Making Math Real: The 4 Operations & The 400 Math Facts

Making Math Real: The 4 Operations & the 400 Math Facts

22 half-day Distance Learning Course  |  9:00 am to 1:30 pm daily  [Pacific Time]
Registration Fee:  $2,849 for tuition & materials binder (shipped)
6 optional academic units
 [see below]


MANDATORY PREREQUISITE:  All students who enroll in this course must have completed the Making Math Real: Overview, K-12.

STRONGLY RECOMMENDED:  It is strongly recommended to have also completed Making Math Real: 9 Lines Intensive as this course provides the complete structure for teaching and developing automaticity for the 100 multiplication facts, which greatly supports the content of the 4 Operations & the 400 Math Facts course.  However, it is also possible to complete the 9 Lines Intensive course any time after completing the 4 Operations & the 400 Math Facts course.

COURSE DESCRIPTION:  This course continues the fundamental development from the Overview, K-12 course for implementing a comprehensive, practical, systematic, and simultaneous multisensory structured methodology in basic mathematics.  It is designed for educational therapists, special educators, and elementary and secondary classroom teachers.  Parents and those who consider themselves non-math majors are especially encouraged to enroll.

This course provides the essential foundation upon which all mathematics will develop: the 4 operations and the 400 math facts.   These are the basis for cognitive development K-5, and all mathematical applications through algebra and beyond.  Over the course of 22 half-days, participants learn how to provide students with this crucial foundation in a dynamic, innovative, intensive, hands-on approach that makes learning successful, fun, and accessible for all students.

Topics include comprehensive methods for teaching the acquisition of all math facts, full units in addition, subtraction, basic place value, number concepts, multiplication, and long division (single-digit and double-digit multipliers and divisors).  Extension and enrichment activities for each unit are presented.  These methods are simplified, practical and ready for immediate professional use in classrooms, private practice or at home.

The focus of Making Math Real is the integration of key cognitive developments that directly support executive function in activating and sustaining working memory.  Working memory for math is the perceptual experience of comprehension: knowing and understanding what we are doing throughout problem solving.  Therefore, a significant focus of this course is on the development of math comprehension through concept-procedure integration, which means the concept(s) of the mathematics and its respective procedure(s) are integrated as one.  The principal structure for developing concept-procedure integration in this course is the systematic guidance of student’s processing from the concrete to the abstract, and participants will learn all the specific simultaneous multisensory structured methods for teaching the four operations from the concrete to the abstract.

The structure of concrete to abstract directly supports the successful transfer of students’ hands-on, concrete integration of the mathematics to its specific reconstruction in abstract-symbolic form.  At the abstract level, all of the meaningfulness of the concrete math experience is encoded within the symbols, and the definition of math comprehension is students’ ability to successfully decode and encode the symbolic codes of math.  The successful transfer of the concrete to the abstract means students use their math comprehension to directly activate and sustain working memory.  The successful transfer of the concrete to the abstract is concept-procedure integration by definition: the concrete experience of the math is its concept; and the abstract experience of the math is its respective procedure. Accordingly, the developmental outcome of concept-procedure integration is comprehension.

An additional emphasis of this course is on the development of students’ automaticity with the math facts.  Automaticity with the math facts greatly reduces cognitive load on working memory, thereby allowing students greater access to deeper levels of cognition necessary for problem solving.   Building automaticity with the math facts requires the development of symbol imaging.  Symbol imaging is a visual-perceptual cognitive tool that provides essential working memory support in the development of automaticity with the math facts.  Symbol imaging is the combination of four self-regulatory executive processes enabling us to perceive, hold, store, and retrieve sequences of numerical symbols, and is therefore, the cognitive basis for learning and retaining the math facts.  Participants will learn the comprehensive and different methods for developing students’ symbol imaging for each of the operation-based math facts, because multiplication/division, addition, and subtraction facts have completely distinct symbol imaging structures.

Extensive color-coding is a critical element of the structure. Please bring 4 colored markers or pencils in blue, green, red and black.

Published on August 19th, 2017
The 4 Operations and The 400 Math Facts: The Essential Building Blocks for All Future Mathematics


Optional Academic Credit Costs & Registration: Optional units of credit are available for select courses at the low cost of $134 per unit, paid directly to CSUEB Continuing Education, by the last day of every course.  CSUEB Online credit registration and payment instructions, along with the MMR grading policy, will be provided on the first day of every class. All credit registrations and payments must be submitted online through CSUEB’s website by the end of each course. No exceptions.

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