Supporting High-Quality Math Learning—After School

Dannette Parsley and Heather Martindill

Under the watchful eyes of her peers, Lucy picks up the dice and contemplates another roll. "I never understood probability until we started playing this game after school. Now, I get it." She then shakes the dice, pauses, and opens her hands so the dice skip across the table. "Man, I got 10 points on this round already—I'm sitting down," says Lucy, who still considers herself a risk-taker. "I used to just keep rolling. Now, I'm strategic!" she explains.

Lucy and her peers in an after-school math enrichment program are caught up in "Bear," a game in which they accumulate points by rolling a pair of dice as many times as they choose, without landing on a particular number designated by their teacher. If the dice land on the specific number, student lose of all their points.

The game of chance is just one way that students like Lucy can gain an understanding of math concepts they otherwise might not get in a regular math classroom. The classroom, according to Lucy, "feels like a lot of numbers and writing on paper." Lucy intuitively understands the contrast in ways of learning; after-school math programs need to build on and enrich the school day, not replicate it. When enrichment activities are both challenging and engaging, they can help students connect classroom learning to their own lives and interests.

High-Quality After-School Mathematics Practices

Although high-quality after-school math programs have common elements, activities can take on a variety of forms. The federally funded National Partnership for Quality Afterschool Learning helps schools develop high-quality, academic enrichment opportunities; the partnership worked with Mid-continent Research for Education and Learning (McREL) to identify six types of high-quality after-school mathematics practices that increase student achievement and improve attitudes toward learning math.

Practice #1: Finding Math
Finding math involves using fun problem-solving activities that bring math into the real world. From cooking to exercise and sports, this practice lets students use everyday activities to make their discoveries meaningful, enhance their understanding of math, and build their enthusiasm for learning. For example, an after-school cooking club can help students make real-life connections to mathematics by measuring ingredients, comparing measurements of liquids and solids, converting between standard and metric systems, and reducing or enlarging yields. Research suggests that students are motivated to learn when activities are based on their interests and prior knowledge, are designed to be culturally relevant, incorporate physical activity, entail social interaction with adults and peers, and provide meaningful learning for students struggling with math.

Practice #2: Math Centers
Math centers are small group stations that let students work together on activities such as puzzles, brainteasers, or problems using manipulatives. Math centers give students opportunities to problem solve, pace themselves, and work independently or with their peers. Research suggests that when students work in small groups they are more likely and willing to explore different approaches to problem solving, and to question, take risks, explain things, and have their ideas challenged.

Practice #3: Math Games
Math games, in addition to tapping children's natural motivation to play, offer several other instructional advantages, including opportunities for choice, high concentration, and informal instruction. The best games encourage active involvement, call for both skill and chance, require students to think deeply, and let students use multiple problem-solving strategies. Games provide students with opportunities to increase their understanding and application of math skills and concepts, gain computational fluency, and hone communication skills as they justify their moves. They also encourage social interaction, immediate feedback, and a safe environment for students to make errors.

Practice #4: Math Tools
Mathematical tools are materials used to measure, count, sort, or evaluate a mathematical problem, such as manipulatives (e.g., beans, counters, blocks), measuring devices (e.g., rulers), pictures, symbols, and technology. Research shows that the use of math tools has a positive impact on student achievement and engagement. They help students think flexibly about mathematics, allow for more creative approaches to solving problems, and explore mathematics with less anxiety. When tools are used productively, students learn to see connections among objects, symbols, language, and ideas. To be effective, students need to work with tools over extended periods, experimenting and observing what happens.

Practice #5: Math Tutoring
Math tutoring supports students' mathematical learning in an interactive, purposeful, and systematic way. Whether with parents, peers, or a community volunteer, tutoring can take place in small groups or in one-on-one sessions as long as it remains targeted to each student's strengths and needs. Research indicates that high-quality, frequent, and consistent one-to-one tutoring has positive effects on student achievement, especially for disadvantaged students—helping them build confidence, improve grades, complete homework at higher rates, and perform better on standardized exams.

Practice #6: Family Connections
Well-designed family connection activities involve parents, caretakers, and community members supporting students' mathematical learning both in and out of school. Family math nights, for example, give parents and students a chance to enjoy mathematics together, foster positive attitudes towards mathematics, and encourage positive relationships between school and families. Involving parents and young people in planning these nights helps to ensure they are more culturally relevant and fun for students. Research shows that family involvement activities encourage families to foster student learning at home, resulting in higher grades and test scores, increased enrollment in academically challenging programs, and better attendance.

Too often, pressure for accountability forces schools to cut back on hands-on, explorative activities that can motivate students to learn. Well-designed after-school programs can instill the joy of learning in students and provide at-risk students with the extra support that can add up to success.

Complete citations for each practice can be found in Afterschool Mathematics Practices: A Review of Supporting Literature. Also, see the Afterschool Training Toolkit, which includes sample lessons, video clips, resources, and guidance on best practices.

Dannette Parsley  is senior director in field services and Heather Martindill is a senior consultant for McREL in Denver, Colo.