FAQ

Complementary Mathematics (CM) is not designed to be a complete math curriculum. Using the metaphor of a grocery store, CM does not aspire to be a Food Lion, Whole Foods or Trader Joes, but rather a favorite farm stand where high-quality locally produced organic foods are available on a consistent basis. Our “foods” are the essential skills, understandings, connections and relationships of mathematics (surprisingly not emphasized in many of today’s math programs) –presented in a way that allows students to become familiar with, practice, polish and become proficient at these key targets. And just like adding a helping of farm-fresh vegetables to any meal, these math offerings will also fortify any lesson.

Many educators have noticed that students are exhibiting diminished manual dexterity and stamina when attempting pen and pencil assignments of any significant duration. To address this situation, most pediatric associations recommend that more academic activities return to the paper/pencil format. Additionally, students have been “screen-timing” for up to eight hours or more each day; an unhealthy dosage by any measure. While “virtual learning” activities can be very beneficial, an unbalanced and over reliance on this medium can be harmful – a healthy dose of reality should always be welcomed.

No. Depending on the math program currently being used in your school/district, many of the CM expectations may already be in place. An exercise designed to evaluate your current math program (based on the National Research Council’s recommendations) has been provided under the “Supporting Documents” tab of this website. The CM resources are designed to naturally build on and flow from the expectations of the prior grades. While schools that adopt CM activities in the early grades will find mastery of the math targets more consistently attainable across the progression to higher grades, it is never too late to implement the CM program; far, far better later than never.

Most definitely. Skipping over the foundational concepts, which underlie the understanding/meaning of more complex topics, leads to a fragile and insecure learning of those complexities. Utilizing materials from other grade levels to insure foundational comprehension is imperative in these instances. Conversely, students who have already mastered the materials labeled for his/her grade level will benefit from accessing the activities designated for higher grade levels. For older students who have not had acquired the skills described within this site, the following ancient proverb applies: “The best time to plant a tree was 20 years ago. The second best time is now.”

No and yes. Across all aspects of learning mathematics, a balance and variety of application and process are essential. In general, when working in the problem-solving realm, students need to feel unencumbered by time expectations and constraints. Especially when engaging in advanced problem-solving activities, students need to be methodical in their approaches and be encouraged to explore, investigate, experiment, sketch, estimate, etc. This is best supported by an unhurried and unpressured setting. So, in general, the answer to the speed question in this scenario is no.
Likewise, when initially learning the basic number combinations, the same methodical approach and support structures are critical components in leading to the understanding and eventual “mastery” of these combinations. So, at this juncture, the answer to the speed question is also no. But because these basic combinations form the foundational understandings of all higher mathematics, they need to be truly understood, totally comprehended and accessible over the long term. The need of instant recognition and recall of these basic facts is essential, and whether you refer to it as mastery, automaticity, reflexivity, ownership or whatever else, only the use of time measurement can convey this expectation. Specifically, these time measurements represent the depth of understanding of basic math facts - it is not about attaining some arbitrary clock expectations. So, in general, the answer to the speed question in this scenario is yes. Please remember that the time expectations presented in our website are intended to be used only after many, many opportunities of deliberative practice and not until progress toward mastery is well under way.

Because when used appropriately, time targets are challenging, motivating, and ultimately gratifying. Consider the countless student hours eagerly spent within the domain of computer games—tens, hundreds, sometimes thousands of hours—spent in the pursuit of faster times, higher levels, and ultimate targets. In this arena, time and targets clearly supply the motivation and enjoyment of the experience, quite the opposite of a fear-inducing activity.

We all experience fear/anxiety when we believe we’ll be perceived as inept, incompetent, or inferior. When using our timed math exercises, these negative emotions can be entirely averted by employing the following strategies:

1). Don’t mention time or speed when initially learning the concept; instead, emphasize the importance of the thorough understanding of the concept;

2). When first beginning to time students, do so over small amounts of material so the students can experience success;

3). Highlight that students can practice the materials on their own, as often as they want, in order to become as quick as desired;

4). Recognize each time a student attains a “personal best” while progressing to the stated goal. State explicitly that each student is striving toward a stated goal and not competing with each other. All students can be winners within this context;

6). Avoid situations where a student, or small group of students, finish last when timing an exercise. Conversely, we recommend recognizing the student with the fastest time in any given timing event, as they can serve as an example to their peers and possibly share strategies as to their successful approach.

And always remind all students that they can become as fast as their diligence and perseverance will propel them.

There is both a free and commercial side to our website. On the free side, we have tried to supply abundant samples of most components comprising the CM website. The commercial side of the site provides an expanded offering of all components shown across the free samples. For example: for each fluency anchor and grade level overview presented in the sample side, there are three additional parallel forms provided within the commercial side. Specifically, in addition to the sample forms A and B there exists forms C, D and E (replete with answer keys). These extra forms allow for use of extended practice and mastery, as well as potential assessment opportunities. A similar expansion of instructional videos, targeted topics and problem-solving resources are also included within the commercial site. We have committed to a very nominal fee structure ($2/student per academic year) so that financial constraints will not prevent access to the expanded materials.

No – nor will it ever be. Our vision includes on-going development and expansion across all components of the site. We are hoping to incorporate short instructional videos and other math activities contributed by users of this website; the work of any and all combinations of students, teachers, parents and community members is welcomed for consideration.

The explosion of technology has revolutionized many aspects of everyday life and that is certainly true across our education system. CM embraces the implementation of technology (we are a website after all) to its best possible use. However, technology can never replace understanding, it can only serve to provide additional pathways to get to that understanding. Also, the structure of mathematics has not changed one iota during the past 20 years -or 200 years. So, the longish answer to your question is a resounding yes.

The acronym represents the studies of science, technology, engineering and mathematics. Of these four studies, math stands alone as the foundational literacy upon which the others are built. Without mathematics, the understanding of science cannot be actualized; without math and science, technology and engineering don’t exist. The converse of these statements is obviously not true.

Those students who have not enjoyed any consistent success and satisfaction associated with the understanding of math (or any endeavor) can begin to develop a negative mindset toward the discipline. Indeed, in extreme cases, students can fall victim to anxiety and dread. The remedy to reverse these maladies is success- early, often and on-going success. Successful outcomes in math class can be ensured by building off previously mastered knowledge with small blocks of new but connected materials. Success must be constantly recognized and acknowledged. The 5^th strand of the NRC’s recommendations clearly addresses these circumstances: “Engaging: Seeing mathematics as sensible, useful, and doable – if you work at it – and being willing to do the work.”