I teach my kids at home and have been doing it for years now. Kids have their own pace of learning. But, more or less, they attain fluency almost in sync unless they are suffering from any learning disability. One simple observation is that kids try to add numbers on fingers at the start, and sooner, they start giving answers without any waiting time. This abruptness in arriving at answers to math problems is nothing but math fluency.
The common activities that I found them doing on their way to attain math fluency are – trying to solve questions in mind (doing mental math) instead of relying upon pen-and-paper-based calculations or counting on fingers. Also, by the way of reviewing the last sessions, they gained requisite practice. It is safer to say that repetitions and practice came out to be the other two important drivers of building math fluency in kids. All these observations have led me to decode math fluency for you.
Let’s explore in this post,
- Components of math fluency
- Why is math fluency important
- Activities to help kids become math fluent
Components of math fluency
Quoting from Kilpatrick et al’s work (2001), “math fluency emerges from the intertwining of mathematical proficiencies that comprise conceptual understanding, procedural fluency, strategic competence, productive disposition, and adaptive reasoning.” Let’s take these components one by one:
- Conceptual understanding: A child can provide the answer in a jiffy when well-versed with the concept. Adding means brining more value to a set, if this is crystal clear, a child automatically starts counting forward to find the sum.
- Procedural fluency: It is the core and the most visible part of math fluency. A kid follows the operational procedure ( adding, subtracting, dividing, comparing) effortlessly when the concept is clear and strategy is fully understood.
- Strategic competence: Procedural fluency emerges from strategic competence. Also, if the conceptual understanding is well-pronounced, kids display strategic efficiency. It shows how this strand model is intertwined.
- Productive disposition: Ability to see math as an operational requirement and appreciate its role in daily activities. For example, adding water to fill the glass to brim is productive disposition of a strategy (that is to fill).
- Adaptive reasoning: Ability to find and work on logic embedded in mathematical operational procedures.
Naturally, the absence of any one of these proficiencies can reflect a poor state of math fluency. While designing the curriculum, therefore, it is necessary to ensure all-around development involving all these proficiencies.
What’s the need?
Will you be able to crack through various exams if you are not math fluent? Except for the cases for whom the provision of math exemption is available, you need to have mathematical fluency to get through the course of choice.
Let’s take another example. How will you look, as an adult, standing in the billing queue and counting the sum of purchases made on your fingers? It will be frustrating to you as well as to others. Hence, math fluency is a skill you will need to perform various daily tasks as an adult.
Math is everywhere. It is evident while playing a sport too. You require adaptive reasoning to understand the speed of the ball coming to you and its projected trajectory to stand in the right location to catch it, right? Hence, fluency in math in terms of calculative lucidity is not enough.
Lastly, you need to be fluent in mathematical thinking to make various decisions like deciding the stride’s length to jump across a hole, raising leg to correct height to climb up the staircase without stumbling, and so on.
To sum up the need of having math fluency, we can say that it is required for:
- Proving academic efficacy for certain courses in student life
- Being a good judge to carry out activities of common occurrence like walking, jumping, running
- Carrying out daily affairs with confidence as an adult
- Managing money matters independently
- Proving supremacy in outdoor recreational activities like sports
It is why it is suggested that math skills are to be incorporated right from the early education years or preschooling. Our cranial capacities deteriorate with time, it is a fact. Hence, to make the best use of cerebral intelligence when it is at the highest, i.e. during childhood, the teachers need to adopt appropriate strategies to build requisite math skills in kids. Let’s take a look at strategies one can apply to build math fluency in kids.
Strategies that might help
Scaffolding means providing requisite introductory support to kids to move them to think and learn deeply about a subject, simply put. Researchers have assessed and analyzed instructional methods in the classroom from time to time. They have arrived upon a common conclusion that students in their formative years need scaffolding. The usual strategies worth adopting to build initial interest in kids are:
- Introducing a concept in a crisp and easily understandable manner
- Using Manipulable resources to demonstrate concept
- Show method and repeatedly to inculcate working memory
- Ask questions to help children reflect on the learning, raise doubts or reproduce learning as per their understanding
- Doing simpler things first to build confidence and a firm base to transition them to more complex topics
Affirmation is nothing but building confidence about a certain skill. In building mathematical fluency, the kids need to be confident about their learning. Hence, they are asked to present ideas. Number talk sessions are one of the ways where kids present their ideas while following social etiquette.
Teachers usually divide the class into small groups and ask them to present the learning of a previous class. By the way of exchange of ideas, sharing thoughts, and applying strategies, the kids mentally revisit the concept learned and try to foray the path ahead.
One of the main roles of affirmation is to evoke intellectual curiosity so that the kids become interested in deeper exploration or moving to more complex problems.
3. Building fluency
Once students are confident of their learning, their natural inclination is to be faster and to attain added accuracy. To build fluency, they try harder to apply strategies learned to come out with a correct answer. Teachers may encourage kids to self-challenge themselves by setting personal targets. Like learning more multiplication tables, moving from single-digit addition to double or triple-digit additions, etc. Or, they can provide a lot of practice materials or doable projects that offer a good pretext for repeat trials and frequent practicing.
Activities to help kids become math fluent
Activities have an important role to play in building math fluency in kids. According to a literature review, activities contribute to building math fluency in the following ways:
- Improve executive functioning
- Add to procedural knowledge
- Enhance fact fluency
- Boost inquisitiveness or questioning ability
Let’s move to the following easily doable activities that help strengthen concepts, apply them and drive the mind to explore further possibilities.
1. Playing with flashcards
Flashcards offer a gamified learning resource to kids. Mathematical facts and the corresponding equations/answers written on the flashcards can fortify associative memory. Kids may speed up the corresponding flashing and matching of the cards to gain the mental agility required to gain fluency. Writing equations like 12 + 17 on one card and matching it with the card that contains the answer as 19 is one of the ways flashcards are used for speeding up calculations.
2. Dodging number activity
Divide kids into groups and make them stand in a circle. Assign kids with numbers ranging from one to 10 or higher. Start with kid numbered 1 and correspondingly kids say 3, 5, and 7 as per their numbers. You can increase cognitive load a little bit by asking them to jump in addition to speaking out the numbers. The activity can help master dodging number and boost cognition too as kids have to remember their turn of uttering the assigned number and jumping
3. Solve puzzles
Solving a fact square puzzle is one of the best ways to train the mind to calculate fast and enhance focus on operational procedures. Make a 3×3 matrix and start by writing a number with the third cell of the first column. You can demonstrate filling the next two numbers by applying operations like add by 2 and subtract by 1. It can be instructed to do in a timed manner to attain calculation fluency. The direction will be as shown.
4. Musical Math
Give kids a set of questions to solve. The operations chosen should be different, comprising addition, subtraction, multiplication, etc. Put the music on and tell kids to solve questions using mental math and keep writing answers till the music runs. Reward the fastest kid for the efforts made. It is an engaging number sequencing activity that kids can use to strengthen math fluency.
5. Make models with base 10 block
Hand over a set of math facts like making a ten, double the number, divide by 2, etc., and ask kids to keep adding the blocks equal to resultant numbers to the given number of blocks. Announce the reward of having a cookie from the jar on completing the model the fastest. This activity offers a multisensory approach to learning and mastering math facts with fluency.
Building math fluency is a must to help kids explore and employ their inherent talent with numbers. Apart from helping to move firmly on to higher academic endeavors, this skill prepares for the life ahead. The course of learning may be having different paces as per the abilities of kids. The use of activities and employing effective strategies to teach may fill the learning gaps and help kids, even with learning deficiencies, to stay pulled into the learning process.
- National Research Council, Education, D. O. B. A. S. S. A., Education, C. F., Mathematics Learning Study Committee, Findell, B., Swafford, J., & Kilpatrick, J. (2001b). Adding It Up: Helping Children Learn Mathematics (Illustrated ed.). National Academies Press.
- Cobb, P., Wood, T., Yackel, E., & McNeal, B. (1992). Characteristics of Classroom Mathematics Traditions: An Interactional Analysis. American Educational Research Journal, 29(3), 573–604. https://doi.org/10.3102/00028312029003573
- Atlas B. (2020): The effects of affirmation on middle school students with difficulties in Maths. Retrieved from https://mdsoar.org/handle/11603/18531
- Cozad, Lauren E. and Riccomini, Paul J. (2016) “Effects of Digital-Based Math Fluency Interventions on Learners with Math Difficulties: A Review of the Literature,” The Journal of Special Education Apprenticeship: Vol. 5 : No. 2 , Article 2