Solving Word Problems in K-12 Mathematics
Final Assignment Part II
Paper Submission
CET 720
Dakota State University
Dr. Dan O. Coldeway
Al Bierschbach
May 2, 2001
Introduction
This paper outlines the efforts of Group A in our web board discussion of solving word problems in K-12 mathematics. I will outline our work in planning the web board discussion and implementing the discussion.
Planning
Group A began the planning process with a series of e-mail messages to one another. The first thing that our group needed to decide was why we were paired together. As Jan and I are both high school math teachers, we understood why we were paired together. Summer was put into group A as her mini-project dealt with 4th grade science, which is a field closely related to math. From that point in the process, we could decide the topic for our web board discussion.
Through the means of NetMeeting, we were able to chat about our topic. We decided to base our discussion focusing on three levels of students: (1) elementary, (2) middle school and (3) high school. Due to the fact that Jan teaches older high school students and I teach younger high school students, I volunteered to present at the middle school level. Jan suggested remediation, and we all agreed that remediation is important topic in the area of mathematics. We needed a central theme to tie our discussion together, so I suggested word problems. The area of word problems is one that we decided would be a good central theme, as students generally need remediation in this area throughout most of their education. We also needed to put this into an assessment method, as remediation generally happens after an assessment takes place. The use of rubrics to assess word problems was method that all of us in Group A were comfortable with.
Presently I do not teach at the middle school level, so I needed to find an area where middle school students work with word problems and may need remediation. I decided that seventh grade geometry was a good area to fit my needs. I was comfortable with this because I presently teach an applied math unit that involves many of the same concepts as seventh grade geometry.
I started compiling my work on my web site, as I decided that it would be easier for my classmates to follow the strategies that I was using for this unit. Over the years of teaching word problems, I have discovered that a step-by-step process is beneficial for students working with word problems. I also learned that key words are very important for knowing which operation should be used while working with word problems. The objectives for my unit are derived from the Geometry and Measurement standards in the seventh grade level of the South Dakota Math Content Standards and the Problem Solving and Communication Standards for the sixth to eighth grade levels of the National Council of Teachers of Mathematics Standards. I modified a web page that I had created for Applied Math to involve practice problems from the Internet for this unit. I also created an assessment of my objectives.
At this point I researched various sites on the Internet with rubrics, and found several that I liked. In our second NetMeeting for planning Group A decided that instead of having one rubric to fit all situations, we would create three separate rubrics to fit our specific levels. This way we could tie it closer to our assignments, and it would be less subjective. No specific rubric was perfect for me, so I took what I liked from a few of them and created my own. We also decided the order of presentation in the second NetMeeting. Jan volunteered to start off the discussion because going in a natural order, highest level to lowest level or lowest level to highest level, made the most sense for our presentation.
In our third NetMeeting, Group A discussed which web sites we wanted our classmates to look over before the discussion, and good ways to start and finish the discussions. We had a difficult time deciding which web sites to present to our classmates. We wanted to limit the readings to three web sites, but there were more than three deserving web sites. The three that we finally decided upon were (1) Assessment and Rubrics, (2) Best Practice in Math Assessment, and (3) Mathematical Problem Solving. We decided that we would each unveil our unit that we designed on our assigned day, thus it would give each day a new focus for our classmates to discuss. We also set up a good introduction and decided that we would all field questions on the last day of the discussion board and give our own summary of the discussion.
Web Board Discussions
Jan began the first day of discussion focusing on solving word problems in high school mathematics. She fielded many comments about people’s apprehensions when it came to the topic of word problems and a few about her rubric. I opened second day with a short explanation of my unit and where it was located. I was happy to see that Cleo agreed with me on the importance of the student showing the process that they used to find the answer, and that points should be removed when work is not shown. Michelle and Gay liked my remediation plan, which involved having the student go to a specific Internet site to work with sample problems. Their comments showed me that I covered the topic of remediation, which was one of the main topics in our web board discussion.
I did get a few questions on the setup my rubric. People were looking at the rubric in a way that I did not intend, but by looking at it again, I understood why they were confused with the design of the rubric. I would give a student from zero to four points for each problem, whichever column on the rubric that their work best fit into. My CET 720 classmates looked at giving a student the number of points at the top of the column for each cell that the student accomplished. With five cells in the last column, this meant that a student could get up to twenty points for a particular problem. I only intended a maximum of four points for each problem. After I explained my intentions for the way that I would score a problem using the rubric, my classmates understood. This exemplifies to me that even though a teacher understands the grading methods for an assessment and thinks it is clear to the students, the students may not understand. Mary and Stacy also pointed out that the diagram section on my rubric went from "inappropriate and unclear" to "clear", with no middle ground. I decided that the words "partially correct" could go in for "clear" in the column with the "3" heading.
Summer led the discussion on the third day dealing with solving word problems at the fourth grade level. She dealt with comments on the performance assessment area on her rubric and with the language that is used in word problems. Summer started the fourth day with an invitation for our classmates to question or comment on the items presented. There were only a few comments about scoring math problems using rubrics and problem solving strategies.
Conclusion
In my judgment we accomplished our goals in this project. We created a total assessment system and designed units to explain how we would use the system within our curriculum area. We proposed questions, answered questions and discussed our system with our classmates. We learned that our classmates did not always initially understand what we created, but with a little discussion they understood our ideas. I learned more about assessment and word problems just by creating this unit and discussing it with others.
References
Assessment and rubrics. (No date). [Online]. Available http://205.119.23.250/curric/rubrics.html, May 2, 2001.
Best practice in math assessment. (No date). [Online]. Available http://www.ncrel.org/mands/docs/6-1.htm, May 2, 2001.
Bierschbach, A. (No date.) Solving story problems. [Online]. Available
http://mhs.madison.k12.sd.us/bierscha/DSU%20Website/CET720/Solving%20Story%20Problems.htm,
May 2, 2001.
Communication standard for grades six to eight. (No date). [Online]. Available
http://standards.nctm.org/document/chapter6/comm.htm,
May 2, 2001.
Fernandez , M. L., Hadaway, N., Wilson, J. W. (No date.) Mathematical problem solving.
[Online]. Available
http://jwilson.coe.uga.edu/emt725/PSsyn/PSsyn.html,
May 2, 2001.
Problem solving standard for grades six to eight. (No date). [Online]. Available
http://standards.nctm.org/document/chapter6/prob.htm,
May 2, 2001.
Seventh grade geometry standards. (No date). [Online]. Available
http://www.state.sd.us/deca/ContentStandards/math/68stand.htm#7geom,
May 2, 2001.
Seventh grade measurement standards. (No date). [Online]. Available
http://www.state.sd.us/deca/ContentStandards/math/68stand.htm#7measure,
May 2, 2001.