# Collaborative Learning in High School Math Explorations

Jillian Adams, Math Teacher, Rush-Henrietta Senior High School jadams@rhnet.org

As a high school math teacher at Rush-Henrietta for eight years, I’ve always struggled with finding ways to make review days for tests more engaging and beneficial for my students. Just handing them a review packet and telling them to work on it doesn’t always go well – often students need motivation to complete it and I’ve tried many things in the past (candy, extra points, scrambled answers, puzzles, etc.). I was looking for a new way to involve all students in the review day process and to make it more meaningful for them overall. This is why I chose to be part of the MCC Fellows Program – I wanted to have the chance to collaborate with colleagues from different schools (RCSD & MCC) and see how their perspective would help me to change my own for the better. I appreciate how the program has helped us step away from our old teaching habits and try new things. It has helped refresh me as a teacher and given me new methods to try in my classroom to keep my students engaged and working.

I chose to do my action research with my Math Explorations classes due to the fact that they are weaker math students who are typically not as motivated, and I was looking for a way to make review days more beneficial both for their test grades, as well as their interest in the material overall. I am teaching four Math Explorations classes this year and I knew that whatever I pursued I would do with all four of my classes in order to keep my grading consistent and to aim for improvement across the board. Math Explorations is a lower level math class for juniors and seniors who often need another math credit for graduation and are not willing or able to move onto a higher math class (usually taken after Geometry, but sometimes a class to take after Algebra II/Trig or PreCalculus). Often these students are the ones who come into the class with a dislike for math and have not been successful in their past math classes for quite some time. My goal has been for them to feel more successful in this class and to enjoy learning about the history of math as well as the interesting facts that have led to the different facts and formulas we use today.

Due to the fact that these students come from a place of struggling with math, often they arrive in my class with attitude and behavior problems. I knew that I would not be starting my action research from day one because I needed to get to know the students first and try to break through their misconceptions and thoughts that they are unable to do well in a math class. Because of this, I taught the first unit of the course as I normally would, and then instituted the change during the second unit of the year: “The Basic Concepts of Algebra.” This is one of our longest units and also one of the most difficult units of the course for students to grasp. Last year (my first year teaching Math Explorations), I remember how difficult it was for me to keep the students’ attention during this unit and how they struggled through the concepts even though it was supposed to be review for them. I figured this would be a good unit to try something new so that I could push for a better outcome than the one I observed last year. Collaborative learning was the route I chose to go because of what the research says – studies have shown that collaborative learning helps students achieve higher levels of thought and retain information longer than students who work quietly as individuals. This shared learning gives students an opportunity to engage in discussion, take responsibility for their own learning, and thus become critical thinkers. **My inquiry question was as follows: “How will using collaborative lessons in my Math Explorations classes improve students’ participation in learning, and impact their understanding of the math concepts being taught?” **

Moving forward with this idea of collaborative learning, I wanted the ultimate goal to be for my students to do a presentation as part of a group of their peers on a specific math topic. The four parts of the presentation would be as follows: introduction/definitions, math problem writer/speaker, real life application, and website. One student would give an introduction of the topic and definitions of any math terms, another would write an example of that math problem on the board and explain it step by step to the class, another student would tell where this type of problem or math skill could be used in real life, and the last student would show a webpage they picked out that explains or relates to the topic. I randomly assigned the students to groups of 4 or 5 (if the group had 5 students, then two of them would do the write/explain the math problem portion), and gave them a problem to base their presentation around. I designed the parts of the presentation so that each student’s part did not depend on another student completing their part due to the frequent absences in the class – this way no one would have an excuse for not completing and presenting their part. Each student needed to prepare their portion of the presentation, show their work on a separate sheet, and then stand up on our review day and tell the class what they discovered. The process would be collaborative in nature because they would need to work with their peers in regards to planning around the same topic and check each others’ work before the presentation day.

From the beginning, I put together some items to help the students in their work. I created a “presentation design sheet” to help the students lay out who was doing what part and give them a place to jot down their thoughts. I also created a “rating sheet” where they would eventually rate themselves and their group members (on both planning & presentation), as well as write what they felt went well and what needed to be improved upon in the presentation process. When I first introduced the process to them, I gave them the presentation design sheet, as well as a list of which students were in the groups and what topics were assigned to them. I created these supports in an effort to ward off any confusion in the minds of the students about what they were about to take part in and to keep everything organized.

At this time I had the students sitting in pairs (as they had been from the first day of school), and I thought that it would work out okay that each day I taught one of the math topics (there were 5 of them altogether that students were doing presentations on), I would have the students gather together in their group and discuss who was doing which part. Unfortunately, the first time I tried this, the students were unwilling to move and unwilling to talk to one another about their plans. At this point I decided to move the desks into 5 groups of 5, and told the students they needed to sit with their group members each day. I thought this would work better because it would make it easier overall to speak to students about their presentation and for them to talk with each other after the topic was taught. This also turned out to be an easier way to address questions during warm up/homework time because if one student had a question, I could give my explanation to the entire group instead of walking around to each student individually. However, once again this did not play out how I expected – students could not manage to sit in their groups of 5 without off-task talking to one another throughout the lesson. It became extremely distracting and made classroom management much more difficult overall. Students were not learning the concepts effectively to begin with because they were too distracted by the peers in their group.

Seeing as this was having a negative impact on student learning (the number one goal), I put the students back into rows and had them sit in the general area of the classroom with their group members, but everyone was facing the front. This proved to be a more effective way to set up the classroom, and we finished up the unit this way. After I taught one of the topics to them, I would go over to the group with that topic assigned to them and ask who was doing which part so that I could make sure they were somewhat organized. Seeing as I ran into so many hiccups along the way so far, I was afraid that the final results of my action research would not go very well, so I decided to manage the design of the presentation better for my students. Originally I meant to have the students pick the example math problem out of the textbook or come up with one on their own, but even trying to get the students to open a textbook to find their topic went poorly, so I decided to give them a specific problem to work with (I actually chose the problems off the review packet for the unit). The presentation design sheets were not being used and many students had lost their copy already, so I gave each student a sheet (colored pink so they wouldn’t lose it as easily) where I outlined exactly what their part of the presentation was and what they needed to write/present for that part. From the beginning, I had planned a day in the computer lab for the students to be able to pull together any information off the internet to help them with their presentation. It turned out that this was the day where we were able to pull everything together. I went around to each student, answered questions, and made sure they were on track to understanding their part of the presentation. Several students were absent on the computer lab days, but I built some time into the beginning of the review/presentation day to be able to get them ready to go.

All in all I was nervous when it came down to the days we were going to have the presentations. With all the absences and the lack of compliance overall I was worried that my plan for the action research being beneficial to my students was not going to work. However, the days the students gave their presentations I was pleasantly surprised. My first class went up as individuals, but the following three classes went up with their group as a whole (this seemed to work out better because students were not as nervous). I called the students’ names out in order of the parts of the presentations and each student did their part. If a student had the “website” portion of the presentation, I pulled the website up on my laptop and scrolled through it as the student explained how it pertained to their type of math problem. At times you could tell they were a little nervous and sometimes I helped them along by asking questions or prompting the parts they should talk about, but I was very happy with the results as a whole. This showed me that the students are perhaps more resilient than you may expect and when it comes down to it – they will follow through and do what they need to. I gave each student a rating sheet so they knew they would be grading themselves and the peers in their group on a scale from 1 to 5 on both planning and presentation. I also told them I would be grading them on their planning and presentation as well, and that a fifth part would be that of a “respectful audience member” grade – being quiet during presentations, asking questions, making respectful comments, etc. The math problem portion of the presentations definitely kept their attention focused as well because it was the same math problem on the review packet they had been given, so each student could follow along and do the problem with the presenter. Knowing that they would be graded in several ways I think helped make them more serious about this, and the classroom environment during the presentations was pleasant.

My data results for my action research were quite interesting overall. The methods I used for data collection were as follows: the rating sheet results (rating themselves, their peers, as well as positives/negatives of the presentation process), test results for Unit 2 and Unit 1 from both this year and last year, overall presentation grades/comments, and my journals from throughout my action research (reflections from my journals are included throughout this narrative).

On their rating sheets, I was surprised to see that the students often rated themselves lower than their peers. Often I would see a grade of 3 or 4 out of 5 for their own grade, when they rated their peers with 5 out of 5. Also, there were two different observations I made about their ratings of their peers. Sometimes you could see their effort to be kind to their peers and not want to give them a poor score (even if the other student did not necessarily do a very good job), but other times they were being very honest and gave another student exactly what score they deserved. The comments on the sheets were very interesting as well. Positive comments included (repeated comments are noted):

- Everyone did what they were supposed to and they all seemed to understand it well (x4)
- It was something we could all handle
- Different point of views and input improved our final answer to the maximum potential (x2)
- Another student helped me with my planning
- I was the person other people asked for help and was the group leader
- I liked the information I found out – My group members were fun and helpful (x13)
- People worked together to make sure everything was correct – they were respectful and responsible
- I like working in a group because it puts less stress on doing a project on your own (x2)
- Working in a group split up the work so it was quicker (x3)
- I enjoyed working in the computer lab because it was different
- People were not distracted in the computer lab and worked hard
- We learned better how to work together (x2)

Negative comments included:

- Communication – we should have checked in with each other more (x11)
- We didn’t work together in the computer lab (x3)
- Every team member needs to show up every class in order for us to be successful (x14)
- We could have helped another student plan who was absent
- People could have had better facts and could have spoke out a little more (x3)
- More detailed examples (x4)
- There wasn’t a lot of focus (x2)
- Group members should focus on the people in their group not other students outside of it (x3)

From the comments above, I noticed that students seemed to really enjoy the project overall, but were sometimes frustrated with the lack of communication in their group as well as the absences that continually occurred throughout the unit.

As far as the data for the unit tests goes, the results are difficult to compare. The Unit 2 test average from this year was 82.1% while the Unit 1 test average from this year was 86%. The Unit 2 test average from last year was 80.4% while the Unit 1 test average from last year was 74.4%. There was a drop from Unit 1 to Unit 2 this year, but some improvement over the average on the Unit 2 test from last year. This is very difficult to draw a conclusion from because there really isn’t a good comparison between two different units or two different sets of students. It is also difficult to compare because we reorganized the order of the units this year and put our more difficult units up front because the students are more motivated at the beginning of the year and these units are also based on math topics the students have background in. Also, these averages do not include retest grades, which could change the results as well. Overall these numbers don’t necessarily show significant results but they are still interesting data to think about.

The students’ presentation grades showed that they really put the effort in overall. The average of my four classes was an 84.9%, which supports that it went decently well overall. There were 7 students (out of 94 total) who were absent and received a 0% for this on-demand formative assessment. If a student was legally absent I excused them from the assignment. On their grade sheet I wrote comments such as:

- Good job on your planning and presentation!
- Absent for planning/presentation day
- Good choice of websites
- Planning sheet needs more work on it for you to refer back to when you present your part
- Good questions asked during class presentations

The Fellows Program expected us to institute some sort of major change in our practice, and this is truly what occurred with me in my classroom this year. I was a little apprehensive about trying to organize presentations in a math class – a practice I think is very rarely used as a teaching strategy in math and the kids probably have little to no background with getting up in front of their peers and explaining math concepts. I had several bumps along the way but found that the struggle was worth it to see the outcome and I think the students enjoyed watching their peers re-teach the concepts from the unit.

When thinking back on my original action research question, I’ve found that there have been several ways student participation and understanding of math concepts have been influenced in my classroom by using these collaborative techniques. By requiring each of them to get up in front of the class, their participation was mandatory, and they put more thought and effort into planning out the information they want to share. I also saw improvement in students asking questions and making respectful comments about the details their peers found out about different math topics. This occurred both within the groups themselves during planning, as well as questions asked by other students on presentation day. Having the students approach a math concept from several different directions gave them a well-rounded view and helped them see the importance of the topics both in math class and in the real world. The actual test data is difficult to analyze overall, but I feel that this unit went much more smoothly this year than last year and I think the kids got more out of it by using the collaborative techniques. Working in groups allowed them to both ask and answer questions, bounce ideas off of each other, and feel confident standing in front of the class on presentation day, knowing that everyone in their group would be speaking about the same topic.

I did find that embarking on this kind of study is a ton of work. Especially as I moved on with the lessons and the day of the presentations drew closer, I felt I needed to organize every step of the way for the students so that this could be done efficiently and effectively. I felt quite a bit of opposition and disinterest from the students, which was difficult to get past but I’m glad I pushed them and was able to get this done. Being able to pull together information and stand up in front of others to explain that information is a life skill they will need in college or the workforce. It is also well known that teaching is the highest form of learning, so if they can stand up and effectively explain the math to others, then that shows me as their teacher that they have learned it to a higher level than just rote memorization or repeated application of the same math concept they watched me present to them in the notes.

Another lesson I learned is that action research is flexible. I made many changes throughout the course of this process that were reactions to the way things were going. I changed their seats twice, created worksheets to help them better structure their information and presentation, and even the kids themselves adjusted by getting up as a group instead of individuals on presentation day. I found that the students could really follow through when it came down to it (especially when they knew they needed to do a decent job for a grade!). From their comment responses to the surveys I think many of them enjoyed doing something different and found value in it.

A major breakthrough for me was when I knew I was going to be formally observed by my head principal and was trying to think of what I could do to make my lesson fresh and exciting for the kids. I came up with the idea to use collaborative learning to provide a way for the kids to show what they had learned. On my observation day, I taught a lesson on a new concept (three ways to solve systems of equations – graphing, elimination, and substitution). I then put the kids into groups based on where they were seated in the classroom, had them decide their roles in the group (facilitator, timekeeper, recorder(s), presenter), and gave them one of the three types of math problems to do together. They all used that class time to display their result on large graph paper, and then the following class they presented their result to the class as a whole. Once again when they presented, I asked them questions to help guide them through the presentation and make sure they mentioned all of the key aspects of solving their problem. I had them get up to present as a group, and even though one person was the specific “presenter”, the rest of the students were responsible for helping answer my questions about their work. It went extremely well and I felt that the second time around with presentations the students seemed much more comfortable.

All of this is evidence to me that using collaborative presentations in a math classroom is a great method for having students explain their work and understand it better themselves, as well as improve the understanding of their classmates. Especially when working with lower level math students there are large stumbling blocks to first getting started, but as I found when I did this work a second time it definitely got easier. The students seem to fight new ideas that they feel uncomfortable with and the most difficult part is getting past that first try, but each successive attempt should make them feel more at ease and willing to do the work. Even if students do not like group work, giving each one of them a role or a part in it will at least make them feel their contribution toward the group is invaluable and make them more willing to collaborate. Math Explorations is a great class to do this in because it’s more flexible – there isn’t a Regents exam at the end of the course or the major pressures of preparing for a standardized test, but rather more freedom to use class time so that the students can learn the topics in more creative and memorable ways.

I also see myself using this type of collaborative/presentation design in my AP Statistics class this year. This is my first year teaching the course, but I’ve found that there are numerous places where I could apply my action research concept to help the students better learn and explain the topics to their peers, especially on our review days. Through the Fellows Program I have purchased a document camera and a Pencast smartpen. Unfortunately for this paper, the items took over a month to be shipped, and it took another week for computer services at my school to install the software on my laptop, so I have not yet had the chance to learn the technology well enough and use it in the classroom, but I plan to do this very soon. I want to use the document camera both in Math Explorations and AP Statistics, so that students can bring up their solution to a problem and display it easily in front of the class and everyone can see their result clearly on the overhead screen. There are numerous uses for the document camera and I need to read through the paperwork that came with it to see more ways I can take advantage of all it has to offer (I could probably find a use for it in my classroom every day!). The Pencast smartpen I plan to use with my AP Statistics classes because they are more apt to make use of my website, where I plan on posting video solutions to different problems. Although I am new to the course, I can see a great need for extra explanations on different concepts and I know that the Pencast is an awesome way to show the kids in my handwriting and with my voice how to properly work through a problem. Also through the Fellows Program I have ordered some books on using projects and puzzles in math classes – I hope that these books will provide ideas on other ways I can integrate collaborative learning into my teaching practice. I also ordered more large graph paper so that I can repeat the work I did during my observation other times this year with the students and they can both display and present their work.

All in all, I am very pleased with my decision to join the Fellows Program and to see what a high impact it has had on my students as well as my teaching. I have been stretched outside of my comfort zone as well (just like the students!), and I know it was a really good thing for me to push myself and gain the experience because I know it will continue to pay off. I’m excited to use the work from my action research again this school year and in school years to come because I have seen the benefits. I will also be using my new technology and purchases from the Fellows Program in the very near future to help the students understand the math better and enjoy the process of learning it. I’m thankful for the opportunity to be a part of this group of teachers who have the courage to explore new pathways and better methods to do what we love to do – pass on knowledge and open up opportunities for our students’ futures.

**Resources: **

**I used the following items from the CCTE Glossary to plan my Action Research:

- Guided Inquiry
- Collaborative Learning
- Problem-Based Learning
- 21st Century Learning
- Differentiated Instruction

**I used the following book and websites:

Ronis, Diane L. Problem-Based Learning for Math & Science – Integrating Inquiry and the Internet. Thousand Oaks, CA, 2008

- This book helped me come up with the idea to have students present problems. Talks about the significance of placing students in groups. Also gave rubric designs for having students grade themselves as well as their classmates.

Virginia Tech Website – Journal of Technology Education: http://scholar.lib.vt.edu/ejournals/JTE/v7n1/gokhale.jte-v7n1.html

- Ask Dr. Math: http://mathforum.org/dr.math/
- Webmath: http://www.webmath.com/
- The Math Forum @ Drexel: http://mathforum.org/library/topics/
- AAA Math: http://www.aaamath.com/
- Coolmath: http://www.coolmath.com/
- Coolmath’s Online Math Dictionary: http://www.coolmath.com/reference/online-math-dictionary.html
- Chili Math: http://chilimath.com/
- Rick’s Math Web: http://www.ricksmath.com/
- Purple Math: http://www.purplemath.com/modules/index.htm
- XP Math: http://www.xpmath.com/careers/math_topics.php
- Math Motivation: http://www.mathmotivation.com/index.html

**Presentation Design Sheet:** AdamsPresentationDesignSheet

**Groups & Math Topics:** AdamsGroups&MathTopics

**Rating Sheet:** AdamsRatingSheet

**Grade Sheet:** AdamsOverallGradesheet