Math education encourages thinking outside box
By Katie Wetherbee
During a seminar in the Chagrin Falls Schools, parents, along with Assistant Superintendent Dr. Sharon Klimm, discussed the trends in mathematics instruction. The conversation soon shifted from educational theory to children. Parents began talking about their children’s challenges and successes with math. One mother asked, “What can we do to encourage our kids to love math? We get so much information on helping with reading, but when it comes to math, I need some ideas!”
Much time and attention in schools is given to reading instruction—and rightly so! However, math holds an equally important place in children’s school experiences. Their competency in this subject has great bearing on their success in school and in the work force. Yet much of the math children are doing is alarmingly unfamiliar to today’s parents.
Components of effective math instruction
While many parents recall math lessons that were teacher-directed and followed by reams of purple dittoes, today’s math classes are more experiential. A class at Orange’s Brady Middle School recently spent time taking surveys and used the information to create pie graphs. Third graders at Gurney Elementary in Chagrin traced objects and calculated area using blocks. These kinds of lessons follow the recommendations of the National Council of Teachers Mathematics to focus on problem solving rather than memorizing formulas.
However, math classes should still strike a balance between higher-level thinking and mastery of “the basics.” The National Research Council’s Mathematics Learning Study Committee suggests several components be included to create an effective, comprehensive math curriculum:*
- Computing: Carrying out mathematical procedures, such as adding, subtracting, multiplying and dividing numbers flexibly, accurately, efficiently and appropriately
- Understanding: Comprehending mathematical concepts, operations, and relations—knowing what mathematical symbols, diagrams, and procedures mean.
- Applying: Being able to formulate problems mathematically and to devise strategies for solving them using concepts and procedures appropriately.
- Reasoning: Using logic to explain and justify a solution to a problem or to extend from something known to something not yet known
- Engaging: Seeing mathematics as sensible, useful, and doable.
*From Helping Children Learn Mathematics by the National Research Council, 2002
Implications for the classroom
These recommendations lead to changes in today’s mathematics lessons. “Our increasingly technical and information-driven world requires that all educators (including parents, the ‘first teachers’) tailor mathematics education in several ways,” said Klimm. She explained that an emphasis on problem solving and student thinking makes math classes different today. “Students must be able to solve problems in non-routine ways in unpredictable contexts,” she said. Klimm indicated the emphasis on student thinking is not only instructional, but an assessment tool as well. “Teaching strategies that encourage students to explain how they got an answer provide information about the level at which students are understanding mathematics. Teachers use this to form questions and guide instruction.”
As mathematics classes shift toward higher-level thinking, classrooms will look—and sound different. “Students are likely to use more hands on materials, use writing in mathematics, and work in small groups—all found by research to enhance learning,” Klimm stated. However, “Accuracy and efficiency are still very important.”
Adjusting instruction for all learners
As with any subject, a “one size fits all” approach is impractical. Research and common sense dictate that even the most rich, hands-on math activity may leave some children confused or frustrated. This can be particularly true of children with learning disabilities. With a greater focus on problem solving, math involves more language than ever before. For children who struggle with reading or processing language, math becomes laborious and confusing. Concepts such as “greater than/less than” or “how much more” elude these children as they attempt to reconcile numbers, symbols and language. “Students must understand the language and symbols of mathematics because contextual clues are lacking in mathematics,” says Diane Pedrotty Rivera in an article for LD Online. To remedy this, teachers often instruct children in math language, and use cue cards or highlighters to help the students process information accurately. Cooperative learning activities can also benefit students with special needs: “Vocabulary and symbolic understanding can be facilitated with peer interactions and modeling,” Rivera writes. Students with disabilities may also benefit from “overlearning” concepts and memorizing algorithms to increase fluency and success.
How parents can help
With all of the changes to math instruction, parents want to know how they can help their children find success in math. Below are a variety of activities to enhance children’s thinking:
- Cook with your child Cooking activities use a variety of math skills, such as addition, fractions and volume.
….and communicate with your child! Third grade teacher Brad Jones encourages parents to “not only ask children for the answer; ask them how they got there.” National Board Certified Teacher Sheri Halagan agrees: “Encourage multiple ways to solve problems and ask them what they’re thinking. Remember,” Halagan continued, “there is always more than one way to solve a problem.”
- Give an allowance…and help them manage their money. For younger children, an allowance provides an opportunity to count money accurately. Older children can learn about saving, borrowing, and even investing!
- Take a vacation Incorporate math by having the children estimate how long it will take to reach a destination, calculate the distance to be traveled and, for those lucky enough to take an overseas trip, learn about time zones and rates of exchange.
- Get back to the basics With more emphasis on problem solving, parents may be concerned that their children are not mastering basic skills. Incorporate these into family life by keeping flashcards in the car and playing games that encourage number and pattern recognition.
- Find math explorationopportunities The Cleveland Children’s Museum and the Great Lakes Science Center provide excellent enrichment. Logic problems, puzzles and games are also ideal math enrichment opportunities.
- Volunteer in math class By participating in math, parents witness the lesson first hand, hear the vocabulary and experience the methods used. This can enhance a parent’s ability to assist the child at home.
- Communicate with your child’s school As parents learn more about the trends in math instruction, they should be sure to share ideas and concerns with the school staff. Partnership in curriculum is critical to students’ success.