Math Innovation + Hard Work = Math Success

A classroom is alive today, full of talking students, busy pencils, and lots of noise. Voices jingle with excitement and curiosity. A nightmare class, you may be thinking. Oh that poor teacher! What's all this commotion about? Well, these students are busy learning math. That's right, you've read that correctly. Students are intently learning as though math is actually cool!

There are no tears, horror, or boredom over the sight of math problems. Recently, math programs piloted in the classroom have created this very picture, and taking some tips from these valuable changes will surely lead your students to math success. As parents, you can also take away certain principles from these programs, ensuring homework time with your child packs an exciting and educational punch!

Program #1: Problem Solving Solves the Day

With a neat history, this program originated from Western Illinois University, where the math education faculty received a grant to pilot open-ended math questions. Realizing that her students were steadily improving in their math skills, a third grade teacher along with other teachers and an education consultant adapted their own problem solving program. Working in groups, students solved open-ended questions and participated in lively discussions, all the while the teacher served as a facilitator.

What is the "What and Why"?

Written explanations are important for students in gaining a deeper grasp of problem solving. Students write what steps they take to solve the problem (the "what") and explain the reason for each step (the "why").

Before, During, and After

The lesson consists of 3 phases:

1. Before: Lasting about 5 to 10 minutes, the Before part includes asking the question or "lighting the spark" (talking about something exciting that the students can relate to: e.g., baseball cards), presenting the problem and asking clarifying questions to ensure students understand the problem. Then students spend several minutes contemplating ways to solve the problem before they discuss the strategies with a fellow student or in a group.

2. During: After thinking of problem solving strategies on their own, students discuss them with their collaborator(s). To ensure that students haven't gone astray on the task, the teacher simply walks around the room and asks more questions, like "what do you think the question is asking?," and "what do you know about the problem?" After everyone is on task, the teacher continues asking questions to generate more discussion. Referred to as Round 2 questions, they can look like this, "How did you get started;" "What did you try?;" "How did you get that answer;" and "Is there a pattern?" It's okay to allow the students to struggle with the problem. This allows the teacher to listen intently, gaining a better grasp of the students' way of thinking. It's recommended to spend about 15 to 20 minutes in this phase.

3. After: Now the teacher facilitates a class discussion with groups presenting on different parts of the problem solving process: Some groups discuss how they began the problem. Other students talk about incorrect strategies they had tried, all the while the teacher addresses misconceptions about the problem. After about 15 to 20 minutes, the students arrive at a correct conclusion together.

Other Tips

Teachers identified other helpful tips: - Begin with easier problems - Put up math vocab words - Write out the math explanations as a class first - Teach the lesson more than once - Present a follow-up problem the next day

A+ Results

Overall, students had more confidence in their solving abilities, utilized a variety of strategies to solve problems, actually enjoyed writing out their "what and why," and were more determined to solve new problems. Those students who performed poorly on beginning problems actually outscored the middle or high scoring students.

Also important, students were better equipped to answer statewide open-ended exam questions, which always makes administrators happy. Quotes from teachers throughout the article illustrated their satisfaction with the program. All in all, using a problem solving approach to learning math proved successful: It appears that both students and teachers experienced growth!

Program #2: A Little Technology Goes a Long Way

Lake Highlands Junior High in Richardson, Texas experienced a technological transformation to help their at-risk students with math. The classroom included the Texas Instruments (TI)- 73 Explorer graphing calculator specifically programmed for math concepts appropriate to junior high and the TI Navigator (a neat device that provides wireless communication between students' calculators and teachers' computers).

1. Length of math class time was increased from 50 to 100 minutes.
2. The ratio of teachers to students improved.
3. An accelerated curriculum was established.
4. Teachers created higher expectations for their students and reinforced these expectations.

You may be wondering how a calculator would enhance math learning. Indeed, sometimes calculators are guilty of impeding learning, because students can use them for arithmetic operations versus using their heads to do the computing. But no so!

These TI calculators had several advantages: Math concepts were shown on each calculator, meaning students had a tangible visual to look at, while they were able to monitor their progress. For teachers, this technology also meant monitoring students' comprehension and progress instantly. This also sped up the classroom overall. Teachers were able to send out math problems and quizzes, while collecting assignments.

Test Scores Improve

Of those students who previously failed the statewide math exam, 33% had passed after participating in the program. Overall, not only did test scores of pilot students increase by 6 points or more, but students improved on other math tests during the year as well.

The Take Home Message

Take these tips home! Try taking these programs and applying them to your classroom or home. Whether it be technology or group work, these changes signified interaction and a new way of learning. Translation: The math classroom transformed into an exciting and curious place, one where students are succeeding. Take advantage of this success too!

By Margarita Tartakovsky, MS

References:

Kim Hartweg & Marlys Heisler. No Tears Here! Third-Grade Problem Solvers. Teaching Children Mathematics, March 2007.

Texas Instruments. From At-Risk to Increased Achievement. e-School News Best Practices in School Technology, Winter Ed.