# [Numeracy 461] Re: Monday Puzzle

Share:

## Archived Content Disclaimer

This page contains archived content from a LINCS email discussion list that closed in 2012. This content is not updated as part of LINCS’ ongoing website maintenance, and hyperlinks may be broken.

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>

>

>

>

> 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

>

>

> ----------------------------------------------------

> National Institute for Literacy

> Math & Numeracy discussion list

> Numeracy at nifl.gov

> To unsubscribe or change your subscription settings, please go to

> http://www.nifl.gov/mailman/listinfo/numeracy

> Email delivered to mtrushkowsky at mail.cuny.edu

>

>

> ----------------------------------------------------

> National Institute for Literacy

> Math& Numeracy discussion list

> Numeracy at nifl.gov

> To unsubscribe or change your subscription settings, please go to http://www.nifl.gov/mailman/listinfo/numeracy

> Email delivered to chip.burkitt at orderingchaos.com

-------------- next part --------------
An HTML attachment was scrubbed...
URL: http://lincs.ed.gov/pipermail/numeracy/attachments/20100803/db3385bf/attachment.html
-------------- next part --------------
A non-text attachment was scrubbed...
Name: smime.p7s
Type: application/x-pkcs7-signature
Size: 2283 bytes
Desc: not available
Url : http://lincs.ed.gov/pipermail/numeracy/attachments/20100803/db3385bf/attachment.bin