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.
Barlow, A. T., & Drake, J. M. (2008). Division by a fraction: Assessing understanding through problem writing. Mathematics Teaching in the Middle School, 13(6), 326-332.
Clarke, D. M., Roche, A., & Mitchell, A. (2008). 10 practical tips for making fractions come alive and make sense. Mathematics Teaching in the Middle School, 13(11), 372–379
Perlwitz, M. (2005). Dividing fractions: Reconciling self-generated solutions with algorithmic answers. Mathematics Teaching in the Middle School, 10(6), 278- 283.
Schaar, Richard J. (2012), Expert Commentary: A New Anchor for fractions: Richard J. Schaar [Video]. San Francisco, CA: Teachscape. Retrieved from www.teachscape.com
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2010). Teaching developmentally.
Elementary and Middle School Mathematics (7th ed.). Boston, MA: Allyn & Bacon.