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NYC Helpline: How To: Teach Math

Helping Students Become Fluent in Mathematics
by Luzviminda “Luchie” B. Canlas

“Developing fluency requires balance and connection between conceptual understanding and computational proficiency.”
—Principles and Standards for School Mathematics, NCTM, 2000

What is fluency? According to the Merriam Webster’s Dictionary, to be fluent is “to be capable of moving with ease, effortlessly smooth and with grace.” Do you want your students to be fluent in mathematics?

Being fluent in mathematics means knowing exactly what to do correctly in a short amount of time when confronted with a problem situation. It is also about being “smoothly and effortlessly” able to make relevant connections and applications between real life situations and the mathematics concepts, ideas, and principles learned. Furthermore, fluency is using one’s computational proficiency in problem situations. Knowing when to add, subtract, multiply, and divide when engaged in a problem-solving situation requires fluency, accuracy, and deep knowledge of content. The rate and ease in applying the computational methods is learned and mastered through meaningful and consistent practice. It is not enough for a student to know how to quickly perform the four operations to be considered fluent in mathematics. It takes much more. How do we achieve fluency in math?

Here are some things we can do:

  1. Provide sufficient and regular practice for the students to develop computational proficiency so that they can master the basic number operations. Make sure you provide sufficient practice in multi-digit addition, subtraction, multiplication, and division. Engage your students in activities and tasks that will make them “see” and understand the basic operations. A deep sense of numbers and their properties, as well as  the various relationships between numbers, is essential.

  2. Since there are so many mathematics terms that have
    multiple meanings and may pose processing problems for our students, we need to systematically and explicitly provide directly and indirectly vocabulary instruction to carefully explain these terms to them. We can use appropriate and varied literacy strategies such as doing math read-alouds (carefully select literature that teach math concepts), performing reader’s theaters, having a lot of visual supports, using graphic organizers (frayer model, semantic maps, semantic features analysis grids, conceptual maps, venn diagrams), using Polya’s Four-Step Problem solving process, and using the SQRQCQ (Leslie Fay, 1965). SQRQCQ stands for :

    • Survey – read the problem fast to get a general gist of it
    • Question – what the problem is asking you to solve
    • Read – reread the problem to find important information
    • Question – identify the arithmetic operations to use and its sequence of use to answer the problem
    • Compute – perform the necessary operations to find the answer
    • Question – check for the reasonableness of the answer

  3. It is very important that we help students know and understand when to use the four operations or a combination of these when solving problem situations. We need to prepare them to make smart choices about which operation to use. We need to teach them to always read the problem carefully, look for relevant information, and disregard irrelevant facts. Remember, it is not enough that students know how to correctly perform mathematical operations. They need to know when to apply which algorithms to solve problems accurately and efficiently.

  4. Students also need to know how to provide reasons, justify, explain, show, and discuss with clarity how they came up with their answers or solutions. It is critical that we teach them how to communicate and organize their thoughts coherently.

  5. We should also encourage students  to find alternative ways to solve the problem or provide a “friendly” critique or feedback to a classmate’s approach or solution to a given problem. They can learn a lot about themselves and their classmates’ thinking by doing this. It is also a great way to build community in the classroom.

  6. Do guided reading in mathematics. During these sessions, make sure that you help your students discover and see the connections between what they are reading and their real life situations, and the value of their prior knowledge. Help them see the significance of mathematics in their lives. Help them to understand how they can apply the context of mathematics in everyday situations. Ask thought-provoking and open questions to challenge their thinking. Encourage them to make predictions, questions, estimations, connections, summaries, and reflections. Here are some examples of questions and question stems you can ask your students during your guided reading math periods:

    • What are some connections you can make?
    • What are some possible solutions you can do?
    • Does this make any sense?
    • Explain why you think that way?
    • How is this same or different as…?
    • What do you notice?
    • Is there another way to look at this?
    • Can you show your thinking using pictures, graphs, lists, etc…?
    • Can you justify your thinking?
    • Do you have examples and counterexamples to prove your point?
    • What questions do you have?
    • Can you provide a reasonable estimate?

  7. Play math games and have a lot of fun learning. You will build fluency in an exciting way by doing this. Search the web for useful interactive games or develop your own games.

  8. Learn to differentiate instruction so you can create tiered lessons and parallel tasks that will meet the needs of your learners. This will help maximize learning that will lead to fluency.

  9. Use technology to teach our “digital natives.” Create Smart Board lessons to develop the fluency of your tech savvy, visual, and tactile learners. Surf the web for lessons that effectively integrate use of technology to enhance the teaching and learning of math concepts.

  10. Make sure that manipulatives are accessible to your students at all times. Some students may need the tactile and visual support to process their thinking. You should know how to make them available to support their thinking as they engage in problem solving. Have routines in place for their care and use to maximize engagement and classroom management.

I hope that this article has given you some guidance as you lead your students to acquiring fluency in mathematics. Our ultimate goal is to make them empowered, self-directed, and autonomous learners who make quick and appropriate choices when tackling problem solving situations. We want them to be fluent in the math language, computation, and decision-making processes. We want them to acquire vocabulary quickly, compute quickly, and think quickly by constantly and consistently providing fun, rich and challenging opportunities for academic growth and development. This way, the road to success and mathematical fluency is smooth and easily reached.

If you have a question or comment about this article e-mail Luchie.


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