[Numeracy 303] Re: Numeracy Digest, Vol 4, Issue 12
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Tue Apr 13 09:36:21 EDT 2010
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Ryan and Steve, thanks for both of your responses!
I agree with both of you that reading ability, certainly, is correlated with scores on the Applied section.
I also agree that exposure to graphs and charts will most likely be highly beneficial to the students and their performance. In fact, because of this line of thinking -- and for inspiration from Kate Nonesuch's excellent and insightful "Changing the Way We Teach Math" -- I will be spending a good portion of this term having students create their own charts and graphs, before moving on to having them read and interpret published graphs and charts.
This is more what I was trying to get at in my not-so-articulate post from before: What are the most *base* skills that are playing into our students limitations in math work, ESPECIALLY in Applied Math. I'm trying to relate it to the work my colleague does in literacy, where their limitations are broken done into constituent skills, such as "decoding".
The problem with the TABE survey as a tool for diagnose is that all we can identify is the breakdown of a whole line of micro-processes. Take for example problems like 6, 7, and 8 in 9M. (For those of you that doesn't use the TABE survey, the questions provide a table of information regarding the price of repairs at a fictional auto shop, "Abe's".) What are the skills sets involved in solving these problems? First and foremost, visual acuity. I think that this alone is a skill that is immensely overlooked and under-considered. I believe this goes all the way back to when our students were considerably younger. This even reaches back to when they are infants and need a highly-skilled parent to do the give and take, call and response parenting that I'm sure we've all seen excellent parents do with ease. Babies absolutely need this to fully develop their fine and gross motor skills. So, perhaps some of our students did not have a care-giver available to do these formative "exercises" with them, or perhaps their care-giver had not learned these artful parenting skills for one reason or another and therefore knew not to do them. Beyond this stage, perhaps some students had poor vision but no visual implements to cover the gap in their visual abilities when they were in the early years of school when math is taught is a much more visual and concrete way. Or perhaps, again, their teacher did not know best practices because they were under-trained or that, possibly his/her class was so overcrowded, understaffed and out of control that using manipulatives was out of the question.
I think these two factors alone can help account for the wild and (seemingly) nonsensical answers that I have received to math questions repeatedly in my years of teaching in Philly. I feel that for many of us, when we encounter a math problem our brain taps into a primordial (so to speak) grasp of the physicality of the numbers before us, so even if we are unsure of how to approach the problem, we still have, at the very least, (1) some notion of how to go about solving it, and (2) a sense of about what the answer should be.
OK, back to the problem. What else do we need in order to approach this problem? Reading ability, of course, comes into play right away. Noticing that the title is "Abe's Auto Repair" helps us to make an inference. But what about the ability of making inferences itself? Isn't that a highly advanced human skill in- and of-itself?
And this has to be closely allied with exposure to the subjects involved; i.e. auto repairs and pricing sheets of this sort. If one has extensive exposure to auto repairs the brain will process this information with much greater facility and, more importantly, it won't recoil at the foreignness of it. Having a notion of repair fees being "parts plus labor" makes this chart much easier to fathom and makes question 8 much more understandable and therefore answerable. In fact, without this understanding, that question is virtually unanswerable. Additionally, exposure to and familiarity with these subjects must then be combined with the ability to process the organization and to garner the appropriate information from the chart: columns of "service", "parts" and "repair time"; the odd middle section that points out that total prices don't include the cost of labor, but in an indirect way; and a "Specials" section which is required to answer both questions 6 and 7.
Given that students of low ability can often frustrate quickly, throwing a question at them right away that requires that they understand (a) that the total is comprised of a both and parts and a labor fee, (b) that "labor charge" is correlated with repair time, and (c) that there is a special on Mondays that affords the fictional customer a $45 reduction on the total fee-- must just lead the student to give up on all three related questions. Or guess on all three.
So, if my student gets one, two or all three wrong- what am I supposed to take from that? The results are virtually uninterpretable.
So, again, to reiterate (re-reiterate?!) my original question. I am struggling intensely with the need to wrap my head around all of the numerous micro-processes/skills involved in the various questions that I am supposed to prepare my students for. Beyond just enumerating what those skills are is a daunting task. Subsequently, I need to figure out how to diagnose which of those micro-processes are breaking down for them, which is clearly going to keep them from being able to solve a problem wherein numerous micro-processes must work in conjunction for the solution to be achieved. And only after both of those, can I then try to figure out how to teach both the micro-processes and eventually the layered questions that involve some number of those processes/skills.
Sorry for the loquaciousness and tedium of this post, but these are the issues that I have been trying to work through. My students need to me to solve these for their future and the DoL requires it of our organization.
Thanks so much for your perseverance if you made it this far; and thanks for any assistance and insight that you may provide.
Happy teaching~~
Andrew J. Isom
Math Specialist
Center For Literacy
North Philadelphia Community High School
isom at centerforliteracy.org
(215)744-6000 ext. 210
-----Original Message-----
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Sent: Mon 4/12/2010 12:00 PM
To: numeracy at nifl.gov
Subject: Numeracy Digest, Vol 4, Issue 12
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Today's Topics:
1. [Numeracy 299] Re: Diagnostics for ABE students (Ryan Hall)
2. [Numeracy 300] Applied Mathematics (Ryan Hall)
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Message: 1
Date: Sun, 11 Apr 2010 15:53:02 -0500
From: Ryan Hall <sryanhall at gmail.com>
Subject: [Numeracy 299] Re: Diagnostics for ABE students
To: The Math and Numeracy Discussion List <numeracy at nifl.gov>
Message-ID: <C7E7A0DE.7803%sryanhall at gmail.com>
Content-Type: text/plain; charset="US-ASCII"
I am glad you asked this question, Andrew, because it is something that I
have been discussing with my math teachers for awhile now.
We use the TABE (survey form, not the complete battery) to assess our
students' math skills and needs. We currently have four levels of math
classes, and we place students in those classes according to the items they
miss on the TABE. We are going on the third year using this system, and it
is working pretty well so far.
There are limits to the what the TABE test can tell us about students' math
skills and gains (an opinion I share with my math teachers); therefore, we
are very interested in finding additional assessments that could be used to
tell us more information. One idea is that we may need to use the complete
battery instead of the survey form of the TABE. Does anyone have any idea if
switching the complete battery form of the TABE would give a better analysis
of students' math skills? Are there other math assessments others find more
beneficial in the ABE math class?
Thanks again for posting this question, Andrew, and I look forward to
hearing about how others assess their students math skills and gains.
Ryan
On 4/7/10 8:29 AM, "Andrew Isom" <isom at centerforliteracy.org> wrote:
> How do you all diagnose your students' math needs? I was wondering if there
> isn't a nice, extensive battery out there that examines and highlights the
> lower level skills as well as higher level skills. I'm thinking about my
> colleague who is a literacy specialist and tests students in various ways,
> usually in a timed fashion, for different literacy skills.
>
> Also, does everyone use the TABE? Our job is to raise our students 2 grade
> levels on the TABE, so I struggle with which skills to prioritize. This is
> especially difficult to answer because of the "Applied Mathematics" section.
>
> Any ideas, advice or suggestions would be much appreciated.
>
> Thanks~~
>
> Andrew J. Isom
> Math Specialist
> Center For Literacy
> North Philadelphia Community High School
> isom at centerforliteracy.org
> (215)744-6000 ext. 210
> ----------------------------------------------------
> 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 sryanhall at gmail.com
------------------------------
Message: 2
Date: Sun, 11 Apr 2010 16:17:19 -0500
From: Ryan Hall <sryanhall at gmail.com>
Subject: [Numeracy 300] Applied Mathematics
To: The Math and Numeracy Discussion List <numeracy at nifl.gov>
Message-ID: <C7E7A68F.780C%sryanhall at gmail.com>
Content-Type: text/plain; charset="US-ASCII"
Andrew,
You also mentioned the Applied Mathematics subtest of the TABE. You said:
"Our job is to raise our students 2 grade levels on the TABE, so I struggle
with which skills to prioritize. This is especially difficult to answer
because of the "Applied Mathematics" section."
In Steve's reply, he said:
"One observation that I have made this year is that a vast majority of
students who read above an 8th grade level score higher on the Applied Math
portion than on the Math Computation portion. I'm not sure why, although I
have a few theories about that."
In the past couple of years that I have looked at our students' TABE scores,
I have noticed that students' reading and applied math scores seem to be
around the same level, while their math comp scores may be several GE's
higher or lower than their reading skills. (I never noticed that students
reading at 8th grade and higher do much better, though.) For this reason, I
place students in their math classes based on the math computational skills
that they need (our math classes are divide up by different math skills).
One big observation I made with the Applied Math subtest of the TABE is that
many students give up very quickly on this test. Students are given about 15
minutes to take the math computation part of the TABE and then about 25 to
take the Applied Math part (survey form, not complete battery). What I
noticed is that students tended to work all the way to the end of time on
the math comp subtest, but then only take 5 or 10 minutes on the Applied
Math subtest. There would be lots of huffing and puffing, and some slamming
of pencils when it came to this part of the test. My thought was that the
items on this were just too foreign for these students to make any sense out
of--either because they couldn't read the directions or word problems, or
because they didn't understand what to do with all the information in the
tables and charts, ... or both, and I went with both...
So, my solution has been to add more reading in the math classes and then
more exposure to charts, graphs, tables, schedules etc. in the reading
classes. We are just ending the first semester of classes where we
implemented this multiple exposure to these types of tasks on a whole-school
level, so I do not have any scores ready that would indicate whether or not
it was as successful as we hoped it would be. We are still working on this
area, so I would love to hear how other programs help their learners with
the types of tasks that are tested on the Applied Mathematics subtest of the
TABE.
Ryan
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