Encouraging students to work and thinking independently is the path to improved problem-solving skills and testing success

Nearly every teacher has students who can solve math problems successfully in class, but then get scores on state assessments that don't reflect their understanding. Some freeze up at test time, others open their test booklets and impulsively raise their hands looking for rescue. And still others write unclear explanations that offer little evidence of their knowledge. The good news—this scenario can be changed! With a few simple techniques, we can boost students'confidence levels, increase independent work habits, and help them maximize their communication skills on test day and beyond.

Create a Supportive Classroom Environment
To build students'math confidence, try to foster a classroom atmosphere that is supportive rather than competitive. One good way is by having small groups of students work cooperatively to solve a single problem, using different strategies. For example, in each group, one student could use manipulative blocks, a second could draw a diagram, and another could do the arithmetic computation. A fourth member could write the solution steps in complete sentences. At the same time, encourage students to regularly seek help and advice from each other rather than always turning to you for help. Post the classroom sign: “Ask 3 Before Me!” This simple message reminds students that they have knowledge and help to give. It tells them: Kids—not just teachers—can have the right answers!
 
As students work cooperatively and begin to look to one another for answers, they gain exposure to a range of problem-solving processes. On top of this, an atmosphere of trust, collaboration and partnership is created. And all of this can help boost their comfort level-and performance-at test-taking time.

Promote Student Independence
Enhancing students'understanding of themselves as capable, independent learners goes a long way towards test success. Start by making all classroom resources readily available. Teach them that tools (manipulatives, dictionaries, calculators) belong to everyone and are there to be used as needed. In this way, you are letting your students know that you trust them to problem solve and to gather the resources they need. A second strategy is to teach students to review what they already know. Show them, for example, how to “take a trip down memory lane” in their textbooks. This is particularly useful when grappling with new material. For instance, if subtraction of greater numbers is proving challenging, have students find the textbook pages where two-digit subtraction with regrouping was initially presented. You'll want to encourage children to eventually look back on their own. This practice reminds students of previous learning successes and links previous and new knowledge in concrete ways.

Cultivate Clear Thinking
When solving word problems encourage your students to articulate their ideas clearly—first orally, and then in writing. This is important practice and will help expand students'critical thinking skills. Plus, they will increasingly recognize the language and format of test questions, building a familiarity that will contribute to their success. Try this step-by-step approach:
  • Step 1: Think. Ask students to think silently about how they might solve the problem, then have them discuss their strategies for finding a solution in groups. Encourage them not to use numbers in describing their strategies; this helps students focus on the problem-solving process, rather than the specific problem.
  • Step 2: Write. After students perform the computations to solve the problem ask them to (individually or in pairs) write an explanation that justifies their answer by describing the steps they took. Make sure students understand they are expected to refer to the specific computations performed.
  • Step 3: Evaluate. Share and discuss exemplary responses as a class. Rather than presenting the problem yourself, encourage students to use a rubric to show that their work includes all of the elements of a complete response. This process helps students increase their understanding of a strong and successful answer.

Build Students'Math Vocabulary
For students to truly understand and remember math terminology, they need to be so familiar with important problem-solving words that they have internalized the vocabulary. Post standard math terms all over your classroom. For example, create a math word wall with your students. Add new words to the wall as the year progresses to maintain a cumulative math glossary. Or at the beginning of each instructional unit, have students work together to make a list of terms and write their own illustrated definitions on sentence strips. This kind of vocab work promotes independence and provides students with correct spellings. And when test time rolls around, your students will have seen these important terms hundreds of times!

Provide Students with Good Examples
When students are asked to write a response to a problem, all too often they write incomplete or even incoherent explanations that offer little evidence of their knowledge. In many cases, students may not have a clear idea of what a good answer should include or look like. Try having students use a rubric as a guide for writing or as a self-assessment tool. Although rubrics vary slightly from state to state, the expectations are more or less the same. For example, a math rubric generally includes the following measures:
  • The solution is correct. 
  • The question posed is answered clearly and completely. 
  • Math terminology is appropriately used. 
  • The solution pathway is explained step by step. 
  • The solution is justified using a computational “check,” estimation, or logical reasoning.
By using a rubric, students will have a better understanding of just what a successful response consists of, and they can put this understanding to use when taking high-stakes tests.

Resist the Urge to Rescue
When a student comes to your desk notebook in hand, it is sometimes hard to resist the urge to fix the problem for him or her. Often, we shoulder too much of students responsibility to learn. They then can end up feeling dependent on us and underconfident about their own skills. But when we help students learn how to utilize their own knowledge and available resources, we give them the chance to take pride in what they can do on their own. As your class learns to work more independently, you may find yourself sending students to the word wall or gently reminding them that you are not going to tell them how to to do a problem, but you are happy to listen to the ideas they have so far. Soon they will come to value their new independence, and when high-stakes assessments are distributed, they will have the ability and the confidence needed to put their best foot forward with confidence.

Robyn Silbey is a school-based math specialist in Montgomery County, Maryland. This article was originally published in the April 2004 issue of Instructor.