[Numeracy 286] Re: Linking word- and number-based language

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George Demetrion gdemetrion at msn.com
Sat Apr 3 16:36:38 EDT 2010



Good afternoon all,



Emphatically agreed on the second sentence of the first paragraph (below). Not so sure concrete operations is the key factor (magic bullet) into meaningfulness, which may (or may not) impede it. If anything, empathetic scaffolding (in which the scaffolding is provided by the students as well as the teacher--definitely my experience) is very close to, if not actually one of the foundational pivots that make meaningfulness possible, which for me is emerging through a combination of solid explanation at a level that can be grasped by all (me included) and plenty of practice.



The caveat I would like to offer is that the teacher's style and inclinations are very much part of the mix, which will factor in a great deal of what will be focused on, including "real-world" verses more abstract mathematical problem solving.



As a low to emerging mid range basic math learner is helping students master the basics. To the extent that my knowledge develops I will likely be able to draw on a broader range of methodology and materials, but I try not to get ahead of myself in what I am able to do in the class, which seems to be working, more or less. This has included--most recently in dealing with order of operations involving absolute values--students showing me how to solve a problem or three.



Among other thing we've established a class environment where people feel okay saying where we're stuck and us figuring out problems, one at a time with everyone participating.



To be sure our two classes are small and the students imbibe the core principles of adult education. To be sure, also, this class would be more than receptive to a format based on the EFF Math Standards, though as a transition to college class, I think the class is better served through a basic skills developmental process.



George Demetrion


Date: Fri, 2 Apr 2010 23:56:22 -0700
From: tesolmichael at yahoo.com
To: mmanly at earthlink.net; numeracy at nifl.gov
Subject: [Numeracy 283] Re: Linking word- and number-based language






Hello Myrna and all,

What I'm suggesting is that in teaching we're dealing with moving targets amongst our learners. The overarching question, in my mind, is what might trigger meaningfulness from the perspective of an individual learner.

Magnitude and quantity simply do not reside in quite the same conceptual realm. Let's consider the notion of the value of math from the perspective of adults who consider themselves to be successful. One "content standard," as represented in Equipped for the Future (EFF) has to do with:

Decision-Making Skills


Solve Problems

Make Decisions

Plan

Use Math to Solve Problems and Communicate (see http://eff.cls.utk.edu/fundamentals/eff_standards.htm).
When we delve into vectors, we are presumably at a "level" beyond what may relate to the math we would even entertain teaching at a "basic and functional" level.

In fact, I'm not even thinking in terms of "low-level" learners, because I embrace the notion of multiple intelligences. We all struggle in face of certain arenas of the mental and affective realms.

A rather vague response, but perhaps a platform upon which further discussion can ensue?

Michael

Michael A. Gyori

Maui International Language School

www.mauilanguage.com







From: mmanly <mmanly at earthlink.net>
To: The Math and Numeracy Discussion List <numeracy at nifl.gov>
Sent: Fri, April 2, 2010 10:50:11 AM
Subject: [Numeracy 281] Re: Linking word- and number-based language





Michael,
Are you suggesting (below) that we use the word “count” instead of “magnitude” for lower level learners?

I would prefer “the distance from zero” as an introduction to the concept since it gives the learner (who uses the number line when thinking of integers) something to visualize. Magnitude is used later when using vectors which have both magnitude and direction.

Myrna





From: numeracy-bounces at nifl.gov [mailto:numeracy-bounces at nifl.gov] On Behalf Of Michael Gyori
Sent: Friday, April 02, 2010 12:13 PM
To: The Math and Numeracy Discussion List
Subject: [Numeracy 279] Linking word- and number-based language




Hello Carol and everyone,



The word-based and number-based language link can be quite a task, can't it?

There is a fundamental difference between the terms quantities and magnitude. Quantities refer to count nouns (persons, places, things, and ideas). 1, 2, 3 people; 1, 2,3 cities; 1, 2, 3 cups of coffee; 1, 2, 3, insights, etc.). Magnitude(s), on the other hand, can refer both to count as well as non-count nouns (tons of love - a noncount noun in this case, vs. tons of coffee beans - a count noun in this case).



One of the characteristics of absolute values, at least for pedagogical purposes, is the use of numbers (math) to - ultimately - (to be able to) count, whether it be a sum, difference, product, or quotient that derives from performing operations on numbers (whether whole, part, or mixed).



The use of the term magnitude might be potentially confounding for a learner. Magnitude is a lower-frequency word, and to delve into its meaning while building mathematical awareness might pose a challenge for learners with limited cognitive underlying proficiency levels. We need to be sensitive to what we wish to accomplish both by teaching and the learning it may trigger.



Michael




Michael A. Gyori

Maui International Language School

www.mauilanguage.com









From: Carol King <cking at lyon.k12.nv.us>
To: mmanly at earthlink.net; The Math and Numeracy Discussion List <numeracy at nifl.gov>
Sent: Thu, April 1, 2010 7:30:33 AM
Subject: [Numeracy 277] Re: Is an absolute value positive?

This leads me back to some of the confusion, while I really liked that example, you have now introduced the new term of magnitude into our discussion of absolute values which my text defines as the distance from 0 and it does not mention magnitudes at all. While I personally understand magnitude and I prefer that as the term for what absolute value is showing in the problem, if my struggling student was to try to use another source to help them they might also run into this language and they feel rather than being helped they are led down another rabbit hole. Why are there so many ways to express in language what this one concept is doing rather than a consistent method?
Carol King
Fernley Adult Education Center
cking at lyon.k12.nv.us





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