STLF Report to CWSEI and Mathematics Department
STLF: Warren Code
Period: 16/8/10 – 10/9/10
Submitted: 15/9/10
Specific activities performed by STLF
1) Professional development
 Attended Facilitator Development Workshop (training to run Instructional Skills Workshops)
at TAG/CTLT (Aug 15, 16, 18, 20, 21).
 Math Department ISW planning meeting (Sep 2).
 Attended NOJO meetings for new STLFs (Aug 19, 26, Sep 2).
 Attended weekly Reading Group meetings (Aug 25, Sep 1).
 Attended Ken Koedinger's talk and subsequent STLF lunch (Aug 17).
2) MATH SEI general meetings/activity
 Meeting with other Math STLFs to discuss project updates (Aug 17, 31, Sep 9), and with
Math-CWSEI Director Costanza Piccolo for more detailed update on several occasions.
 Meeting with Sarah Gilbert to discuss project status (Aug 26).
 Attended Calculus Workshops Database meeting to discuss features and planning for this new
software (Sep 1).
 Worked with Sandra Merchant and Joseph Lo to adapt the C-LASS for physics to mathematics
(working title Mathematics Attitudes/Perceptions Survey, MAPS). The version in Appendix A
below is being given to students in Math 104/184, Math 100/180, Math 220 and Math 307 this
term as an initial trial.
 Along with the other Math STLFs, provided feedback on Louis Deslauriers' (Physics) math
review test. I also produced some new pictures for his divergence and curl questions.
3) Course-specific meetings/activities
MATLAB Labs (Math 152 and MECH 2)
1. Completed review of Mech 221 (Brian Wetton's portion) computer labs, caught various typos
and included feedback on a number of the activities.
2. Developed ideas for in-lab diagnostic activities focusing mainly on loops over matrices and
loops involving more abstract data structures that are stored in matrices, such as when each
column represents a different kind of quantity and/or iterating over two related matrices in the
same loop. Instructors were amenable to introducing these in the labs. We will aim for Lab 5
(already due for some work) in Math 221 (Term 1) as the first case.
3. Analysis of data from two major cohorts:
a) Last year's MECH 2 students: Met with MECH 2 coordinator Pete Ostafichuk to review
final project reports from the last few years (Mech 223, final session of the MECH 2
program). It was suggested that students have started to use Matlab more in their final
MECH 2 projects (in Mech 223), as opposed to Excel. This would be great if true, but I
wasn't able to convince myself of this shift in my initial examination of student reports
from the last few years; it seems that students usually use Matlab for certain parts of their
projects, but use Excel other times depending on the data collection devices for their
experiments.
b) This year's MECH 2 students: Question-by-question data from the Pre-Post test for Math
152 2009W is included as Appendix B below. A subset of these appeared on the incoming
quiz for MECH 2 (still waiting to receive those results). Question-by-question data from
the April 2010 Math 152 exam still needs to be obtained.
MATH 104/184 – Differential Calculus for Social Sciences
1. Met with Instructor In Charge, Mark MacLean, several times to discuss plans for the upcoming
semester. Materials for the first three weeks have been produced for the other instructors to
review and provide their feedback.
2. Weekly learning guides (we are calling them "Fresh Sheets") are being provided for
instructors. These contain a list of topic-level learning goals (previously, the course only had
course-level goals), suggested problems for the topic, suggestions for examples, and a list of
potential pitfalls or concerns for the material, as well as descriptions of the scope for each
topic. Includes many textbook references.
3. Attended Mark MacLean's classes for the first week to observe clicker questions and in-class
activities in action. Provided feedback to the instructor in person after the lecture times, as
well as follow-up emails from my written notes.
4. Attended the first of the instructor meetings where instructors can ask questions and provide
input (this will be more encouraged as the term progresses) into the common materials.
5. Developed invention/discovery activity on compound interest and its relation to the number e
for use on first day of class in one section (see Appendix C). Results from the activities will
appear in future reports.
6. I am on the list of people who receive email from students asking for help in the online
homework system (WeBWorK). Out of 1200+ students, there were only about 60 emails in the
first week (there is a full TA to help respond), with technical issues and some confusion about
one question which was poorly phrased.
Current Project Status (material prepared by either STLF or other members of the MATH SEI)
Materials will be summarized and attached (as possible) next report.
Plan for immediate future work
MATLAB Labs
1. Have TA obtain question-by-question sample data from the April 2010 Math 152 exam (am
waiting on class list for this year's Mech 2, since those will be
2. Discuss analysis from previous terms with instructors; prepare some reports.
3. Review MECH 2 incoming quiz responses once they are available.
4. Update Math 152 project website when report is ready.
MATH 104/184:
1. Check in with other instructors for feedback on the course materials: what is working, and
what else could they use?
2. Develop more discovery/invention activities for the coming weeks.
Appendix A: MAPS current version
This is a survey of your attitudes and perceptions about math; these 40 questions all have the response choices Strongly
Agree, Agree, Neutral, Disagree and Strongly Disagree, and should take less than 10 minutes. Please choose the response
that matches your opinion, not what you think an instructor might say or want to hear.
A summary of the data collected from this survey will be given to your instructor to help improve the course. Your
instructor will not have access to your individual results.
1) An obstacle to learning math is having to memorize all the necessary information.
2) When I am solving a math problem, I try to predict what would be a reasonable answer.
3) It is useful for me to do lots and lots of problems when learning math.
4) After I study a topic in math and feel that I understand it, I have difficulty solving problems on
the same topic.
5) Knowledge in math consists of many disconnected topics.
6) When I solve a math problem, I find an example that looks like the problem given and follow
the same steps.
7) I find that reading the text in detail is a helpful way for me to learn math.
8) There is usually only one correct approach to solving a math problem.
9) I'm satisfied if I can do the exercises for a math topic, even if I don't understand how
everything works.
10) I cannot learn math if the teacher does not explain things well in class.
11) I do not expect math formulas to help my understanding of the ideas; they are just for doing
calculations.
12) I study math to learn things that will be useful in my life outside of school.
13) If I get stuck on a math problem on my first try, I usually try to figure out a different way
that works.
14) Nearly everyone is capable of understanding math if they work at it.
15) Understanding math means being able to recall something you've read or been shown.
16) To understand math I talk about it with friends and other students.
17) If I am stuck on a math problem for more than five minutes, I give up or get help from
someone else.
18) If I don't remember a particular formula needed to solve a problem on a math exam, there's
nothing much I can do to come up with it.
19) In doing a math problem, if my calculation gives a result very different from what I'd expect,
I'd trust the calculation rather than going back through the problem.
20) In math, it is important for me to make sense out of formulas and procedures before I can
use them correctly.
21) I enjoy solving math problems.
22) Mathematical formulas express meaningful relationships among measurable things or
amounts.
23) Learning math changes my ideas about how the world works.
24) To learn math, I only need to memorize solutions to sample problems.
25) Reasoning skills used to understand math can be helpful to me in my everyday life.
26) We use this statement to discard the survey of people who are not reading the questions.
Please select Agree (not Strongly Agree) for this question.
27) It is a waste of time to understand where math formulas come from.
28) I find carefully analyzing only a few problems in detail is a good way for me to learn math.
29) I can usually figure out a way to solve math problems.
30) School mathematics has little to do with what I experience in the real world.
31) There are times I solve a math problem more than one way to help my understanding.
32) Being good at math requires talent.
33) It is possible to explain mathematical ideas without using equations.
34) To understand math, I sometimes relate my personal experiences to the topic being studied.
35) When I am solving a math problem, if I can see a formula that applies I don't worry about the
underlying concepts.
36) If I get stuck on a math problem, there is no chance that I will figure it out on my own.
37) When learning something new in math, I relate it to what I already know rather than just
memorizing it the way it is presented.
38) I avoid solving math problems when possible.
39) To prepare for a math test, I only need to memorize solutions to examples.
40) I think it is unfair to expect me to solve a math problem that is not similar to any example
given in class or the textbook, even if the topic has been covered in the course.
Appendix B: 2009W Math 152 Pre-Post Test results, question-by-question
1. Setup
Numbering scheme differed on the pre and post, due to change of survey questions at the beginning.
These are the numbers used in the analysis.
Out of a total population of 787 students in Math 152, there were 417 students that took both the pretest on time and post-test and responded that they took both tests seriously or at least gave a serious
attempt to each question but gave up and guessed. Quick interviews with a sample of students in their
first labs (the pre-test was supposed to be done prior to Lab 1) matched the "seriousness" response in
similar proportions to the pre-test results.
Correlation with lab grades and other scores is done with this group of 417. The response patterns
reported below refer to the total of "serious" respondents for each test, just to give a sense of what
were useful distractors.
In the pre-test, the multiple choice responses were in a fixed order, which seems to have led to an extra
bias on response "a" (also confirmed in the quick students interviews). On the post-test, the multiple
choice responses were randomized and this seems to indicate distractors more clearly.
2. Response Record
Q1: Simple loop, no matrices. Similar to Apr 2009 exam question.
What are the values of x0 and x1 that will result from the following
Matlab code?x0=1;x1=1;for i=1:3 xnew=x0+x1; x0=x1; x1=xnew;end
Exam results (open ended) 2008W: most answered 3,5
Most popular incorrect: 1,2 and a couple each of 2,3 and 3,4
Pre-test results (mult choice) of those who took "seriously" 2009W:
3,5: 38%
1,1: 24%
2,3: 18%
2,4: 16%
3,3: 4%
Post-test results 2009W:
3,5: 78%
1,1: 11%
2,3: 7%
2,4: 4%
3,3: 1%
Q2: Define 2x3 mtx, asks for output of a linear row-vector expression that uses the : operator to pick
out each row.
What would be the output of the following lines of Matlab code?
A=[1 2 3; 4 5 6];
A(2,:)-4*A(1,:)
Pre-test results (mult choice) of those who took "seriously" 2009W:
0 -3 -6: 34%
-2 -11: 30%
-2 : 18%
0 -2 -11: 10%
1 : 8%
Post-test results 2009W:
0 -3 -6: 92%
-2 -11: 5%
rest are small
Q3: Define two matrices and a vector, asks for operation that results in error (dimension mismatch).
Suppose you define the following variables in Matlab:
A=[0 2 3; 1 0 2; 1 1 1];
B=[1 -2 1; 0 -3 1; -1 1 -2];
x=[1;1;1];
Which of the following Matlab commands will result in an error message given the above definitions?
Pre-test results (mult choice) of those who took "seriously" 2009W:
x*A: 18%
x'*B: 25%
B*x: 18%
A*B': 15%
A*B: 10%
B*B: 14%
Post-test 2009W:
x*A: 76%
x'*B: 14%
B*x: 6%
A*B': 2%
A*B: 1%
B*B: <1%
Confusion probably arises out of a lack of familiarity with the "prime" operator, which is the transpose
operator in Matlab.
Q4: Matrix access and vector multiplication.
What would be the output of the following lines of Matlab code?
D=[3 0 0; 0 3 0; 0 0 1];
x=[1; 1; 1];
lambda=D(1,1);
lambda*x
Pre-test results (mult choice) of those who took "seriously" 2009W:
a column vector in which each entry has the value 3: 18%
a row vector in which each entry has the value 3: 12%
error message (was response "a" in pre-test):
24%
a scalar whose value is 3:
19%
a scalar whose value is 1:
12%
a row vector in which each entry has the value 0:
9%
a column vector in which each entry has the value 0: 4%
a scalar whose value is 0:
3%
Post-test results 2009W:
a column vector in which each entry has the value 3: 75%
a row vector in which each entry has the value 3: 14%
error message :
6%
others are small
Q5: using a loop to build a matrix with a pattern
What are the entries in the last row of A after executing the following Matlab code?
n=4;
A=zeros(n,n+1);
for i=1:n
A(i,i)=n*i;
end
Note: open-ended response where a text field is provided. The use of brackets was not strictly
enforced in determining correct responses.
Pre-test results of the 412 matched students:
2% correct
Post-test results of the 412 matched students:
39%
This is about the highest level of question difficulty, as it is a loop over a matrix pattern where the
incrementor appears both in a matrix index and as the element in the assignment.
Q6: representing a linear system (basic syntax, and a lin alg question)
Which of the following MATLAB commands would you type in to define the augmented matrix A
associated with the following linear system?
x + 2y + 2z = 1
2x + y + 2z = 1
2x + 2y + z = 1
Pre-test results (mult choice) of those who took "seriously" 2009W:
A=[1 2 2 1; 2 1 2 1; 2 2 1 1]:
34%
A=[1; 2; 2; 1; 2; 1; 2; 1; 2; 2; 1]: 21%
A=[1 2 2; 2 1 2; 2 2 1; 1 1 1]:
21%
A=[1:2:2; 2:1:2; 2:2:1]:
16%
A=[1 2 2 1: 2 1 2 1: 2 2 1 1]:
8%
Post-test results 2009W:
A=[1 2 2 1; 2 1 2 1; 2 2 1 1]: 84%
A=[1 2 2 1: 2 1 2 1: 2 2 1 1]: 13%
A=[1 2 2; 2 1 2; 2 2 1; 1 1 1]: 2%
others are small
The only confusion here is the syntax error of using colons instead of semi-colons, but this could also
be a reading error (notice how the colons are the strongest distractor in the post-test, weakest in the
pre-test).
Q7: dividing a row at a time using a loop
Suppose the variable A is defined as a 3x3 matrix with nonzero entries. In what way is the matrix A
changed by the following lines of Matlab code?
for i = 1:3
A(i,:)=A(i,:)/A(i,1)
end
Pre-test results (mult choice) of those who took "seriously" 2009W:
Each row of A div by the first entry in that row.: 32%
Each entry of A div by the entry in the first row and first column.: 19%
first column of A div by the entry in the first row and first column.: 19%
The first column of A div by the last entry of the first row.: 17%
Each column of A div by the first entry in that column.: 13%
Post-test results 2009W:
Each row of A div by the first entry in that row.: 82%
Each entry of A div by the entry in the first row and first column.: 6%
first column of A div by the entry in the first row and first column.: 1%
The first column of A div by the last entry of the first row.: 3%
Each column of A div by the first entry in that column.: 9%
Appendix C: In-class discovery activity related to continuously compounded interest and
properties/derivation of the number e.
1. Scenario:
Students are given the formula for compound interest (should have been covered in high school, but
provided here as a reminder), A = P(1 + r/n)^(nt). We tried this both as a worksheet (students asked to
work in pairs or threes and to hand in their work, given about 20 minutes) and as a clicker question
(answer alone, show the even distribution, discuss, answer again) in two sections of Math 104.
2. Question posed to the students:
You borrow $1000 from a loan shark for one year. You are offered a choice to determine how much
you will repay: you may either pay back $3000 at the end of the year or pay at a nominal annual rate
of 100% but compounded at a rate of the loan shark's choosing (i.e. the loan shark will choose the
value of n in the formula). Which would you prefer?