There is a raging debate among educators attempting to determine if the time we spend teaching rapid recall of math facts is enough to bring our efforts to fruition. Most educators agree math fact fluency is beneficial, but how we get students there is always hotly debated causing the greatest conversation and concern to revolve around our methods. Perhaps the bigger question is, “Are our efforts worthy of our time?”
An important concern for many teachers is the time constraints we add to math fact fluency practice since it has been observed that some students develop math anxiety from timed tests. I have also observed overwhelming math anxiety in children and adults when they are asked to produce quick results before they are ready. Yet, it has also been proven to me that math methods can include racing against time without creating fear and anxiety in children and/or adults when trained teachers control the learning environment in the following ways and means.
- Cognitive Concepts – Students must be 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 at this level that all math fact strategies should be taught. However, only the best strategies transfer equations into long-term memory as known facts.
- Multi-sensory Memorization – Students must not practice unknown facts against the clock. Practice, especially timed practice, is effective only when practicing facts that are known and/or readily calculated through strategy. Using a multi-sensory approach to memorization of facts is among the best strategies.
- Retrieve and Release – Practice of known facts is effective, but practicing unknown facts is futile and frustrating. Repeated usage of known facts though processing mathematics is practice. However, repeated practice of retrieving and releasing facts is highly effective when the practice targets known facts, practice is distributed daily like vitamins, and practice is meaningful to the student.
2nd Step in Math Fact Fluency – Multi-sensory Memorization
In the following chapters we will discuss using multi-sensory memorization of facts, the second step in math fact fluency. 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 mathematically and morally. 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.
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 they want stored in 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 the sensory processing, they are easily retrieved through sensory recall using auditory, visual and tactile cues.
Appealing to the Occipital Lobe
Regarding math facts, displaying a fact 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 stored by the occipital lobe. However, there are certain things to consider.
The occipital lobe contains memories associated with and stimulated by sight. Traditionally, we display a fact i.e. 6×8 on a flash card without the answer. That is acceptable only if the student is being assessed. If your desire is to appeal to the occipital lobe to retrieve math facts from memory, the equation must be accompanied by the answer since the brain will capture an image of the equation before storing it. You will recognize the student using a visual cue to pull the fact forward when they look away from the card while staring at something unseen by you.
If the image of the fact pulled forward via a visual cue does not include the answer, the very thing needed by the frontal lobe will be missing! The student will have informed the frontal lobe that 6×8=? providing nothing 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
Math fact equations complete with answers are comparable to sight words and reading fluency.
Before students can fully benefit from memorizing a vast array of sight words to increase reading fluency, students must know the letter symbols and the sounds attached. In comparison, students will best remember 6×8=48 when they know the number symbols and numerical values of the equation.
It is important for students to know what 48 looks like spatially and numerically before they begin memorizing equations equivalent to 48. Mathematical cognitive concepts are learned in the first level of math fact fluency. Recognizing numbers and their values contribute greatly to the next step of math fact fluency—multi-sensory memorization. Students that have processed through all the math fact fluency steps sequentially will more readily move into computational fluency.
Fact Fluency vs. Computational Fluency
Fact fluency and computational fluency are often used synonymously, but they are not the same mathematically. It has been my experience that fact fluency is prerequisite to computational fluency. However, quickly recalling facts does not guarantee the mathematical flexibility with numbers necessary for successful computational fluency. Fact fluency defines how quickly a student can retrieve and release 6×8=48. Computational fluency defines how readily the student recognizes the familial relationship between the following equations:
- and much more!
If fact fluency is taught with effective strategies and methods, math anxiety will be relieved and computational fluency will flourish. Therefore, the speed and agility a student has in recalling facts is not the proof that our math fact methods worked. We need more proof and so do our students. Math fact fluency must propel our students toward computational fluency before we are certain our methods are effective and highly qualified. Appealing to multiple senses in the memorization process is the key to success in the second step of math fact fluency.
Appealing to the Temporal Lobe
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
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 students see the equation their teachers are saying 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.
After repeatedly stating the equation out-loud, over-time the student will see the equation and prompt the brain for a tactile cue. The student will say, “Six times eight equals…” and 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.
This completes the second step of multi-sensory memorization of math facts. Once facts are stored in long-term memory, students should begin the process of retrieving and releasing the fact through usage of facts in mathematical problem solving and through fact practice, the third step in math fact fluency.
Implementing the Multi-Sensory Memorization of math facts in your classroom.
The second step of math fact fluency is easy and affordable. Many teachers make over-sized flash cards to flash to their students as they see, hear, and say the facts. There are more than 600 facts in all four operations of addition, subtraction, multiplication and division. Of course, when you add the vertical view to the horizontal view, you now have more than 1200 facts.
Also, mature learners making it to adult hood without learning their facts should be exposed to the facts in a pre-algebraic view, so the language of Algebra will not be foreign to the learner. The pre-algebraic view is also a good challenge and computational fluency prep for students reaching the pinnacle of fact fluency before their average classmates. Once you add the pre-algebraic view to the vertical and horizontal views you now have more than 1800 facts.
Learners of facts, especially young learners, should not be overwhelmed with too many facts at once. It is wise to arrange the facts into small groups or levels. The traditional groups are 1s, 2s, 3s, etc. Math Facts Matter divides addition and subtraction by sums of 5, sums 6 to 10, sums 11 to 15, sums 16 to 20, and 11s to 12s and their INVERSEs. These levels align to grade levels providing better real time practice of facts within classroom curriculum.
Another possible solution, in addition to using over-sized flash cards, is using Power Point slides. The challenge is being able to quickly group and regroup cards and slides by appropriate levels, operations and views. A software program designed to do that is quicker and easier to select facts within perimeters.
In addition, based upon the maturity of the learner, teachers will want to determine how many seconds students view the fact as the see, say and hear the equations. Another consideration is the ability to give even more time to students to write the fact. Writing the facts they see, hear and say provides an opportunity for eye, brain and hand coordination improving the opportunity for long-term memory storage.
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 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 even cross operations including a mixture of addition/subtraction
- How many facts displayed (system randomly pulls the number of facts from selected level)
- How long each fact is displayed (longer for writing the fact)
- Which view or a combination of views (horizontal, vertical and/or pre-algebraic)
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 the fact is replaced.
Accountability for the Mature Learner
For the mature learner that needs external motivation, the accountability of a weekly math fact quiz is no different than 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 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 student at the beginning of the year, give them more time or less 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 watch as these take part. 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. 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!