WELCOME TO THE MAKING MATH REAL: OVERVIEW, K-12
Transformative as an Introduction, Invaluable as a Repeat
Recently I have been extremely pleased to note the number of experienced Making Math Real practitioners who have elected to take the Making Math Real: Overview, K-12 course again. The unanimous motivation: “There are so many layers of learning and understanding in the Overview, and now that I really understand how MMR works, I am ready to make all those deeper connections”.
What Makes Making Math Real Different?
This is one of the most frequently asked questions we receive, and its answer is the basis of the Making Math Real: Overview, K-12. The Overview course is extremely voluminous and provides the necessary introduction to the structure and methods of Making Math Real to prepare educators for the up to 680 hours of content courses that follow (see the full list of courses here). The introduction is necessary because the Making Math Real simultaneous multisensory structured methods are historically unprecedented. Making Math Real is the first and only comprehensive pre-K through calculus prescription for teaching that emphasizes integrating the development of executive function and working memory within every math lesson. The focus on the development of the essential self-regulatory executive processes that directly support students’ abilities to initiate, activate and sustain working memory distinguishes Making Math Real from every other method, program, textbook, or software.
Functional Math Education: Addressing the Root Cause Rather than Treating the Symptom
Working with thousands of students and teachers nationwide over the last 43 years has consistently indicated to me that any degree of math struggle is not related to students’ lack of math ability, intelligence, or motivation. Rather, the root cause(s) for challenges in learning math is more related to teaching practices that do not activate students’ working memory and/or relative underdevelopments in students’ executive processes that support working memory, because without sufficient ability to activate and sustain working memory, students cannot access their native intelligence, and therefore, are unable to express what they know.
Therefore, a major emphasis of the Making Math Real: Overview is the introduction to the connection that we can successfully teach all students once we understand this developmental basis for successful teaching and learning, because the profound limitation affecting math education, has been and continues to be, focusing entirely on math content skills disconnected from the development of the self-regulatory executive processes that directly support students’ abilities to initiate, activate and sustain working memory. Without working memory activated, students are “perceptually blind” and consequently must rely on procedural memory rather than understanding and knowing what they are doing.
I have seen innumerable math programs come and go, and each new version is a repackaging of math content that has yet to address the developmental basis for successful teaching and learning. This is why there has been no effective positive change in math education outcomes across the decades (according to research data), in particular for the gap in achievement and special needs populations.
From the “2018 Brown Center Report on American Education: How Well are American Students Learning?”:
“…Since NCLB’s (No Child Left Behind) early years, scores have largely plateaued at levels of nationwide performance that many Americans find underwhelming, leaving still-large gaps between historically advantaged and disadvantaged groups.”
And from “NAEP (National Assessment of Educational Progress), the Nation’s Report Card: 2015: Mathematics and Reading at Grade 12”:
“In comparison to 2013, the national average mathematics score in 2015 for twelfth-grade students was lower” and “In comparison to the first year of the current trendline, 2005, the average mathematics score in 2015 did not significantly differ.”
Research has identified the critical value of executive function and working memory in student success in math, even to the extent that by kindergarten, a student’s relative development of several key self-regulatory executive functions and working memory predicts future success or struggles in math. Research has identified the source of the problem, but unfortunately has yet to propose any specific, direct, and practical way to incorporate it into teaching.
Making Math Real is the first and only to successfully integrate research within its methodologies, and this is another major emphasis of the Overview: present the research, define working memory, present which self-regulatory executive processes directly support working memory, and how to structure these developments while teaching math.
The Main Takeaways from the Making Math Real: Overview
In support of the multifaceted focus of the Overview, the course is organized into three main sections: 1) Pedagogy 2) Structure 3) Sensory-Cognitive Development. The following are some of the main takeaways from each of the three sections.
Pedagogy: The Research Connections
from Cognitive Science and Neurobiology
- Making Math Real is for all students, not just for those who struggle or who have special needs
- Math should never hurt
- How Making Math Real is different from every other method, program, textbook, or software
- Direct, explicit, sequential, incremental, systematic, connected, and simultaneously multisensory structured
- Math is a perfectly interconnected architecture in which any concept/application taught in any grade has direct connections to the math coming in later grades
- “It’s the teaching that ensures success, not the program”: the art and science of teaching math
- The research connections from cognitive science and neurobiology that define how the brain does math and how Making Math Real puts this research directly into teaching practice
- The connection of finger gnosis and the left angular gyrus and their relationship to number processing
- Define executive function, working memory, and processing as well as their function in supporting math learning and how to integrate their development within every math lesson
- Top-down and bottom-up: the two-way relationship between executive function development and processing development
- The development of executive processes takes time, many of which needed for success in math develop beyond the k-12 years
- Working memory is comprehension and comprehension means “You know that you know”, not the memorization of procedural commands disconnected from comprehension
- Diagnostic teaching: clinical observations of students’ affective and cognitive behaviors provide basis for adapting curriculum delivery
- Define simultaneous multisensory structured methods
- Making Math Real is a clinical methodology that empowers educators to prescriptively reach all students and is not a program (curriculum)
- Making Math Real simultaneously serves Response To Intervention (RTI) tiers 1 through 3 students
- The two strands that develop numeracy, what numeracy means, and the two distinct brain activations that support the development of numeracy: exact math and approximate math (mental math)
- Define “Codes of Math”: a system of interconnected codes from pre-k through calculus that provide user-friendly symbolic codes to express what is real
- Decoding and encoding in math, equally as important in math as they are in reading
Structure: The Hands-On Section
- Nothing succeeds like success. Frustration, anxiety, and confusion are not helpful in fostering student grit and persistence
- The structure, what it means and its role in successful teaching: guaranteeing successful processing
- Two different structures spanning k-12: Concrete to Abstract for k-5, Integrity of Incrementation for pre-algebra through calculus
- The developmental focus for activating working memory: symbol imaging for k-5, detail analysis for pre-algebra through algebra 2
- Simultaneous multisensory structured methods: in-class demonstrations of concrete to abstract and integrity of incrementation
- Incrementaton: each current learning activity builds the tools for the next learning activity, and each next learning activity adds only one new element
- The successful transfer of the concrete, hands-on experience to the abstract symbols
- A true concrete experience is far more than using manipulatives
- Using the mathematically correct manipulatives: not just any manipulatives will do
- Developing the language of math
- The essential use of gestures and prompts: centralizing students’ perceptual focus
- Providing effective scaffolding to support students’ working memory and executive function
- Developing students’ independent processing ability
- Differentiated structures of teaching
- Creating comprehensive and prescriptive problem sets
Building the Tools of Working Memory
- The role of symbol imaging for learning and retaining the math facts
- The activation and development of symbol imaging while teaching the multiplication facts
- The critical distinction between authentic processing and rote processing: rote processing is anathema and must be avoided at all times
- “The Antidote to Rote”: automaticity with the math facts: fluent retrieval and storage does not mean rote memorization
- Automaticity with the math facts significantly reduces cognitive load enabling increased access to working memory to support math reasoning and problem solving
- Focus on central processing: perception and association: imaging and organized storage
- Developing processing speed, cognitive efficiency, and cognitive endurance
- Math facts speed tests are strongly contraindicated
Epiphanies for Some, Synthesis for Others
The Making Math Real: Overview course is an intensive, exciting, and rewarding learning experience, and whether you are new to Making Math Real or a returning Making Math Real practitioner seeking synthesis, I look forward to seeing all of you in a future Making Math Real: Overview course.