July 1 – 7 Online Video and Connections

Topic 1: Equality – the Soul of Mathematics

Carpenter, Franke, Levi Chapters 1,2 & 3 (this is your textbook – so it is not linked here)

Watch Videos (CD that comes with book) as they are indicated in the readings. video symbol for carpenter

For instance, in Chapter 2, you will need to watch videos 2.1, 2.2, and 2.3.

EQUALITY discussion – Watch this when you are reading CARPENTER, Ch. 2

Discussion Board – Ask three people to define and explain equality (with regard to mathematics) in this way (using these questions):

Q. 1) How would you define the mathematical term “equals” or “equality”

Q. 2) Is 1 tomato equal to 1 potato?  How,  or Why, or why not? Explain what you mean and how the definition of equality helps to understand your explanation.

Q. 3)  Is there some way that you can imagine that 2 tomatoes would be equal to 1 potato? How,  or Why, or why not? Explain what you mean and how the definition of equality helps to understand your explanation.

Make note of how they define and describe equality.  Post your findings here in this google form.  Answering the questions in the Google Form is your Discussion Post (2) for this week.

https://docs.google.com/a/ncsu.edu/forms/d/1hSl1vf-cLUe3f1C17SRooYky-OE4XbNtar8GcR2yJhM/viewform?usp=send_form

Discussion board 2 by July 7. 

Topic 2: How do we develop student thinking about abstract and concrete ideas?

Carpenter, Franke, Levi Chapter 4

Blanton, Chapter 6

Q&D Write-up 1—’video reflection’   (technically, this write-up does not have to be a reflection of any particular video). Due July 7.

One Page Questioning and Discourse Write-up (1)   Upload your one page paper on our Moodle page.

Option 1)

What have you noticed so far about Questioning Techniques and Moves?  Be specific about ideas you have already started to have about how to ask better questions.   If you want more specific direction from me, you could also answer “Challenge” questions  2, 3, and/or 4 from Chapter 2 of the Carpenter book.  Remember this is a one page write up.  So state an idea you want to discuss and then go after that idea.  Do not wander from idea to idea within the page.  Focus in on one idea (‘I had not thought before about how important your example set is to your conversations about the commutative property…” and give some specific examples (of how you would specifically prompt a student, what responses you might expect, why you think it is a good question to ask, etc.).

For full 5 points, BE SPECIFIC, Quote from, and make clear references from the readings of the week.  A strong write-up will include some very specific bouncing off points that connect directly to your readings or videos from the week.  Specific references (on page 23 of Blanton the author suggests the following for developing discourse…) or quotes and connections from videos (‘when the teacher asks “blah blah blah”  the teacher responds “blah blah blah”, this made me consider…”)

 

Option 2)

What does it mean to teach a student to generalize an idea? How is it helpful to go from a language statement to a mathematical statement that conveys the same idea?  Bounce around some idea about this.  For instance, I might want to think about what I have learned about Piaget-ian stages in the past and how that may or may not affect my thinking about young students’ abilities to generalize. (Here is a website that does a nice job of providing an overview for Piaget ideas.  See figure 4.6)  Can a student in the ‘concrete operational stage’ think abstractly (for instance, could they make and defend a conjecture about, say, adding odd numbers to each other?) ?  What about the ‘pre-operational’ stage?

For full 5 points, BE SPECIFIC, Quote from, and make clear references from the readings of the week.  A strong write-up will include some very specific bouncing off points that connect directly to your readings or videos from the week.  Specific references (on page 23 of Blanton the author suggests the following for developing discourse…) or quotes and connections from videos (‘when the teacher asks “blah blah blah”  the teacher responds “blah blah blah”, this made me consider…”)

Also Remember –

Due July 10:   Q&DWrite-up 3–Formative Assessment of Order of Operations – Write up a one page report on your assessment of student’s understanding of the Order of Operations Remember to video tape your interview with student.

 

 

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