Third Grade How many sevens did I say?; Why don't you read it?; True because * is same |
KF111400 |
4.1 - 4:10 |
Conjectures: 98+0=98 |
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 b+b+b-20=16 |
Fourth grade |
Cody |
5.2 - 1:52 |
Open Number Sentences 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 Odd + odd = even |
Conjecture - proves by drawing lines on white board and pairing. |
Thad |
7.2 - 3:08 |
Justification 0*5=5*10 |
Second grade |
Mike |
8.1 - 3:28 |
Further Justification 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. |