Learning Outcome 1
This is an Action Research Project.
Clear
Goals
A. Abstract
I researched and developed an alternative assessment
technique for teaching calculus (MAC2311).
The purpose was to determine if an alternative assessment technique, writing assignment, would be beneficial
to student understanding and retention of material. In Calculus 1, a
particularly difficult topic for the students to grasp is the Mean Value Theorem
(MVT). This may be the first course where a student needs to “prove using
theorems.” It is my
experience/hypothesis that theorem-writing abilities are directly related to
the ability to effectively communicate. As such, I wanted to add a writing assignment
to my course to help the students hone their skills at explaining mathematical
concepts with words. I hoped this translation from mathematical symbols to the
English language would help to solidify the material as well as transfer it
from short-term memory to long-term memory.
A series of writing assignments and assessments were implemented. The results revealed statistically
significant evidence that the students made a larger improvement in score on
theirfinal exam after completing the writing assignment.
B. Research
Question
Will a writing assignment, as a formative assessment technique, in Calculus 1, increase the students’ abilities to perform and retain mathematical concepts?
Adequate Preparation
A. Learning Outcome Statement: Develop alternative assessment technique(s) to improve calculus student's ability to learn.
B.
Background
from Multiple Perspectives
- Student Perspective
For the last few semesters, I have had my students complete a "muddiest point" CAT at the end of the unit. About 80% of the respondents mention that the Mean Value Theorem concept was the most difficult for them to grasp. Also, students often mention “proofs” in the end-of-semester evaluations under the heading “What assignment/activity I liked least.”
- Colleague Perspective
I had heard about using writing assignments to articulate mathematical concepts from other math professors, but I wasn’t sure if this was a “mainstream” mathematical assignment. I did ask in a department meeting if other calculus professors were using this technique, and none were. So, I thought I’d try it out and see for myself if it was a useful teaching tool.
- Expert Perspective
In preparation for this action research project, I consulted the literature to confirm that incorporating the writing of mathematical solutions was a valid assessment technique. I was happy to find that the National Council of Teachers of Mathematics advocates that “one of the best ways to assess how students actually solve problems is to ask them to explain their reasoning, that is, to write about their math (NCTM, 1989).”
Through the use of writing in the mathematics classroom, students can “clarify their thinking, recognize and appreciate the connection between mathematics and other disciplines, and communicate their thoughts, ideas, and understanding about the subject with other students” (Burchfield, Jorgense, McDowell, & Rahn, 1993). Using writing in mathematics can also be useful to teachers. Drake and Amspaugh (1994) observed that teachers who add writing to their class often find it easier to recognize and diagnose the nature of students’ conceptual problems. I was encouraged by existing research that seems to suggest that using writing to teach mathematics is indeed worth of further exploration. Existing research seems to suggest that using writing to teach mathematics merits further exploration.
Attending the seminar “Writing as a Tool for Learning,” presented by Helen Clarke, helped me understand the link between writing and thinking skills already imbedded in my math courses. I learned concrete strategies for incorporating writing strategies in my instruction and assessment, as I will explain in my methods section of this project.
Brookhart, S.M. (1997). The relationship of classroom assessment to student effort and achievement in the college classroom. Paper presented at the annual meeting of the American Educational Research Association, Chicago, IL.
Burchfield,
P.C., Jorgensen, P.R., McDowell, K.G., and Rahn, J. (1993). Writing in the
Mathematics Curriculum. Re-trieved July 24, 2000, from http://www.geocities.com/kaferico/writemat.htm.
Cross, P. K. & Steadman, M.
(1996) Classroom Research: Implementing
the Scholarship of Teaching. Jossey-Bass:
Drake, B. M. & L. B. Amspaugh (1994). What writing reveals in mathematics. Focus on Learning Problems in Mathematics, 16.3, 43-50.
Educational
assessment of students 2nd ed..
Meier, J. & Rishel, T. (1998) Writing in the Teaching and Learning of
Mathematics, MAA Notes Number 48, Mathematical Association of America,
1998.
National Council of Teachers of
Mathematics (1989). Curriculum and
evaluation standards for school mathematics.
I also attended
the following Teaching/Learning Academy Seminars on Essential Competencies
during the first year of my tenure process:
·
Scholarship of Teaching and Learning, Presented
by TLA Staff
·
Assessment: Using the Principles for Good
Practice as a Conceptual Model for Assessing Student Learning, Presented by Dr.
Susan Hatfield, Assessment Coordinator,
·
Course Design: From Learning Outcomes to
Assessment, Facilitated by Patrick Nellis
· Writing as a Tool for Learning, Facilitated by Helen Clarke
- Self Perspective
From my teaching experience, it has seemed that students in Calculus 1 have a very difficult time with proofs, such as the Mean Value Theorem (MVT). I’ve overheard successful math students saying things like “Well, I just hope he doesn’t put more than one MVT question on the test…. I know all the other stuff, but I’ll never be able to do a proof on my own.” To address this problem, I decided to test whether adding a writing assignment to my course would help students understand the MVT concept better. I hoped this translation from mathematical symbols to the English language would help to solidify the material as well as transfer it from short- term to long-term memory. Hence, the research question was whether an alternative assessment technique would be beneficial to student understanding and retention of material. So, to summarize, what I did to achieve/accomplish this Learning Outcome was to research different alternative assessment techniques, decide upon a writing assignment as an alternative assessment technique, create the writing assignment, implement it in my Calculus 1 class.
A. Methods and
Assessment Plan
- Student Learning Outcomes
a. The students will be able to articulate mathematical concepts
using words rather than symbols.
b. The students will be able to use the Mean
Value Theorem to solve problems and prove related results.
- Performance Indicators of Student Learning Outcomes
The student will be able to
a. Create accurate word descriptions for each step of the theorem
b. Verify mathematically and graphically that the proper conclusion was drawn
- Teaching
Strategies
Step 1: The students first learned the Mean Value Theorem
(MVT) using the text and traditional methods
Step 2: Students have a MVT question on their Chapter Test. Data was collected on each student’s performance on the MVT Test question.
Step 3: The writing assignment was given, which required
them to take the MVT question from the test and explain, only in English words,
the MVT proof and its solution.
LO 1, Artifact 1: Writing Assignment
Instruction Sheet
Step 4: The writing assignments were evaluated and returned, along with a copy of an exemplar of student writing (with permission from the student, of course!)
LO 1, Artifact 2: Example of Student Writing
Step 5: The Final Exam included a MVT question similar in nature to the MVT test question. Data was collected on each student’s performance on the MVT Final Exam question.
Step 6: Statistical Analysis of the student work was performed.
- Assessment
Strategies of Student Learning Outcomes
- The MVT writing assignment (CAT)
- MVT question on final exam.
- Action Research Methodology Design
Assessment Method for ARP The statistics for this project was a matched-pairs type analysis comparing each person’s individual score for the MVT final exam question with their own score on the MVT question from the chapter test. As a control, since I had only given the writing project one semester, I also compared the differences of those students’ MVT final exam question with their score on the MVT question from the chapter test. Lastly, I compared the differences between the control group and the experimental group. I only included students in the study who completed the course and therefore had both scores (Final Exam and Test Scores) for comparative purposes.
Significant Results
Click on “Project Results” for complete documentation.
B.
Interpretation
of Results
My hypothesis, “writing assignments in Calculus 1 will increase the students’ ability to perform and retain mathematical concepts” was assessed first by determining if the “difference” column was positive. In other words, students performed better on the Final Exam MVT question than on the Chapter Test MVT question. This is, obviously, not taking into consideration other factors, which may have brought about the learning (improvement shown). However, since the writing assignment is the only other learning/formative assessment activity in place, which addresses this topic in the time between these two assessments, it seems fair to infer that there is a causal link. Conclusion: There is statistically significant evidence that the students who had the writing assignment scored higher on the Final Exam MVT question than they did on the Chapter Test MVT question (p = .00003), while the students in the control group did not (p = .0593). While both groups had higher mean scores on the Final Exam MVT question than on the Chapter test MVT question, only the class with the writing assignment had statistically significantly higher scores.
My hypothesis, “Writing assignments in Calculus 1 will increase the students’ ability to perform and retain mathematical concepts” was also be assessed by determining if the difference column for the Writing Assignment Class is greater than the difference column for the Control Class. Since factors, such as extra time to review/relearn material are present in both classes between the two tests, one would expect the Final Exam score to be higher (hopefully.... if they studied for the Final!). Hence, comparing the differences in individual scores between the two groups will help to filter out the other intervening factors and determine if the writing assignment was actually beneficial in helping the students do better when they saw that type of question again on the Final Exam. Conclusion: There is statistically significant evidence that the students made a larger improvement in score on their Final Exam after completing the Writing Assignment. Thus, I have been able to show, through this Action Research Project, that writing assignments in Calculus 1 will increase the students’ ability to perform and retain mathematical concepts.
It is well understood by this author that this classroom research had small n's and was performed on only two classes, but this information, along with anecdotal information gathered by years of teaching, leads me to believe that incorporating writing assignments in my calculus class will be beneficial to my students, and thus I will continue to utilize it in my calculus classes.
Reflective Critique
A. Reflection on the Action Research Project
|
Understandably, the t-tests were
used here as an informal gauge of success, not as part of rigorous
statistical research. As such, it is understood that certain underlying
assumptions (such as randomization, sample size, etc.) were not realistic
goals in the preparation of this action research project. Even so, the results of the t-tests indicated that not
only do students perform better on the Final Exam after having completed the
writing assignment the students perform significantly better than the class
that had no writing assignment. My experience with this assignment was such that I would
not only assign it again next semester, I would also consider adding more
writing assignments to other proof portions of the Calculus class (such as
the Intermediate Value Theorem, Rolle’s Theorem, etc…) The students seemed to
like the assignment. Three of them mentioned it on the student evaluations
form I give out at the end of term under “What assignment/activity I liked
most,” and no one mentioned it under “What assignment/activity I liked least.” |
B. Reflection
on the Essential Competencies
Assessment Reflection
I studied various forms of alternative assessment before deciding on writing assignments as a formative assessment technique. Perusing Angelo and Cross's Classroom Assessment Techniques (1993), I was trying to find an alternative assessment technique that would helpful in learning how to write proofs. Although I found many interesting assessment techniques I can use, such as the Muddiest Point and Documented Problem Solving, I couldn't find something I thought was directly translatable to writing proofs. I knew I wanted something that would “provide feedback to students that fosters learning and provides information to the professor about students’ achievement of learning goals for the course” (Brookhart, 1998), but it needed to be able to assist in proof-writing skills. After a tour of other literature, I decided upon writing across the curriculum because there was evidence that “restating a problem in one’s own words is a recognized way for students to demonstrate comprehension and not merely memorization” (Nitko, 1996). This made sense to me and seemed to be just what I was looking for. It linked writing with math, which are the two concepts needed in proof-writing! I decided to have the writing assignment after the first test simply to get a benchmark of how they were doing without it. I was able to determine that the assignment I gave did improve student learning, as evidenced by higher final exam scores on that particular type of problem. This project is a clear example how I was able to “evaluate effectiveness of assessment strategies and grading practices” (Assessment Indicator). Now that I have the evidence indicating that the writing assignment was an effective tool, I will include it in the future. However, I think I will truly use it as a formative assessment before the students even take their chapter test on the MVT. Through my research, I was very enlightened to see how many alternative assessment techniques I could utilize in the teaching of mathematics. In the future I plan to make use of more formative assessment techniques to improve student learning and my teaching.
Scholarship of Teaching and Learning Reflection
Action Research can be defined as “ongoing and cumulative intellectual inquiry by classroom teachers into the nature of teaching and learning in their own classrooms” (Cross and Steadman, 1996). I thought the process of incorporating all indicators of the Scholarship of Teaching and Learning by methodically going through an action research project helped me to concentrate on what I wanted to learn (does writing help students perform and retain mathematical concepts), make a plan to collect certain data, then analyze the data, and then form conclusions that I could learn from. These steps, laid out for me in a methodical fashioned allowed me to dig deep and find something that I thought I could improve upon and test my theory. Being so methodical in this classroom research gave me confidence that the outcomes would be valid (at least for these classes). In general, I have always "improved" my teaching based on my intuition as to what was working and what was not. Action research allowed me to have an answer based on more than "gut", which is reassuring for a scientist!. By engaging in this action research project I was able to “produce professional work that meets the Valencia Standards of Scholarship, build upon the work of others (consult literature, peers, self, students), demonstrate relationship of SoTL to improved teaching and learning processes and demonstrate current teaching and learning theory & practice” (SoTL Indicators).
Although I spent a lot of time in the development of the
action research plan, the implementation, and the analysis, the process was not
as huge an undertaking as I originally thought. Yet, I clearly learned
something from what I did, and that is very valuable. I now have evidence that
indicates that using writing in calculus is beneficial to the students. That’s
huge, especially since most calculus professors might not think to include
writing as a learning tool and formative assessment method. Additionally, I
also now have the skills to perform more action research projects in the
future!
Professional Commitment Reflection
I will be presenting the results of this project, as well as
sharing this assignment with all interested colleagues, at our next department
meeting. I’ve even thought it would be nice if I could share my results in a
college-wide setting, perhaps through a Leadership Valencia workshop.
Additionally, I would love to present the action research project results at a
National Conference such as NCTM or MAA or NISOD, if I were to get selected.
The process of working through an entire action research project is, to me, part
of professional commitment. Through the Teaching Learning Academy I was
encouraged to “access faculty development programs and resources” (Prof. Comm.
Indicator) in order to learn more about action research. Through doing an
action research project, I have shown that I am committed to finding out what
works and what doesn’t work for my students, not just trying to do the same old
thing as last semester. As an identified Valencia Essential Competency,
Professional Commitment states “
I will present this project to my ILP review panel and Osceola mathematics department. i will post this project on the Valenica Action Research Project Builder.