[Numeracy 461] Re: Monday Puzzle

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Chip Burkitt chip.burkitt at orderingchaos.com
Tue Aug 3 15:58:20 EDT 2010


Very helpful! Thanks.

On 8/3/2010 2:09 PM, Mark.Trushkowsky at mail.cuny.edu wrote:

>

> I have observed something interesting in my students, when it comes to

> the equal sign, and I wonder if others have had similar experiences.

>

> I've taken to asking my students what they think the equal sign means

> and while there is usually one student can express that it means that

> the expression on one side is the same as the expression on the other

> side, the vast majority of students say something imprecise, like

> "equals means the answer". If you think about it, that makes sense -

> when using a calculator, one pushes "=" to get the answer; problems

> are often written with an equal sign followed by a blank space,

> implying "the answer" should follow. I know some of us have enough of

> a conceptual understanding of "=" to be versatile in our use of it,

> but we should be conscious of the fact that we need to give our

> students a consistent and deep sense of what we mean, especially

> considering the misconceptions they often bring to class.

>

> I like to have this conversation with students where first I make a

> list of all of their definitions of the equal sign. Sometimes I have

> them write it on a post-it note and put it on the board. Then I try

> to provide exception to the definitions that students tend to give,

> which are often mathematically imprecise. For example, if a student

> says "an equal sign means the answer", I'll give an examples to help

> them see that their definition does not always fit and that they can

> strive for one that does always fit. For example, I might ask them to

> consider that definition with "8 + __ = 35". I'll try to keep doing

> that until we have a precise definition (from the students own words)

> that explains exactly what an equal sign means.

>

> My goal is for this activity is three-fold:

> 1) I want to ellicit students misconceptions because that is where I

> need to begin my teaching - I need to know where they are coming from

> to know what work I need to do to help them see the limitation of

> those misconceptions and help them move beyond them

> 2) I want to model what it means to "know" or "test" mathematical

> knowledge

> 3) I want students to have a mathematically precise understanding of

> the equal sign

>

> Doing this activity really emphasized for me how important it is to

> not take for granted that students see the same things as we do when

> they see mathematical symbols, and how important it is to have them

> explain their use of symbols. It is also important to help students

> recognize the need for precision and how to go about testing and

> refining observations to get there.

>

>

> Mark Trushkowsky

> Mathematics Staff Developer

> CUNY Adult Literacy and GED Program

> 101 W. 31st Street, 7th Floor

> New York, NY 10001

> 646-344-7301

>

>

>

>

>

> *"Istas, Brooke" <IstasB at cowley.edu>*

> Sent by: numeracy-bounces at nifl.gov

>

> 08/03/2010 12:49 PM

> Please respond to

> The Math and Numeracy Discussion List <numeracy at nifl.gov>

>

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> To

> <numeracy at nifl.gov>

> cc

>

> Subject

> [Numeracy 457] Re: Monday Puzzle

>

>

>

>

>

>

>

>

>

> Hello All!

>

> I am glad that many of you are contributing to the discussion with

> your methods for approaching these problems. My learners seem to

> really like these warm-up questions or brain teasers. Ladnor made a

> good point with his comment about the “=” symbol. I have seen the

> misuse of the equals symbols in many classrooms not just in adult

> education but in college/university classes, too (I have even been

> guilty of misusing it myself). *Does anyone else have an opinion about

> the misuse of math symbols? Does it create more math confusion? What

> other math symbols do you feel are misused and lead to further math

> frustration with learners?*

>

> Let’s discuss this!

> Brooke Istas

>

>

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