# MAT Blog

There are many instructional tips and shortcuts to help new middle school math teachers; however, finding practical solutions for fractions can seem tiresome. Keep in mind, there are no quick fixes. Teaching and learning fractions takes time, focus and rigor. With practice, you'll soon see what works best for you and your students. Here are some tips to get you started:

1. Take time to build conceptual knowledge. This tip is number one for a reason: it is critical! A big part of making sense with numbers includes using them in context. Without knowing the meaning of a number, it can become difficult for students to choose a proper strategy.

2. Relate to prior knowledge and draw from experiences. Students may lack conceptual knowledge due to inexperience— therefore you must give examples of everyday uses of the concept, such as figuring recipes in cooking, or determining retail costs at half-off sales.

3. Provide an activity that can give students everyday uses of fraction concepts. Make a concept more concrete by engaging children with things they’re interested in. Children of all ages enjoy food, sports and the arts. Bring in a few pizzas or pies and have them work out some authentic…and delicious exercises.

4. Use a “less is more” approach for math with both in class work and homework. When more than 10 questions are assigned, it typically means the focus of homework has changed from conceptual understanding to drilling of procedures. When emphasis is placed on using and mastering strategies instead of simply showing a student’s work, both written and verbal explanations of math concepts tend to improve. Assign a few key problems to solve by selecting from the strategies taught in class. This encourages students to draw from prior knowledge that is likely linked to other mathematics lessons. (Bay-Williams, 2010)

5. Always have an anchor to the lesson. It is helpful to have a versatile anchor to a lesson such as a number line that makes sense in more than one context. (Schaar, 2012)

6. Integrate writing often. A written response in mathematics helps strengthen student learning, which can build deeper understanding. It gives students an opportunity to organize their thoughts related to the math topic, which helps clarify their thinking. Student writing can also provide you with valuable insight into their mastery of math concepts. Teachers can use writing assignments as either an informal or formal assessment tool.

7. Use a variety of manipulatives. Multiple representations of problems help all learners better grasp mathematical concepts. No student is too old for using hands-on manipulatives to solve problems. Be creative! Students can use tiles, marbles, beans, rice, dice or any of the typical "learning store" items available to teachers.

8. Provide picture models. This is just another way to represent a problem for visual learners. Again, students are never too old to use drawings, photos, and graphs to express mathematics.

9. Use short cuts only when they can be explained. Be careful here, since using these last two tips improperly can generate poor results and misunderstandings. Short cuts or tricks should only be allowed when a student can explain the meaning behind their result. For example, researchers found that when students used the procedure for dividing fractions by fractions, many were unable to accurately explain their results (Perlwitz, 2005).

10. Integrate technology to open new ways of learning. Use computers and calculators only when it will increase efficiency and concepts are already understood. Although using these devices will help students become more accurate and speedy with answers, using them too often can lead to a procedure and answer-oriented classroom.

In the end, a successful classroom is one that takes time to focus on concepts in a way that allows students to build their own knowledge. In order to build new knowledge, students need to experience math and be allowed to use their own strategies. They also need everyday context to problems, or an anchor, so that real meaning can be developed.

You’ll gain practical advice and instructional best practices like these from the Marygrove Master in Art of Teaching Middle Level Mathematics program. Enroll now, and enhance your career! Fall classes begin September 4.

#### Heather Patacca is a fourth year teacher and will be graduating the MAT program in the summer of 2013. She has previously taught ninth grade algebra and sixth and fourth grade pre-algebra. She and her husband live in Ohio with their beautiful three-year-old son.

##### Elementary and Middle School Mathematics (7th ed.).  Boston, MA: Allyn & Bacon.

Middle schoolers are often naturally social and many of them love to work in groups during class. The middle school mathematics classroom is a wonderful environment for promoting these social learning connections while mastering math concepts. There are a variety of cooperative learning strategies that benefit the middle school math student. Here are three excellent ones you can use now:

1. Jigsaw Lessons are not puzzling at all.
Often implemented in social studies or science, a jigsaw lesson can work equally well in the math classroom. Certain mathematical concepts, such as geometry, lend themselves nicely to the jigsaw format.

As in all jigsaw lessons, the teacher will divide the class into groups and within each group assign students numbers. The number of students in each group is dependent on the number of concepts in the jigsaw lesson.  For a lesson on triangles each student is assigned the task of creating a specific triangle based on defined attributes.

For example, one student in the group may be asked to create an acute scalene triangle while another student is tasked with creating an obtuse isosceles triangle. All students in the class with the same task form a temporary new group to complete it and plan ways to explain it to their original group. Once the triangles are created, the group will reconvene with their starting team. Each group member must then display the triangle, describe the assigned attributes, and clarify the process they used to complete the task. By sharing ideas and answering questions, students have the opportunity to reinforce their own understanding and learn from one another.

For your reference, we found an excellent, thorough description of the jigsaw instructional strategy from Instructional Strategies Online, by Saskatoon Public Schools in Canada.

2. Quiz Show helps students win at math literacy.
Using the quiz show format teachers can plan a cooperative learning activity that spans an entire unit and provides a fun review session before the final assessment.  It is great for learning math vocabulary and reviewing concepts.

The teacher begins by assigning groups at the outset of the unit.  This is best done using heterogeneous, or mixed, groups so that students will collaborate, learn, and become stakeholders in the group's success. Over the course of the unit's instruction, the groups will meet periodically to write quiz show questions. The teacher can front load these collaborative question-writing sessions by providing a framework for questions or requiring a specific format (multiple choice, multi-step problem solving, true/false, etc). These questions will be submitted to the teacher as possible questions for the final quiz show competition.

On the quiz show review day the students compete in their original teams and the teacher chooses the questions that will be asked.  (You should include some questions written by students and others that you have composed yourself).  The students will review the unit material, enjoy working in teams, and be thrilled when one of their own questions is used!

3. Student Peer Coaching is more than a game…it’s leadership training.
Teachers may choose to use peer coaching in the middle school mathematics class in an effort to give students the opportunity to observe how others approach problem solving.  Since students have different ways of solving the same problem, giving them the chance to learn from one another allows each to experience a different perspective.

Implementing peer coaching as part of a math lesson requires a simple structure and is highly effective at expanding students' understanding. The teacher assigns students a partner (or small group) and they work together to solve a problem as a cooperative group. The group must come to a consensus on the problem solving steps, computation, and the final answer.

Eventually, each student will be responsible for completing a similar problem independently. Adding a self-reflection journal question that asks students to identify a part of their problem solving process that was impacted by working with others will provide data about the effectiveness of the peer coaching.

No matter which strategy you try, we know each of these promises to engage and enlighten your socially-oriented middle school students…many of whom are afflicted with severe cases of spring fever…especially on those seemingly never-ending Fridays!

Download our Guide on the Highly Effective Instructional Strategy of Cooperative Learning for a brief refresher on how to conduct it with success!