MAT Blog

Often used as a buzz word in education to describe a wide variety of learning activities, “cooperative learning” is defined as "…a teaching arrangement that refers to small, heterogeneous groups of students working together to achieve a common goal." (Kagan, 1994). These groups are designed for students to work together to learn, discover, and have shared responsibility for the group's learning.

Although these structures are beneficial for any subject area, cooperative learning in math can be a powerful way to provide a variety of learning opportunities for students. There are several different structures that teachers can employ when planning cooperative learning in math.

1. Positive Interdependence. This means that the gains of individuals in a group are positively correlated with teammates.  Positive interdependence drives core cooperation; what benefits one team member benefits the whole group.  Altering a simple game of Math Bingo can promote positive interdependence. Instead of each student getting their own Bingo board, the teacher can assign pairs of students to share one board. The teacher then displays equations and asks students to complete the equation with their teammate.  Students work the problem together and then check their board, relying on each other to determine the correct answer. An individual cannot win the game without her partner, so the interdependence is crucial.

2. Individual Accountability. Each student in a cooperative learning group is responsible for an individual learning product as a share of the group work. In regards to cooperative learning in math, individual accountability requires each group member to possess the necessary knowledge and skills to perform or produce the work.  A complex problem solving scenario is a great way to promote cooperative learning in math and the necessity of individual accountability. The group can solve the multi-step problem together, assisting one another, and providing support; but each student is responsible for turning in their own solution and the teacher will select students at random to share their group's solution.  Even though they worked together, each student must be able to perform or produce the work.

3. Equal Participation. This essentially refers to the division of labor, as groups divide the work among all members and each student is responsible for his share of the work.  The activity should not be dominated by one student in the group and no one can opt out of participation. When teaching a unit on graphing, a teacher could use equal participation to show how a single set of data is interpreted differently based on the type of graph used.  Each group would receive a single set of numerical data and be required to analyze and interpret the data together. Then, individually, each group member would use the data to construct a different type of graph (bar, line, pie, area, etc).  This is a great activity to help students learn which graph works best for which kind of data. Since each team member is responsible for the same task, (construction of one graph), the participation is equal.

4. Simultaneous Interaction. This is the easiest structure to execute for cooperative learning in math, as it simply allows students to have multiple cooperative interactions with other students in a single session.  Instead of a teacher asking one student (sequential interaction) to show how to solve a problem, he can ask students to share with another. Students can "turn and talk" to a peer sitting nearby and explain how they solved a certain problem. If the students have solved the problem differently, or arrived at two different answers, they would then work together to discover the correct solution or learn more about each others' process. This can be repeated numerous times with students partnering with a different student each time. Try doing a math relay—teams can take turns trying to solve a division problem, for example.

If you haven’t tried cooperative learning for math lessons, you are missing an excellent opportunity to allow math learning to be a truly fluid process for students. For some, it is not critical, but for those students who learn best by doing, and talking—such as kinesthetic and auditory learners— cooperative learning math groups can produce absolutely amazing results in your classroom.

Saxon Math is a widely used math curriculum that provides a unique, "spiraling" instructional approach that revisits previously taught concepts and integrates it with new learning. It distributes direct instruction, daily computational practice, and ongoing, frequent assessment throughout the course of a school year instead of focusing connected skills into targeted units. This unique approach allows students to gain new knowledge while constantly reviewing previously learned skills. Teachers across the country have discovered the many virtues of Saxon Math, including:
• Hands on Activities. Particularly in the primary grades, direct instruction often occurs through hands-on activities and the use of manipulatives.  Students are encouraged to use manipulatives as a tool to discover and understand mathematical concepts.  Each hands-on activity connects not only to the targeted skill at practice, but will link to future lessons on related topics. There is a structured scaffolding of the lessons; students will progress from concrete application, to pictorial representation, to abstract application.

• Daily Mixed Practice.
Each day there is a computational component of the Saxon Math curriculum. The difficulty of the computational skills, as well as number of problems, gradually increases as students' computation abilities also increase.

• Real World Problem Solving and Applications.
Mathematical skills are not taught in isolation or as an unrelated algorithm.  Saxon Math identifies real world problem-solving opportunities linked to the math skills. When students are challenged to apply their mathematical learning to real world problems, they understand the importance of math outside the classroom.

• Frequent Assessment.  At the end of every five lessons, an assessment occurs over previous learning. Due to the frequency of the assessments, teachers are able to quickly identify when a breakdown in learning has occurred. They are able to address any misunderstanding almost immediately instead of waiting for a larger, more comprehensive assessment.  And because the assessments are cumulative, students are expected to retain previously taught skills and demonstrate continued mastery.

• Adaptable To a Wide Range of Classrooms. Saxon Math can be used in a general education, inclusion, pull out, or resource classroom. Teachers are able to use the printed curriculum as a starting point and then can differentiate for a variety of learning needs.

• Online Activities and Connections. There is a wealth of Saxon Math activities available electronically for additional practice, review, or extension.  Students are able to use the electronic connections to practice using manipulatives, play a learning game, or receive additional learning support. Additionally, there are online eBook versions of each student text.

• Teacher Technology Resources. Saxon Math has also created a wealth of technology resources for teachers including instructional resources, an Assessment Generator, eGradebook, and Instructional Presentations. These resources support teachers in their instructional planning, differentiation, and assessment.

Saxon materials are often found where home schooling materials are sold.

Weigh in on your experiences with Saxon Math in the comments section below. We’ve found that K-3 teachers love it because the program is well-scripted, including a morning meeting portion. What do you think?

Successful math teachers have certain qualities that make them the experts they are. These are the teachers who are requested by parents, year after year, because of their knowledge, style and handle on the subject; they know what really works for students.

Many textbooks and scholars will say that math teachers should have an extensive knowledge and love of mathematics. This is very helpful, but if math is not the sole reason you get up each morning, don’t worry. A healthy command of mathematics literacy is just fine.

Good primary math teachers, in particular, seem to possess an endless amount of patience, because there are many different ways that students actually learn mathematics. And they learn at many different speeds. Math teachers are not frustrated by do-overs. Or complete start overs.

Understanding Piaget’s theory on how youngsters create logic and number concepts is time well spent for math teachers. It underscores the necessity of knowing your students, so you can serve them well.

A recent blog from the National Council of Teachers of Mathematics speaks to the need for teacher preparation programs to change, in order to avoid teaching children rules before they are developmentally ready to understand them.

Flexibility is key, too, since addressing multiple intelligences takes time, and lots of creative energy. Try skip counting to that beloved wedding reception staple “Macarena” for kinesthetic learners. “2-4-6-8…Heyyyy, Multiplication!”

Math teachers need the ability to do quick error analysis, and must be able to concisely articulate what a student is doing wrong, so they can fix it. This is the trickiest part of being a good math teacher. It helps if you have natural ability—but in time, this can be developed. Ask any veteran math teacher, and he’ll tell you that after ten years, you get pretty good at continuous formative assessments. And the Macarena, too.

Plus, don’t even try to send home math homework that isn’t specifically targeted to what students are learning in class. With math, you must be explicit. Precision is the name of the game, so your homework direction must be, too.

Remember that more isn’t better when assigning math problems. Five to 10 focused problems works well. And please return that checked homework the next day, whenever possible, with examples of how your student can improve. You’ll be glad you took the time. It will show in your students’ increasing independence, knowledge and confidence.

EdWeek’s blog  announced a new initiative last October called the Mathematics Teacher Education Partnership to prepare secondary math teachers for the rigors of new common math standards. That’s excellent news for districts, teachers and  students— not to mention for parents who simply cannot help their children with middle school math homework, no matter how hard they try.

Lastly, it’s important to note that good math teachers never live in the past. They live in the here and now. The past is full of all kinds of outmoded algorithims and dated math terms—the very terms that teachers themselves must unlearn so they can re-learn, and keep re-learning. So as you can imagine, a good math teacher appreciates change, and even welcomes it.  Throw in a little daily enthusiasm, and you have exactly what it takes to be a great math teacher.