[Numeracy 461] Re: Monday Puzzle
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Tue Aug 3 15:58:20 EDT 2010
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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>
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> 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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