What and How of Fluency Anchors

The Fluency Anchors presented here for each grade level, PreK – 8, represent the most fundamental (and important) relationships with numbers: addition/subtraction/ multiplication/division, place value, order of operations, etc. Simply put: they are the building blocks of understanding math. As with most components of the Complementary Mathematics website, several parallel forms of each expectation (goal) are provided in order to allow students the opportunity to develop deep understanding of the topic(s), and then practice, polish and become proficient with that goal. To ensure a comfortable and supportive approach to each new topic, we have found that by focusing on small blocks of the Form A until the student has developed a complete mastery and “ownership” (a can’t be stumped kind of attitude) of that portion of the goal builds confidence, and confidence is the enemy of anxiety. At the early stages of each component, deep, rich and interactive discussion should accompany the completion of the exercises. Students need to hear the thinking and strategies of their classmates and teacher as their understanding begins to deepen around the topic. No student should ever feel rushed or pressured when first learning and understanding the Fluency Anchors. Student discussion should also include the reality that people of all ages learn different topics at different rates and additional practice when necessary is not only permitted, but highly recognized and praised. Specifically stated: the learning expectations remain the same for all students, the amount of time and practice to achieve those expectations vary with the respective needs of the learner.

The scientific findings of brain activity around learning math (see graphic under research tab) clearly show that the number of reinforcements/repetitions applied is directly related to the level of understanding attained. We have found that 4 -5 minutes a day, every day, provides for a sound opportunity for learning. Even better, an additional 4 -5 minute session as a homework component will enhance the learning.

After the examples on Form A and Form B have been thoroughly utilized and mastered, additional parallel forms can be created by the teacher/class for enhanced understanding, or can be purchased on the commercial side of this website. Total mastery of these goals (which includes instant recognition and recall of the materials) fits the definition of two of the five strands of math proficiency as defined by the National Research Council’s findings: Strand #2 –Computing: Carrying out mathematical procedures, such as adding, subtracting, multiplying and dividing numbers flexibly, accurately, efficiently, and appropriately; and Strand #5 – Engaging: Seeing mathematics as sensible, useful, and doable – if you work at it – and being willing to do the work.

Also provided here are suggested time targets for each Fluency Anchor. They are supplied to give students/teachers some parameters around how efficient (fast) is fast enough. While the suggested times may seem too aggressive at first, most students can easily reach them when using a consistent approach to practicing the Fluency Anchors. Going forward, our goal is to collect sample videos of various students, at each grade level, completing the Fluency Anchors in about half of the time listed in the respective expectation chart. In the meantime, we have provided some short instructional videos highlighting the essence of various math understandings connected to the Fluency Anchors.

Students take their cues from their teachers and other supporting adults. Teachers who model authentic energy, enthusiasm and appreciation for learning/mastering these Fluency Anchors will find their students adopting and embracing these same characteristics!