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Research & Rationale

Kagan Structures and High School Algebra

Jodi Van Wetering, Math Teacher
Downers Grove North High School

To cite this article: Van Wetering, J. Kagan Structures and High School Algebra. San Clemente, CA: Kagan Publishing. Kagan Online Magazine, Spring 2009. www.KaganOnline.com

Study Abstract
This article summarizes the positive impact Kagan Structures had on student achievement and student attitudes in my high school Algebra classes. The study is based on the test scores and student surveys of 114 students in five classes: three Algebra 300 classes and two Advanced Algebra 300 classes. The study includes before Kagan and after Kagan achievement comparisons as measured by average class scores, student survey results and comments, as well as my own personal reflections on teaching and learning using Kagan Structures.

Academic Achievement – Class Averages
The data presented compares average test and final scores from the 2005-2006 school year and the 2006-2007 school year. In 2006-2007, I began using Kagan Cooperative Learning strategies. Since the courses I taught, course content, and tests were the same for both school years, the results serve as a good comparison of instructional strategy: teaching Algebra classes using traditional instruction vs. using Kagan Structures.

The following charts illustrate the gains Kagan Structures had on student achievement on Algebra 300 classes as well as Advanced Algebra classes. Notably, there was a consistent improvement in the student achievement across the board. In no case did traditional instruction outperform Kagan Structures.

Algebra 300

Algebra 300 – 3 Classes
Test Name 2005-2006
Class Average
Class Average
Chapter 5 Test 80.97% 83.65%
Chapter 8 Test 76.31% 77.05%
Chapter 10 Test 78.32% 84.03%
Semester 1 Final 78.8% 83%

Advanced Algebra

Advanced Algebra – 2 Classes
Test name 2005-2006
Class Average
Class Average
Chapter 5 Test 73% 77%
Chapter 10 Test 78% 82%
Chapter 11 Test 78.55% 83.97%
Semester 1 Final 71.8% 77%

Survey of Student Attitudes
I administered the same survey to all five classes in the 2006-2007 school year. Students responded anonymously to statements about their attitudes towards cooperative learning and Kagan Structures on a scale of 1 to 4 (Strongly Agree to Strongly Disagree). Please see the Appendix for the actual survey. Below is an agree vs. disagree breakdown comparison on key survey statements, a summary of all survey results, and student comments on the survey.

Key Survey Statements

I enjoy working in groups

I feel I have a better understanding of mathematics from working in a group.

If I could choose my math class for next year, I would prefer one that used cooperative learning strategies on a regular basis.

Summary of Cooperative Learning Survey

Over 90% of students stated:

  • They felt comfortable working in groups
  • They felt comfortable asking group members questions

Over 80% of students stated:

  • They enjoyed working in groups
  • They felt more inclined to ask a group member a question before asking the teacher
  • They find their group members helpful
  • They would choose a math class that used cooperative learning strategies on a regular basis

Over 70% of students stated:

  • They have a better understanding of mathematics from working in a group

Over 60% of students stated:

  • That being in a group has helped them become more successful in math
  • They enjoyed the Simultaneous RoundTable cooperative learning strategy

Comments Made by Students on the Survey

  • "I think working in groups is helpful and fun! It shows me that other people may be having the same problem or something I can help them with or they can help me with."
  •  "I think it is easier working in teams with people you know because you don't feel weird asking questions."
  • "I really like the groups in this class. Don't change anything."
  • I enjoy math class for the first time. I learn and have fun.
  • "Cooperative learning does help me in mathematics. It allows me to practice while having fun."
  • "I enjoy working in groups, the other people help if I have questions and I feel comfortable in the groups."
  • "This teaching method is very good."
  • "I enjoy cooperative learning because sometimes it is easier to ask the group questions to find answers than it is asking the teacher."
  • "I like working in groups a lot because I can discuss with them. It also makes the class a lot less boring because you get to talk with them."
  • "I really like the Inside-Outside Circle activity. I think it should be done every other day!"
  • "You are by far one of my favorite teachers because you stay organized. I personally love working alone and privately, it's just how I was raised. I would prefer rows, but I enjoy the games we play. Keep doing what you are doing."
  • "The only reason I am not too fond of group activities is because I'm not really a people person, but that's been changing this year."
  •  "Working in groups is awesome! It is a lot better than normal learning."
  • "I like sitting next to smart people. You should group kids who are accelerated with kids who are struggling."
  •  "I got to know my classmates more."
  • "I thought that the way we have learned is really good, I mean I understand better."
  • "I think cooperative learning makes whatever we are learning more understandable."
  •  "I think that working in groups helps the class to become more engaged in what we are learning, by being able to ask questions and work together."
  • I enjoy working in a group like this because that way I can socialize and discuss what I am struggling with. I like comparing answers during review. I'd much rather learn this way than in rows with a lecture.
  • "I think that learning while we are in our groups can be better than being in rows. I like your style of teaching because the way you give us notes to take. You explain things perfectly. I think that the activities we do are very helpful too. I look forward to working like this in the future. Thank you for being such a good teacher."
  • "Overall the math class is good. I sometimes have fun in here and you do a great job of teaching. There is no need for changes."
  • "Being in a group isn't necessarily directly linked to succeeding in math for me, but it does help. It's a friendlier environment. Usually, it's easier to ask a friend for help rather than the teacher."

 Reflections on Learning and Using Kagan Structures

Students engage in a fun teambuilding activity to
set the stage for team work.

I was first introduced to Kagan Cooperative Learning by my current principal, Maria Ward. At her previous school, teachers had been trained in Kagan Cooperative Learning and found the structures improved student learning and student engagement in the classroom. After being intrigued by this type of cooperative learning, I asked to attend a training session. I then attended a one-day session presented by Jennifer Evans and I was amazed, and without a doubt I was hooked. I had never before attended a conference that was so engaging and I could immediately see how this could impact my students' achievement and understanding of math. I couldn't wait to learn more and begin introducing structures into my classroom. I requested to attend the Kagan Summer Academy in Florida. I attended the five-day cooperative learning training that summer and once again was blown away.

After using Kagan Cooperative Learning in my classroom for an entire year, I was then given the opportunity to attend the School Trainer Summer Academy. I was extremely excited to become a school trainer and share how amazing Kagan is with other teachers in my building. I have now trained ten other math teachers in my building. Kagan is alive and well in the math department at Downers Grove North High School.

As a teacher, Kagan Structures are a part of my classroom on a daily basis. My students usually do some type of warm up activity whether it is a Sage-N-Scribe, Simultaneous RoundTable, or a teambuilding activity. My students' understanding of mathematical concepts such as translating quadratic equations, simplifying exponential expressions, and retaining mathematical vocabulary has greatly increased with the use of Quiz-Quiz-Trade and Inside-Outside Circle. Students explain step-by-step procedures to each other using RallyCoach and practice problems using Find Someone Who. One of my favorite ways to review concepts is by using Showdown. The number of ways to incorporate all of the structures into the classroom is endless. I am constantly using a variety of structures to teach mathematical concepts and to allow my students the opportunity to practice. Kagan Structures allow immediate feedback to the student and to the teacher. 

Since I have incorporated the Kagan philosophy into my classroom, student achievement has improved in Algebra and Advanced Algebra with Trigonometry. I attribute the achievement gains to cooperative learning strategies that continue to keep students' actively engaged. Kagan Structures promote positive interdependence, individual accountability, equal participation, and simultaneous interaction. Through the use of structures, teambuilding and classbuilding, students are motivated and encouraged to participate. Consequently, they have improved their problem-solving skills, and communication skills. They have a greater mathematical understanding and new tools for checking for understanding and content mastery. As a teacher, I have increased my ability to create an environment where relationship skills and social skills are taught, encouraged, and fostered.

Students feel that my classroom is a warm, friendly environment. They have gotten to know their classmates and feel comfortable asking questions. They have stated that math is fun again. And as a result of all of this, their mathematical scores have increased. Kagan has changed my life as a teacher and I am a better educator because of Kagan.


Cooperative Learning Survey
This survey is anonymous. Please do not put your name on it. Please circle 1-4 for each of the following questions.
1 = Strongly Disagree
2 = Disagree
3 = Agree
4 = Strongly Agree
  1. I enjoy working in groups.
  2. I feel comfortable working in groups
  3. I feel comfortable asking my group members questions
  4. I feel more inclined to ask my group members questions before asking the teacher
  5. I find my group members to be helpful
  6. I feel I have a better understanding of mathematics from working in a group
  7. Being in a group has helped me become more successful in math
  8. I have enjoyed the Simultaneous Round Table cooperative learning strategy
  9. I have enjoyed the Find a Friend cooperative learning strategy