[MATHEDCC] Why Johnny can't Read

Martha Haehl (haehl@KCMETRO.CC.MO.US)
Wed, 3 Nov 1999 19:07:42 -0600

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Some things that seem to be having an effect on student success and =
ability is addressing the problem "Johnny Can't Read" by expecting =
Johnny to read and helping Johnny read mathematics rather than try to =
make math accessible without reading.

I focus on language in many ways. In Basic Mathematics, my skills-based =
worksheets and quizzes include many questions asked in words--like "Find =
the sum of - 9 and 3.85." "Give an example, if possible, where the =
product of 4 negative numbers and 3 positive numbers is negative. If =
not possible, explain why not." I have students answer questions about =
a chapter before we cover the chapter. The questions require some =
interpretation beyond copying a definition from the book. For example, =
"What is the associative law for multiplication? Demonstrate the law =
with the numbers 8, 22, and 17." Another example of a preview question =
is "On the following grid, plot 5 points that lie on the x-axis and =
write both coordinates of each point you plotted." Then the next =
question is, "What do the coordinates of the five points have in =
common?" The next question is, "What is an x-intercept of a line? =
Which coordinate of an x-intercept is zero?"

In Basic Math and Beginning Algebra, such techniques are very helpful. =
It is harder in Intermediate Algebra because students tend to try to =
answer questions without reading and fill in answers from their memories =
which is frequently muddled. I think I am going to start requiring them =
to write the page number of the text where they found the answer.

Another technique that seems to work with learning skills is competency =
testing. My students get a number of 20-point (generally 5 questions) =
quizzes during the semester that are skills-based. I do not give =
partial credit when grading a problem and the students have to make 80% =
or higher to get credit for the quiz. If they do not meet the =
competency, they have to rework the quiz and have it checked off by me =
or a tutor in the math lab before taking a replacement quiz. A student =
must make an 80% average on all of the quizzes to make a C or higher in =
the class. (On the first retake--or if a student missed the quiz--the =
maximum score is 90%, after that it is 80%. The grade penalty for =
retakes seems to cut down on students missing on quiz day and on =
students trying the second time before they understand the material.)

Many hands-on activities are helpful. I tried a new one this semester =
in Beginning Algebra that I picked up at an NCTM-regional conference. =
Students who wanted to draw a picture did so and I copied the pictures =
on a transparanciy which I clipped to a sheet of graph paper with the =
axes marked through the center of the paper. Each group of students got =
a picture and had to identify enough points on the picture to render a =
decent duplication of the drawing. (They gave a sequence of points and =
wrote STOP when there was a break in the drawing, then picked up with =
the next sequence of points.) I had extra drawings for groups who =
finished early. Then the groups exchanged sequences of points and =
plotted the points to reproduce the picture. I had them draw the =
reproduced picture on a transparancy. Then we overlayed the reproduced =
picture on the original to see how well the groups did--by the way, very =
few points that were off. I particularly liked the activity because =
students got a lot of practice plotting points. They also dealt with =
points that had decimal and/or negative coordinates without particular =
difficulty. Having them plot that many points would have been an =
exceedingly boring task attached to no purpose the students could see. =
My students in that class have learned graphing better than my previous =
classes.

Martha
----- Original Message -----=20
From: Robert L Kimball=20
To: Dorrit O'Hallaron=20
Cc: mathedcc@archives.math.utk.edu=20
Sent: Wednesday, November 03, 1999 10:17 AM
Subject: Re: [MATHEDCC] Why Johnny can't..

To Dorrit and the list serve:=20
As chair of the department I have the responsibility and the =
opportunity to visit each class as the students complete the =
course/instructor evaluation. I have been doing that over the past two =
weeks.=20
1. I have been very pleased with the students' comments regarding =
instruction. They tell me how much the instructor seems to care, how =
willing they are to go over material or explain it differently, to meet =
with them out of class, and how knowledgeable they are in their subject. =
And, I could go on. Since we strive to follow the standards in what we =
teach and how we teach, these comments have been very rewarding.=20
2. I had several students come up to me, after I dismissed the =
class, and tell me how much better they are doing in math because of the =
way we are presenting the material, and I think, because of what =
material we are presenting. We try to use a great deal of hands-on =
activities, spreadsheets, group work, projects and less lecture. The =
students are very involved in the lessons. In the courses we teach for =
non-math intensive AA and AAS degrees, the content is carefully selected =
and taught in the context of applications. The emphasis is not on =
algebraic manipulation-rather, it is on problem solving, understanding =
the solution and selecting the appropriate tools for solving the =
problem. For example, two students (older ladies) came up to me after a =
Mathematical Models class. They both said how much they understood slope =
because of the applications (depreciation, pitch, inventory...) that =
were used to show how meaningful slope is in so many applications. They =
said that the definition of slope had been drilled into them in high =
school, but they never understood it before. They said they were very =
glad that we were changing the way mathematics is taught--making it more =
applied and more meaningful. I must say though, that there were several =
students who said they didn't like all the "word problems." However, =
they agreed that they would see a great many word problems in their =
intended major (business).=20
Thanks for the opportunity to share, glad you asked.=20
Rob=20
=20

Rob Kimball Chair, Mathematics and Physics Department=20
Office: 919-662-3602 Wake Technical Community College=20
Home: 919-266-0850 Raleigh, North Carolina 27603-5696=20
Visit the department's web site at http://www.wake.tec.nc.us/math=20
and the C.H.I.M.P. web site at http://www.wake.tec.nc.us/math/Chimp=20
=20

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Some things that seem to be having an effect on = student=20 success and ability is addressing the problem "Johnny Can't Read" by = expecting=20 Johnny to read and helping Johnny read mathematics rather than try to = make math=20 accessible without reading.
 
I focus on language in many ways.  In Basic = Mathematics,=20 my skills-based worksheets and quizzes include many questions asked in=20 words--like "Find the sum of - 9 and 3.85."  "Give an example, if = possible,=20 where the product of 4 negative numbers and 3 positive numbers is=20 negative.  If not possible, explain why not."  I have students = answer=20 questions about a chapter before we cover the chapter.  The = questions=20 require some interpretation beyond copying a definition from the = book.  For=20 example, "What is the associative law for multiplication?  = Demonstrate the=20 law with the numbers 8, 22, and 17."  Another example of a preview = question=20 is "On the following grid, plot 5 points that lie on the x-axis and = write both=20 coordinates of each point you plotted."  Then the next question is, = "What=20 do the coordinates of the five points have in common?"  The next = question=20 is, "What is an x-intercept of a line?  Which coordinate of an = x-intercept is zero?"
 
In Basic Math and Beginning Algebra, such techniques = are very=20 helpful.  It is harder in Intermediate Algebra because students = tend to try=20 to answer questions without reading and fill in answers from their = memories=20 which is frequently muddled.  I think I am going to start requiring = them to=20 write the page number of the text where they found the = answer.
 
Another technique that seems to work with learning = skills is=20 competency testing.  My students get a number of 20-point = (generally 5=20 questions) quizzes during the semester that are skills-based.  I do = not=20 give partial credit when grading a problem and the students have to make = 80% or=20 higher to get credit for the quiz.  If they do not meet the=20 competency, they have to rework the quiz and have it checked off by me = or a=20 tutor in the math lab before taking a replacement quiz.  A student = must=20 make an 80% average on all of the quizzes to make a C or higher in the=20 class.  (On the first retake--or if a student missed the quiz--the = maximum=20 score is 90%, after that it is 80%.  The grade penalty for retakes = seems to=20 cut down on students missing on quiz day and on students trying the = second time=20 before they understand the material.)
 
Many hands-on activities are helpful.  I tried = a new one=20 this semester in Beginning Algebra that I picked up at an NCTM-regional=20 conference.  Students who wanted to draw a picture did so and I = copied the=20 pictures on a transparanciy which I clipped to a sheet of graph paper = with the=20 axes marked through the center of the paper.  Each group of = students got a=20 picture and had to identify enough points on the picture to render a = decent=20 duplication of the drawing.  (They gave a sequence of points and = wrote STOP=20 when there was a break in the drawing, then picked up with the next = sequence of=20 points.)  I had extra drawings for groups who finished early.  = Then=20 the groups exchanged sequences of points and plotted the points to = reproduce the=20 picture.  I had them draw the reproduced picture on a = transparancy. =20 Then we overlayed the reproduced picture on the original to see how well = the=20 groups did--by the way, very few points that were off.  I = particularly=20 liked the activity because students got a lot of practice plotting = points. =20 They also dealt with points that had decimal and/or negative coordinates = without=20 particular difficulty.  Having them plot that many points would = have been=20 an exceedingly boring task attached to no purpose the students could = see. =20 My students in that class have learned graphing better than my previous=20 classes.
 
Martha
----- Original Message -----
From:=20 Robert L Kimball
To: Dorrit O'Hallaron
Cc: mathedcc@archives.math.utk.edu=
Sent: Wednesday, November 03, = 1999 10:17=20 AM
Subject: Re: [MATHEDCC] Why = Johnny=20 can't..

To Dorrit and the list serve:
As chair of the = department I=20 have the responsibility and the opportunity to visit each class as the = students complete the course/instructor evaluation.  I have been = doing=20 that over the past two weeks.
1.    I have been = very=20 pleased with the students' comments regarding instruction. They tell = me how=20 much the instructor seems to care, how willing they are to go over = material or=20 explain it differently, to meet with them out of class, and how = knowledgeable=20 they are in their subject. And, I could go on.  Since we strive = to follow=20 the standards in what we teach and how we teach, these comments have = been very=20 rewarding.
2.     I had several students come = up to=20 me, after I dismissed the class, and tell me how much better they are = doing in=20 math because of the way we are presenting the material, and I think, = because=20 of what material we are presenting.  We try to use a great deal = of=20 hands-on activities, spreadsheets, group work, projects and less = lecture. The=20 students are very involved in the lessons.  In the courses we = teach for=20 non-math intensive AA and AAS degrees, the content is carefully = selected and=20 taught in the context of applications. The emphasis is not on = algebraic=20 manipulation-rather, it is on problem solving, understanding the = solution and=20 selecting the appropriate tools for solving the problem. For example, = two=20 students (older ladies) came up to me after a Mathematical Models = class. They=20 both said how much they understood slope because of the applications=20 (depreciation, pitch, inventory...) that were used to show how = meaningful=20 slope is in so many applications. They said that the definition of = slope had=20 been drilled into them in high school, but they never understood it = before.=20 They said they were very glad that we were changing the way = mathematics=20 is taught--making it more applied and more meaningful.  I must = say=20 though, that there were several students who said they didn't like all = the=20 "word problems."  However, they agreed that they would see a = great many=20 word problems in their intended major (business).=20

Thanks for the opportunity to share, glad you asked.
Rob =
 =20

Rob Kimball       Chair, Mathematics = and=20 Physics Department
Office:=20 = 919-662-3602          &= nbsp;     =20 Wake Technical Community College
Home: =20 = 919-266-0850          &= nbsp;    =20 Raleigh, North Carolina 27603-5696
Visit the department's web site = at http://www.wake.tec.nc.us/math=20
and the C.H.I.M.P. web site at http://www.wake.tec.nc.us/m= ath/Chimp=20
 

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