Most educators agree math fact fluency is beneficial, but how we get students there is always hotly debated. Timed math fact fluency practice causes some students to develop math anxiety. Racing against time doesn’t have to create fear and anxiety in children and/or adults. Student practice of unknown facts, especially against time, is both frustrating and futile unless the learner is prepared. Trained teachers can control the learning environment with good practices and preparation. Student preparation for practice and rapid recall of math facts includes consideration of learner maturation as well as targeted, distributed, and meaningful practice.
- Maturation – Students in early elementary, grades K-2, rarely have the cognitive endurance to practice facts against a timer without developing math anxiety. Using other nontraditional methods of practicing facts will measure a young learner’s increased rapid response over time.
- Give young learners all the time they need to complete a set of facts. The next time they practice the same set of facts, their goal will be to meet or beat their personal best time.
- Learners are competing only against the standard they set, a delay in increased speed is acceptable, and improvement is obtainable. Your assurance in the classroom will decrease and diminish anxiety with this practice.
- This activity should NOT be considered a test or graded. It is merely an activity to monitor and measure achievable goals.
- Targeted Fact Practice – Learners of all ages develop math anxiety when practicing unknown facts.
- Only known facts should be practiced.
- Practicing unknown facts is frustrating to the student and affirms their lack of confidence in rapidly recalling facts.
- Distributed Fact Practice – Fact practice is like a daily vitamin. A megadose of vitamins is not only less effective but can also be harmful.
- Effective fact practice includes 3-5 minute daily practice sessions.
- Math fact marathon will be less effective and even harmful.
- Meaningful Fact Practice – Fact practice is most effective when it is considered meaningful by the learner when practice is varied, engaging, and targeted. Practice should sometimes be monitored and measured.
- Worksheets, usually disdained by academia, are highly effective when fact practice is varied with other methods. i.e. games, manipulatives, strategies, etc.
- sA variety of games readily available for the learner to choose from is very important since learners have varied interests and learning styles. Both individual and multi-player games appealing to varied interests and learning styles should be readily available.
- Games, activities, and worksheets should target a small identified group of facts. Too many unknown facts frustrate and disengage the learner. Activities should align with the group of facts targeted by direct class instruction.
- Expect only what you inspect. Periodic math fact quizzes of targeted facts will increase the meaningfulness of math fact practice. The most meaningful practice time is the 3-5 minutes prior to a math fact quiz.
Fact Fluency vs. Computational Fluency
Fact fluency and computational fluency are often used synonymously, but they are not the same mathematically. Fact fluency defines how quickly a student can retrieve and release 6×8=48. Computational fluency defines how readily the student recognizes various visual presentation of numbers and their values appropriate to their grade level. Computational fluency requires students to increase numbers quickly and also break them down. In addition, how quickly does a student recognize the familial relationship of various equations? i.e. 6×8, 8×6, 48/6, 48/8, 4×12, 6x-48, (5×8)+23, 144/3, etc.
Computational fluency also includes the learner’s ability to move fluidly backward and frontward on a horizontal number line as well as up and down on a vertical number line. How quickly do they recognize the operation signs and more importantly how quickly do they intuitively know which operation to use in solving problems? Not only do they need to quickly know which direction they need to move, but do they need to move incrementally or exponentially on the number line while problem-solving?
If fact fluency is taught with effective strategies and methods, math anxiety will be relieved and computational fluency can flourish. Math fact fluency is a 3-step process while fact fluency requires at least 4-steps. Computational fluency is really what we are seeking. However, since math fact fluency is prerequisite to computational fluency we will first concentrate on the 3-step process to math fact fluency.
The three math fact fluency steps include: 1. Cognitive Conceptual understanding of numbers, symbols, and values. 2. Multi-sensory Memorization method of storing facts in long-term memory. 3. The rapid Retrieve and Release of facts to and from the frontal lobes thru targeted practice.
- Cognitive Concepts – Students are persuaded to accept and embrace our arbitrary arithmetic system including assigned symbols and values. Signs and symbols become familiar and embraced using number exploration coupled with manipulatives, methods, and strategies. It is primarily at this level that math fact strategies should be taught. However, good strategies transfer equations into long-term memory as known facts. Materials, methods, and manipulatives used in American classrooms surpass those of many other nations. I give us a passing grade for fact fluency step-1.
- Multi-sensory Memorization – Math fact fluency step-2 is the MISSING LINK in America’s classroom. There is a debate among educators regarding the teaching of facts thru strategy or memorization. We should do both. In fact, memorization is merely a strategy. Sometimes it is not the best strategy. i.e. properties of ones and zeros; skip counting for 2s, 5s, 10s, and 11s; doubles and near doubles; etc. Using a multi-sensory approach to memorization of facts is an excellent strategy. COUNTDOWN the only solution on the market designed to promote multi-sensory memorization. Plus, it is priced right! More information is included.
- Retrieve and Release – With the widespread use of technology in the schools, the student practice of retrieving and releasing math facts is addressed. Therefore, I give us a passing grade at the elementary level and encourage you to consider implementing step-2 Multi-sensory Memorization before you discard your current investment. If your school teaches fact fluency step-1 and step-3 and you are disappointed with the results, please consider math fact fluency’s MISSING LINK – Multi-sensory Memorization step-2 before you discard your current efforts.
Math Fact Fluency MISSING LINK – Multi-sensory Memorization step-2
The cerebrum of the brain is divided into four lobes: frontal, temporal, occipital, and parietal. The frontal lobe contains a person’s ability to problem solve both morally and mathematically. The frontal lobe does not reach full maturity for most people until about the age of 30 years. The other lobes (temporal, occipital and parietal) protect the frontal lobes by acting like sentinels protecting the frontal lobe from being overwhelmed.
The temporal, occipital and parietal lobes work in part to block out sights, sounds and sensations so the frontal lobes can process information without interruption. Since the temporal, occipital and parietal lobes are designed to throw away anything deemed a distraction to the cognitive concentration going on in the frontal lobe, educators must present information worthy of long-term memory in a manner that attracts the temporal, occipital and parietal lobes.
These lobes have much to do with sensory processing, so we must appeal to the sensory memory of each lobe. Using the sense of sound, sight and touch will engage these three lobes in receiving and holding information. Once these memories are stored through sensory processing, they are easily retrieved through sensory recall using auditory, visual and tactile cues.
The designer of Math Facts Matter calls this method the see, say, hear and write method. It is an old-school method…the baby that was thrown out with the bath water. Many in education are reluctant to revisit the past, but consider the following: Today, only 1 of 10 college students can pass a basic multiplication test at 40 ppm. Fifty years ago, any sixth grader was expected to pass with 60 ppm.
Clearly, something has changed and not to our advantage. The creator of Math Facts Matter: COUNTDOWN studied the research and found a way to improve previous practices making these methods current for today’s classroom. Plus, with the use of today’s technology, instruction implementation is complete in less than 3 minutes per day!
Appealing to the Occipital Lobe – See Method
Displaying math facts in defined ways will appeal to the occipital lobe. A fact should be displayed for an amount of time appropriate to student maturation. The older the learner, the less time the fact must be displayed for it to be captured by the brain and stored by the occipital lobe. The occipital lobe contains memories associated with and stimulated by sight.
Traditionally, we display a fact (6×8) on a flash card without the answer. That is acceptable only if the student is being assessed or playing games. The brain recognizes when the student is in practice mode and will capture an image of the equation for long-term storage. The learner will then appeal to the occipital lobe to retrieve math facts from memory using the stored image as a visual cue.
If the visual cue pulls 6×8 without the answer, the frontal lobe will miss the very thing useful to the high rigor mathematical process. Therefore, when appealing to the occipital lobe by displaying math facts, always include the answer with the fact. i.e. 6×8=48 You will recognize the student using a visual cue to pull the fact forward when they look away and stare at something unseen by you.
NOTE: Mathematics has long been recognized as a language. Math fact equations complete with answers are comparable to sight words. Storing these fact statements improves the fluency of fact recall and mathematical processing in a way similar to the manner sight word recognition improves reading fluency.
Appealing to the Temporal Lobe – Hear Method
We have discussed appealing to the occipital lobe to store facts easily retrieved by visual cues. We will now discuss storing facts by appealing to the temporal lobe. Memorization of facts comes by repeatedly hearing the information stated auditorily by a trusted source. When teachers lead their class in saying out-loud the fact students are viewing, they trust the teacher as an expert. What she says out loud, they believe.
Believing the fact to be true as the teacher states it appeals to the temporal lobe which accepts the fact into long-term memory. You will know a student is pulling a fact from the temporal lobe via an auditory cue when you hear them softly repeat to themselves, “Six times eight equals… Six times eight equals… Oh yeah, six times eight equals forty-eight!”
Appealing to the Parietal Lobe – Say Method
The fourth and final lobe within the cerebrum is the parietal lobe which has to do with taste, temperature, and touch. Our students could not appreciate the sense of touch without a parietal lobe. When we think of touch, we think of fingers and skin covering our outer body. However, one of the greatest sensory areas regarding touch is found in the mouth. When babies explore something, they first pick it up, usually with their hands. Then, the object goes straight to their mouth!
As teachers say the fact statement out-loud, an effective teacher requires them to say the equation with her. This method appeals to the parietal lobe through the sense of touch. For each equation students repeat, the tongue will thrust against the roof of the mouth and through the teeth as the lips purse in a distinct and peculiar way. As they state the equation a unique sequence of movement within the mouth is recorded by the brain. In recalling the fact statement via a tactile cue the parietal lobe will be prompted, and when the learner says, “Six times eight equals…”, forty-eight will fall out.
The brain will recall the recorded sequence and spit the equation 6×8=48 right out the learner’s mouth! You will know a student is using a tactile cue to pull forward a fact stored in the parietal lobe when you see them silently moving their lips to repeat the sequence recorded by the brain.
Tying it All Together – Write Method
When I mention the sensory lobes, many believe writing is the tactile portion of the solution. Writing the fact statement does have a tactile element to it, but it is much more than that. Writing the fact statement is an eye-hand-brain coordination activity that ties all the senses together so the appeal coming from the frontal lobe appeals to all three lobes simultaneously.
When the coordination of the various cerebrum lobes is complete, the fact statement will be returned based upon the individuals preferred learning styles and/or learning abilities. As the process becomes more fluid, it will not be apparent which cue pulled it forward first. The brain’s response time to a sensory cue will result in a response time that is less than a second…actually, .6 of a second!
COUNTDOWN – practice mode
Countdown is a highly effective computerized program providing homeroom teachers and/or math teachers with a quick and easy teacher tool to provide the MISSING LINK to fact practice. Countdown allows the teacher to target specific groups or levels of facts appropriate for the learner’s grade level. In addition to selecting grade levels, teachers can also be very specific regarding the following practice conditions:
- Fact group(s) – Teachers can select mixed levels and operations allowing for review, new fact introduction and prep for next level
- How many facts displayed? Teachers select all the facts within level(s) but restricts the system to a specified number of facts to display. i.e. 114 facts from 3 levels (2 review and 1 current). Teacher’s settings command the randomly pulls only 25 facts for today’s practice and/or test.
- How long is each fact displayed? COUNTDOWN allows the teacher to give younger learners more time to view and respond to fact statements. Or the teacher may vary practice sessions with only see, hear, and say method. The next session the teacher may want the learners to see, hear, say and WRITE the fact statement and want more viewing time allowed by the settings.
- Which view or a combination of views (horizontal, vertical and/or both)? Facts should first be delivered horizontally like a word. It is the easiest view for the brain to store in long-term memory. Once the horizontal view can be retrieved from long-term memory, the brain can more easily flip the stored view to respond to the vertical view.
NOTE: Refer to the attached list of settings recommended for each grade level.
COUNTDOWN – test mode
COUNTDOWN is also a computerized teacher tool with an assessment mode. Countdown adds a means of accountability, especially for the older student. Please be aware that kindergarten, first grade and even some second-grade students may not be mature enough for timed fact tests unless special care is provided.
Young Learners and Timed Tests
For the young learner I would not assign a grade to these “tests” in early learning grades. In fact, I would never call them a test to the young learner. Instead, I would use the term “race” to entice them. Give the early students the maximum time appropriate for their grade and the minimum amount of recommended facts. I would even ask them to put their pencils down and allow them to observe the fact “race” before they engage in the challenge. Then challenge them to “race” the timer as they write the entire equation they see, hear and say. Some students will finish before others. To keep that student engaged, challenge him/her to see how many times they can write the fact before it disappears from view.
Accountability for the Intermediate Learner
Intermediate learners may need external motivation. The accountability of a weekly math fact quiz is effectively similar to a spelling quiz. Select the level your students were assigned for practice, determine how many seconds each fact will be viewed and how many facts are shown. If you choose ten facts, the system will randomly pull ten facts from the level of facts you selected.
In the beginning, use the maximum allowed time for their grade level. If it is too challenging for your learners at the beginning of the year, give them more time or fewer facts on the quiz. As the year progresses, increase the number of facts and reduce the amount of time when appropriate. Your goal will be to get them to respond to the facts within the least amount of time appropriate for their grade level.
As students develop speed while maintaining accuracy, the classroom teacher will determine when or if it is time to once again challenge the class by reducing the allowed amount of time. Invite your class to the challenge. If you sense anxiety or you have students that appear about to cry, it may be too soon to challenge them. However, with some encouragement on your part, many students will want to take the challenge.
Let the other students participate as spectators while their other class members are challenged. It will only last a few seconds. One other tip: When reducing the time allowed, you may also reduce the number of facts displayed…at least when you begin the new challenge. Therefore, students that are easily frustrated will not have to sustain for very long. You will notice some of your “spectators” joining the challenge without being prompted. Soon all your students will be more receptive to the new challenge.
Administrators can also use Countdown’s test mode. Do you want to know the level of math fact fluency within your student body? Countdown allows you to measure each class using your personal code without leaving your office! Or use Space Challenge, our FREE product for 2019 to auto measure multiplication.
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