### Observing Best Practices in a Mathematics Classroom

Wednesday, May 18th, 2016AUTHOR: Virginia Keasler, Secondary Math Specialist

Walking into a math classroom, an observer of the lesson may view many modes of instruction. The list may include:

- Teacher shows students step by step problem solving and expects students to do problems in the way they are instructed
- Students sitting quietly in rows
- Students rotating around stations exploring challenging problems
- Students are working on a problem together in groups, some individually, not necessarily doing exactly the same thing
- Students engaged in critical thinking
- A few students working at the board while others watch
- Students who have completed their work and are waiting for the next problem
- Teacher asking probing questions about the way students are attempting to answer questions

Generally you may see one or both of the two prevalent approaches to mathematics instruction. In the more traditional approach of instruction, skills-based, teachers may focus on how to solve the problem, show that problem solving strategy, and then require the students to quickly repeat that strategy. This method focuses on developing computational skills.

In concepts-based instruction, teachers have students solve a problem in a way that makes sense to them and then explain how they solved their problem. This method helps students be aware that there is more than one way to solve a problem.

You may be trying to decide what is the best way, but most researchers (e.g., Grouws, 2004) agree that both approaches are important, that teachers should strive for procedural fluency that is grounded in conceptual understanding.

There are three critical components to effective mathematics instruction (Shellard & Moyer, 2002):

- Teaching for conceptual understanding
- Developing procedural literacy
- Promoting strategic competence through meaningful problem-solving investigations.

In an effective classroom an observer may see the teacher

- Accepting students solutions to challenging problem which includes their explanation how they found their solution and the reason they chose to try their method.
- Posing interesting questions to students to spur their interest in the problem.
- Encouraging students to see that problems are challenging and that you sometimes have to search more than one method to find the answer.
- Instilling the belief that the goal of answering the question is attainable and worthwhile and can even be “cool”.

In an effective classroom an observer may see the student

- Solving the problem themselves and not just “mimicking” the procedure shown to them by others.
- Challenging themselves to investigate a meaningful question.
- Sharing their ideas with each other and as a group
- Using various ways to show their work
- Conducting an experiment by analysing data and coming to a conclusion
- Are using calculators where appropriate
- Using manipulatives to engage in problem solving to help form a concrete understanding of the concept where needed.

The National Center for Educational Achievement (NCEA, 2009) examined higher performing schools in five states (California, Florida, Massachusetts, Michigan, and Texas) and determined that in terms of instructional strategies, higher performing middle and high schools use mathematical instructional strategies that include classroom activities which:

- Have a high level of student engagement
- Demand higher-order thinking
- Follow an inquiry-based model of instruction – including a combination of cooperative learning, direct instruction, labs or hands-on investigations, and manipulatives
- Connect to students’ prior knowledge to make meaningful real-world applications
- Integrate literacy activities into the courses – including content-based reading strategies and academic vocabulary development

Additionally, NCEA researchers found that it was important for teachers to create classrooms that foster an environment where students “feel safe trying to answer questions, make presentations, and do experiments, even if they make a mistake” (p. 24).

In summary, while both methods are important, teachers must reach students where they are and in the method that works best for each of their students. While procedural learning is important to learn math facts and algorithms, students still need to be challenged, allowed to learn by exploring, and encouraged to keep trying knowing that math is meaningful and a huge part of the environment around us everyday.

**References**

The Education Alliance. (2006). *Closing the Achievement Gap: Best Practices in Teaching Mathematics. *Charleston, WV: The Education Alliance.

Grouws, D. (2004). “Chapter 7: Mathematics.” In Cawelti, G, ed., *Handbook of Research on Improving Student Achievement. *Arlington, VA: Educational Research Service.

National Center for Educational Achievement. (2009). *Core Practices in Math and Science: An Investigation of Consistently Higher Performing Schools in Five States. *Austin, TX: National Center for Educational Achievement.

**Shellard, E. & Moyer, P.S. (2002). What Principals Need to Know about Teaching Math. Alexandria, VA: National Association of Elementary School Principals and Education Research Service.**