Recently I have exchanged email through an intermediary with a student in year three of the IMP curriculum. Since my previous post on IMP considered only the year 1 text, I thought it would be interesting for members of this list to hear what a current student had to say about the program and get some idea of what a 3rd year veteran of the program thinks about it. Obviously, this is just one student's view, so it should not be interpreted as completely typical of every student's experience in an IMP classroom. Still, I am sure that there are a number of this student's experiences which are typical of most IMP students. The student's average grade over the three years of IMP is a 3.0. At the end I will analyze report # 95-4 from the Wisconsin Center for Education Research on the IMP program.
QUESTION ONE: How often does the teacher give out worksheets that are not part of the text material?
ANSWER: The teacher usually gives out worksheets not part of the text at the beginning and the end of our units. Like a few days ago we got a worksheet with actual math equations like 12 + C = 3C + 4, that wasn't part of our new unit. We did them and the next day in class when we were going over them, our teacher said something like, "Hey, you guys need to be paying attention because I've noticed you guys aren't that good at this".
COROLLARY QUESTION: If students have difficulty with the worksheets, does the teacher spend enough time with the students to make sure they all "get it", or does it seem to be just something to do before the next IMP unit?
ANSWER: They're just there to pass time till the next unit. They're not that hard, so most of the class gets it.
QUESTION TWO: What is your estimate of the time you spend in groups doing work versus time doing work as an individual?
ANSWER: I'd say that 75 percent of the time we are working in our groups. Our teacher always wants us to help each other out, but sometimes if you really understand what's going on, you just zoom through the assignment, not waiting for the rest of your group.
COROLLARY QUESTION: Does the teacher have students rate their group members on participation that becomes part of the grade for each student? Are projects ever done where each member of a group gets the same grade based on the group's effort?
ANSWER: No, we have never rated our fellow group members and given them the grade that becomes the grade for that student. Sometimes we would grade ourselves on how we did, but that was it, and it never became a final grade. In my memory, there is only one time in recent memory where we did anything as a group and got a group grade.
QUESTION THREE: Does the teacher ever give a lecture? How often?
ANSWER: I'm not too sure how you define 'lecture'. But on a daily basis, she goes over the homework with us by asking us to present. We present and then she asks the class if the answer is correct, we talk about it, she interprets it, and then she starts talking about the in-class work that we need to do and lets us work on it.
COROLLARY QUESTION: In this case I am defining lecture as where a teacher teaches a concept directly, for example, "the slope of a line is rise over run. If you have two points...", etc. This would be in contrast to a class where students are not taught directly but kind of figure things out for themselves.
ANSWER: Our teacher never gives lectures the way you say. We usually figure stuff out for ourselves, present it, the teacher will redefine it and then say, "Well this is a function, etc. etc."
QUESTION FOUR: What are grades based on?
ANSWER: Grades are based on three things: Homeworks, in-class activities, and assessments. The homeworks are worth the least, usually being 5 points, while the in-class work is usually 10 points, and the assessments, which include POWs, and portfolios and tests are usually worth around 20 points each.
COROLLARY QUESTION: What kind of tests are they? Are they comprehensive, that is, do they cover all material up to the point of the test or just material in a unit? Do you have a semester final exam? Also, based on your experience in IMP for the past year and a half or so, what percent of the grade is tests versus homework, versus POWs, versus in-class activities?
ANSWER: Tests usually aren't comprehensive, they only cover one or two things in a unit. The last unit test that we had, we had to create a 45 degree angle. Our entire unit we did constructions, the distance formula, and graphs, and she has us construct an angle. We have an end of the trimester test no matter if we are in the middle of a unit, the teacher will just make up something. I haven't a clue about the percents. (remember, I am in IMP). To get a good grade you do need to do all the work, it's not easy.
QUESTION FIVE: Do a lot of kids get off task? What does the teacher do?
ANSWER: Yes, students do get off task, not a lot, but some do. Usually it depends on who you are sitting with, if it's someone you know, you are more likely to talk to them and not pay attention. We switch tables about every three weeks and when we were in our last seating chart, we talked a lot, but we just got a new seating chart, and I've noticed it's been more quiet. Our teacher usually says "I expect you to be quiet and paying attention to your fellow classmates". Then we usually pretend to stop talking and be quiet, but in a minute or two, we're back where we were.
QUESTION SIX: Was your attitude about IMP different the first year you took it compared to what your attitude about IMP is now?
ANSWER: My attitude was different my first year, because IMP seemed fun and interesting. I thought that I would be able to learn a lot of math through the fun games we played. I remember our very first unit, we didn't do any math at all, we learned to make in-out charts but that's about it, the rest was all words.
COROLLARY QUESTION: What has changed the most about your attitude towards IMP?
ANSWER: What has most changed in my attitude? I'd say the realization that I will be in remedial math in college, that I'm not actually learning anything that will help me on my SAT's and ACTs, that I'm wasting an hour pretending to do math, and that people lied to me when I was in 8th grade and said that IMP was a good math program and that I would learn and be able to go to college fully prepared. So realizing these things has most changed my attitude.
QUESTION SEVEN: How much of the writing does the teacher actually seem to grade?
ANSWER: I would have to say that our teacher grades a lot on our writing, because most of our answers require a written explanation as to why it is correct. Like right now we have a POW where we have to write a 3-5 page paper on population growth and how it can affect things and how things can affect it. Some topics that they suggested are "Pros and cons to birth control", "population growth and the food supply", "population growth and pollution", etc. We complained that this was a math class and that we shouldn't be writing research papers. I don't exactly remember what my teacher said in response, but it was something like "Well, if students are bad in math and good in writing, they can still pass the course." this reminds me of last year, when I was still unaware of the non-math education in IMP, I had to write another paper, this time on bees, for our "Do Bees Build it Best" unit. I honestly don't understand how my teacher can teach us this and not see a problem in it.
QUESTION EIGHT: What is the best thing you like about IMP?
ANSWER: I really can't think of a thing that I like. And now that I think about it, that is strange. I really don't like anything in my IMP class. I've always commented to my friends that there "Aren't any boring days in IMP", but I'm usually refering to the other students in the class any how, we can still make it bearable. What we do, it isn't fun, it's not that interesting, and I never feel like I'm learning.
QUESTION NINE: What is the worst thing you dislike about IMP?
ANSWER: The worst thing about IMP is the fact that I know that I'm not really learning anything that will help for the SATs, ACTs, or for college. I'm not learning anything.
QUESTION TEN: What do other students who are not IMP students at your high school, say when you describe what happens in IMP to them?
ANSWER: When I talk about IMP to other students at my school who aren't in IMP, they usually laugh and say how happy they aren't in that math class, they also ask "Do you actually learn anything in there?" and my usual response is "no". Some ask "What do you do in there?" I tell them, and they respond "That's so simple" and laugh some more. I've decided to sign up for a summer math program, in the attempt to augment some of my math, so we'll see what happens with that.
QUESTION ELEVEN: Below are some math questions I would like you to try and answer.
1) Can you find the intersection of two lines? Example: y = 3x - 2, y = 4x-5.
2) when are lines parallel and when are they perpendicular?
3) Can you derive (prove) the pythagorean theorem, either using Euclid's proof or another way? Do you know what the pythagorean theorem is?
4) What is a function?
5) if f(x) = -3x + 2, can you find the inverse of the function?
6) Do you know the laws of exponents and the laws of logarithms?
7) What is the probability of rolling a five or less with two 6-sided die?
ANSWER:
1) I can't find the intersection of any two lines.
2) Parallel lines are two lines that are next to each other but that don't ever intersect. Perpendicular is when they intersect with each other.
3) The pythagorean theorem is A^2 + B^2 = C^2. I cannot derive a proof of it.
4) A function is related to slope, the rate of things. That's all I know.
5) I can't find the inverse function.
6) I don't know either of the laws. We have never covered them in class.
7) I don't know the probability of the dice, but I'm sure that some others in class can do that. I don't think I was paying attention during the "game of pig" unit.
COMMENT AND ANALYSIS:
It seems obvious that this young man does not feel that IMP has helped him learn the mathematics that he needs to do well in college. But this is not a definitive study, merely an anecdote. One definitve study that can tell us more about IMP's effectiveness is a study quoted by IMP in their spring 1995 Evaluation update. This study, report number 95-4, is "Impact of the Interactive Mathematics Program on the Retention of Underrepresented Students: Class of 1993 Transcript Report for School 2: "Hill High School"", by Norman Webb and Maritza Dowling. Excerpts from this report have also appeared in the winter 1996-1997 edition of WCER Highlights and is available on-line at the WCER website. Both the IMP update and the WCER highlights article make much of the fact that SAT scores for IMP students were nearly identical with those of non-IMP students in one carefully matched group. But what about other groups at this high school? When comparing student groups it is always important to consider the student population from which they are drawn.
In report 95-4, not only are matched groups compared, but also females, males, blacks, whites, other(Asian, Native American, Pacific Islanders, etc.), and hispanic. When compared against each other in these groups, IMP students in every category except other appear to be more of an elite group in terms of their CTBS scores. I say "appear to be", but this can be tested by statistical hypothesis testing. The hypothesis: IMP students and controls have different mean scores. Choosing an alpha of .05, the means can be compared by simple t tests. The null hypothesis would be that there is no difference between the IMP students and the non-IMP students, either on their 7th grade CTBS scores or on the SAT Math scores for IMP or control. Thus, if p < .05, the null hypothesis is rejected and my hypothesis is accepted. Below are the t values and p values for the various groups in the report. When t > 0, the mean for the IMP (or future IMP) group is above that of the control group. I have also included the numbers of each group tested in parentheses, and my data has been double-checked by a statistician.
7th grade CTBS scores SAT Math scores
all kids I(81) C(125) t=6.60 p<.0001 I(71) C(111) t=0.95 p=.34
female I(50) C(73) t=5.51 p<.0001 I(43) C(63) t=1.04 p=.30
male I(31) C(52) t=3.67 p=.0004 I(28) C(48) t=0.46 p=.65
black I(17) C(43) t=4.04 p=.0002 I(14) C(32) t=0.79 p=.44
other I(10) C(17) t=0.78 p=.44 I(7) C(17) t=-1.09 p=.30
hispanic I(5) C(13) t=3.32 p=.005 I(4) C(7) t=0.08 p=.94
white I(48) C(49) t=3.23 p=.002 I(45) C(54) t=0.29 p=.77
Note that for all groups except other, the null hypothesis is rejected for
7th grade CTBS scores. Thus, IMP students in most categories had higher math
achievement as 7th graders than non-IMP students who took algebra or other
math classes. (not included in the study were a 25 percent group of the
population at the high school who took geometry or higher math classes as
freshmen). But note the p values for SAT math achievement. Here the null
hypothesis is accepted for all groups. And the trend in t values between
the CTBS and the SAT is the same for all groups.
The conclusion seems to be that lower achieving students in the non-IMP groups made up a tremendous amount of ground on the IMP students in terms of math achievement between 7th grade and the time that the SAT was taken, usually in 11th grade. From this data it appears that IMP is a great leveler, not by pushing lower achieving students up, but by holding higher achieving students back.