# From the Desk of David Berg, E.T. – New Course Change

## NEW COURSE CHANGE

### The 9 Lines Intensive is Now a Prerequisite Course for the 4 Operations and Fractions Courses (and All the Higher Level Courses)

The 9 Lines Multiplication Fact Acquisition and Application Strategy® is the most internationally renown of all the Making Math Real Simultaneous Multisensory Structured Methodologies K-12. It is extremely effective, powerful and develops the automatic retrieval and immediate application of the 100 multiplication and the 100 division facts, which I consider to be the most valuable mathematical developments students achieve in the elementary grades.

Automatic retrieval of the multiplication and division facts significantly reduces cognitive load within all problem solving related to multiplication and division involving whole numbers, fractions, decimals, polynomials, rationals, exponents, logarithms, etc. Therefore, once the 9 Lines Multiplication Fact Acquisition and Application Strategy® has been introduced to students, it provides the necessary fact finding basis within the vast majority of problem solving content areas in mathematics from the time of its introduction (typically in early third grade) through calculus and beyond. Since the 9 Lines has direct connections to and applications for all the higher level Making Math Real courses: the 4 OperationsFractionsPre-AlgebraAlgebra 1, Algebra 2, and Geometry Part 1 and Geometry Part 2, the 9 Lines Intensive course is now a mandatory prerequisite for all these higher level Making Math Real courses (see the List of Prerequisites).

PRE-ALGEBRA READINESS: THE 4 OPERATIONS THROUGH FRACTIONS AND DECIMALS AND THE 400 MATH FACTS

Completing fifth grade does not necessarily indicate students’ readiness for pre-algebra – only the full concept-procedure integration of the four operations through fractions and decimals and automaticity with the 400 math facts does. Success in pre-algebra relies heavily on the developments achieved in the elementary grades because the major fundamental for elementary grades mathematics is addition, subtraction, multiplication, and division through fractions and decimals when we know how much we have; and the major fundamental for algebra is also addition, subtraction, multiplication, and division through fractions and decimals, but in algebra, we may not know how much we have, because in algebra, there are variable expressions and variable equations. Additionally, the combination of learning fractions and decimals across the four operations and developing automaticity with the 400 math facts during the elementary grades directly supports the development of automaticity with the integer facts and rational numbers applications across the four operations necessary for simplifying variable expressions and solving variable equations. To cover this voluminous and essential foundation in elementary grades mathematics, I have created two seminars: Making Math Real: The 4 Operations & 400 Math Facts and Making Math Real: Fractions, Decimals & Advanced Place Value.

SINCE SO MUCH OF THE CONTENT IN THE 4 OPERATIONS AND FRACTIONS COURSES IS BASED ON THE 9 LINES, IT PROVIDES MAXIMUM ADVANTAGE TO HAVE TAKEN THE 9 LINES INTENSIVE PRIOR TO THESE COURSES

The most immediate practical applications of the 9 Lines Fact Acquisition and Application Strategy® is structured for all the math in third through fifth grades that is related to multiplication and division with whole numbers, fractions and decimals. But the 9 Lines is related to much more than just the applications of multiplication and division. The 9 Lines is used to teach the Doubles addition facts and provides necessary support for almost all fraction applications including finding lowest terms and equivalent fractions, addition and subtraction with proper and mixed fractions with unlike denominators, Greatest Common Factors, cross simplifying fractions, Least Common Multiples, factoring whole numbers, primes and composites, prime factorization, transformations of mixed and improper fractions, comparing and ordering fractions, exponents, and more. All the math just listed is presented in the two essential foundational courses for pre-algebra readiness, Making Math Real: The 4 Operations & 400 Math Facts and Making Math Real: Fractions, Decimals & Advanced Place Value. In addition to learning the world’s best methodology for teaching the multiplication and division facts, learning the 9 Lines before enrolling in either of the two essential foundational courses provides maximum advantage for all Making Math Real course participants.

TO FACILITATE FULFILLING THE 9 LINES INTENSIVE PREREQUISITE FOR THE 4 OPERATIONS AND FRACTIONS COURSES, IT IS OFFERED TWO TIMES PER YEAR, EVERY YEAR

Making Math Real: The 9 Lines Intensive is offered twice each year, in spring and summer, and each offering is scheduled immediately after the spring and summer Making Math Real: Overview K-12. Every year there are two opportunities to complete the powerful 9 Lines Intensive prior to either of the two essential foundational courses, Making Math Real: The 4 Operations & 400 Math Facts and Making Math Real: Fractions, Decimals & Advanced Place Value, each of which is offered every other fall. The next Making Math Real: The 4 Operations & 400 Math Facts is scheduled for fall 2023, and the next Making Math Real: Fractions, Decimals & Advanced Place Value is scheduled for fall 2024.

DO NOT MISS OUT ON TAKING THE TWO MAKING MATH REAL ESSENTIAL FOUNDATIONAL COURSES – MAXIMIZE YOUR ADVANTAGE AND MAKE YOUR PLAN TO ENROLL IN THE 9 LINES INTENSIVE NOW

Please visit the Making Math Real Calendar for Courses and List of Prerequisites pages to help you plan for the courses you want and need.

Be well and stay healthy.

David Berg, E.T.
Founder & Director of the Making Math Real Institute
Creator of the Making Math Real Simultaneous Multisensory Structured Methods

SAVE THE DATE
The Spring 2023 semester opens for registration on Oct. 26 @ 9:00 am PT and includes the Overview K-129 Lines Intensive and new Mental Math Intensive mini-course.

# From the Desk of David Berg, E.T. – Spring Sneak Preview

## SPRING SNEAK PREVIEW EDITION

### Announcing a Brand New Intensive Mini-Course Coming This Spring: Making Math Real: Mental Math

The Mental Math Intensive Mini-Course will provide an unprecedented focus on purely mental math applications that have never been presented in any Making Math Real course to date, which include incremental progressions of mental math applications and development focusing on the expansions of the math facts across the four operations to support mental multi-digit problem solving.

The focus of the Mental Math Intensive will be on:

• Brand new material, never before presented in any MMR class
• Extensions for all students as well as accelerated learners
• For all 4 operations math facts
• Expansions of the addition and subtraction facts with specific mental applications within two and three-digit addition, subtraction, and multiplication problem solving
• Expansions of Balancing 0s to introduce “Simplifying 0s”
• Expansions of the division facts in combination with increasing and decreasing decimals by powers of 10 to mentally solve multi-digit decimal and whole number division problems
• Mental solving for missing addends, minuends, and subtrahends in 1, 2, and 3-digit problem solving
• Deepen integration of symbol imaging
• Increasing and decreasing by powers and multiples of 10 using multiplication and division
• Opens the door to the unlimited expansions for accelerated learning

As presented in the Making Math Real: Overview K-12, the development of numeracy is based on two separate domains of mathematical processing and development:

1. Exact Math: the paper-pencil-based algorithmic structures of problem solving.
2. Approximate Math: the integration of mathematically-based organizational structures supporting mental math applications including estimation and numerous forms of mental problem solving.

Each of these domains is completely distinct in terms of the way the brain activates and applies their respective structures, and therefore, the way in which we structure their respective instruction to students is also completely distinct. Exact Math is a parietal-temporal integration and its instructional structure is both “concrete to abstract” and the “integrity of incrementation”; and Approximate Math is a frontoparietal integration that relies heavily on the development of a significant array of regulatory executive processes that support front-to-back connections in the brain as well as the integration of a strong number sense-based mental organizing system. The way the brain processes each of these is entirely different, so all instruction must account for these differences, therefore, we do not use paper-pencil structures to teach and apply mental math structures, and we do not use mental math structures to teach and apply paper-pencil structures.

The successful and comprehensive development of numeracy requires balanced distribution of paper-pencil and mental math instruction and development across the grades K-12, and it is incumbent upon all math educators to account for this distribution within lesson planning and scopes and sequences within and across the grades.

OPENING A DOOR

Although there are ample inclusions of mental math structures and development throughout all the Making Math Real courses, this new Mental Math Intensive Mini-Course will provide an unprecedented focus on purely mental math applications that have never been presented in any Making Math Real course to date. These unique mental math incremental structures are also part of, and open the door to another domain of Making Math Real that has never been presented publicly: Making Math Real for the accelerated learner.*

* Important Note: The mental math structures included in this mini-course are intended for ALL students, not just for the accelerated math student.

The mental math incremental structures presented in this new Intensive Mini-Course will introduce the earliest levels of expansions to the basic MMR structures, and will provide the basis for possible ongoing expansions outside the parameters of this introductory course. Therefore, all the mental math methods presented in this course are appropriate for all students, not just for accelerated students.

THE FOCUS

Since the development of automaticity is far more challenging for the addition and subtractions facts, the focus of this mini-course will be on the expansions of the addition and subtraction facts with specific mental applications within two and three-digit addition, subtraction, and multiplication problem solving as well as deepening the developmental integration of symbol imaging. In addition, mental applications for solving for missing addends, minuends, and subtrahends will be included, which provide the specific organizational structures for solving the more challenging addition and subtraction-related word problems. Lastly, mental applications of multiplication and division for increasing and decreasing by powers and multiples of 10 will be included to support mentally solving multi-digit whole number and decimal division problems.

Since all the content in the Mental Math Intensive Mini-Course is based on the content from Making Math Real: The 4 Operations & 400 Math Facts, all participants must have successfully completed Making Math Real: The 4 Operations & 400 Math Facts course to enroll in the Mental Math Intensive Mini-Course.

The Making Math Real Mini-Intensive Courses provide rare opportunities for receiving specialized content that is not presented in the regular courses – ONCE OFFERED, EACH INTENSIVE MINI-COURSE MAY NOT RETURN TO MMR’S CALENDAR FOR COURSES FOR SEVERAL YEARS. They are not to be missed.

Be well and stay healthy.

David Berg, E.T.
Founder & Director of the Making Math Real Institute
Creator of the Making Math Real Simultaneous Multisensory Structured Methods

# From the Desk of David Berg, E.T. – Back to School Edition

## BACK TO SCHOOL EDITION

### Math Means You Know That You Know, And If You Know, You Know Making Math Real is the Gold Standard of Math Education

Math means knowing that you know – not memorizing what procedure to use. There is a profound distinction between the two: the former refers to a deep integration of knowledge and comprehension in the brain and in the body, and the latter refers to applying a memorized series of procedural commands that do not require comprehension of the application, rather, sufficient access to memory in remembering what to do.

THERE’S NO MATH IN IT!

Since the teaching of math so frequently presents instruction as a series of commands to be memorized, instructional practices also frequently attempt to rely on procedural catch phrases such as “carry the 1′, “copy (keep), dot, flip”, “do the opposite” or “slash and dash”, “north and down”, “move the decimal to the right (or left)”, or “daddy-mommy-sister-brother” to help students to try to remember what to do. All these representative examples of procedural commands are dissociated from the comprehension of the mathematics that underlie the creation of them; and this is important to understand: the procedural commands replace the actual mathematical functions and applications – just do __. Furthermore, throughout my time in school and what I continue to observe occurring in classrooms, is these catch phrases are delivered as a hope and a prayer that the students will “just remember”.

• “Carry the 1” refers to renaming in addition or multiplication when a sum or product is between 10 and 19 inclusive in a place, and the new value, the “1”, is carried to the next place. The digit that is carried is expressed as a “1”, but it is referring to 1 new ten, or hundred, or thousand, etc., not a “one”.
• “Copy, dot, flip” is referring to the transformation of a divisor to a multiplier when dividing fractions. Since the catch phrase has no connection to the reasons why the divisor is transformed to a multiplier or to why it is exclusively the operator (divisor) that is “flipped”, students frequently forget which operand gets flipped, so they may flip the first fraction, or to be safe, flip them both, so the catch phrase is attempting to help them remember what to do, but without any understanding of why: copy: keep the first fraction the same; dot: multiply (the dot expresses multiplication); flip: make the reciprocal of the second fraction.
• “Do the opposite” and “slash and dash” refer to subtraction with integers. However, the failure rate with these catch phrases is exceedingly high as, unlike “copy, dot, flip” it does not attempt to account for which integer is to be transformed to its opposite signage. Consequently, since this catch phrase is dissociated from all conceptual connections to transforming signage as well as why subtraction with integers requires this transformation, students are frequently ungrounded and disconnected as they cannot remember which of the integers needs the opposite signage (the operator, not the operand). Frequent error response includes making the first and/or both the first and second integers with opposite signage; and since this procedural command has no grounding with the function and purpose of operations, comprehension of signage, and the understanding of why this is necessary, students feel free to do whatever – there’s no meaning to it anyway… just like “copy, dot, flip”…
• “North and down” refers to where the numerator goes: “n” for north goes with “n” for numerator, and “down” refers to where the denominator goes: “d” for down goes with “d” with denominator. This catch phrase is only targeting where each part of a fraction “goes” rather than the comprehension that “numerator” literally means “the one who numerates, which means the one who counts; and we count to find out how many; and denominator literally means the “one who names the group”. In addition, the fraction bar refers to “of the”, so the comprehension of all fractions is “how many of the group” which directly indicates “how many” is up, “of the” is the fraction bar in the middle, and “group” is below to express the totality: how many of the group.
• “Move the decimal to the…” refers to increasing or decreasing decimals by powers of 10. Moving the decimal is mathematically impossible because the decimal (point) is a symbolic wall that separates whole units from parts of a unit, and that “wall” can never be moved. Furthermore, this catch phrase requires “moving the decimal” in the opposite direction indicated: if increasing, the decimal is moved in the direction of decreasing; and if decreasing, the decimal is moved in the direction of increasing.
• “Daddy-Mommy-Sister-Brother” refers to an incomplete mnemonic device to help students remember to Divide-Multiply-Subtract-Bring down for long division applications. First, this mnemonic omits the crucial application of checking the values of the differences made from the “Subtract” step. However, most importantly, this catch phrase, similar to “north and down” for fractions, only targets remembering what to do: Divide-Multiply-Subtract-Bring down, but it does not provide any comprehension for why do we divide – what does divide tell us? Why do we multiply – what does multiply tells us? Why do we subtract – what does subtract tell us? Why do we check and for what are we checking? Why do we bring down – what does bring down tell us?

Since these catch phrases are all dissociated from the comprehension of why we do these things, I refer to each and all of these instructional practices as “There’s no math in it!”. I believe the reason math is so frequently taught as a series of procedural commands is due to an ongoing long-term cycle of educators passing on the same procedural commands they learned in school to their students without questioning and investigating what the actual comprehension and meaning of the mathematics really are.

WOULDN’T YOU LIKE TO LEARN THE
“WHY” OF THE MATH, ALL THE MATH?

Math means you know that you know, and wouldn’t you like to learn the “why” of all the math mentioned above as well as ALL the math from pre-k through calculus? Then, I look forward to seeing you in an upcoming Making Math Real: Overview K-12.

IF YOU KNOW, YOU KNOW MAKING MATH REAL IS THE GOLD STANDARD

Register Today to join me at the next online Overview K-12 course
for parents & educators on Aug. 27-28 through Sept. 10-11, via Zoom.

Be well and stay healthy.

David Berg, E.T.
Founder & Director of the Making Math Real Institute
Creator of the Making Math Real Simultaneous Multisensory Structured Methods

# From the Desk of David Berg, E.T. – Special Summer & Fall Edition

#### Completing the 9 Lines Class Before the Fractions Class: The Highest Advantage for Maximizing Your Learning

For those of you new to Making Math Real, The 9 Lines Multiplication Facts Acquisition and Applications Strategy is the best known and most widely practiced of all the Making Math Real Simultaneous Multisensory Structured Methodologies K-12 around the world. The 9 Lines is extremely effective, powerful, and develops the automatic retrieval and immediate application of the 100 multiplication and the 100 division facts. I consider the development of automaticity with the multiplication and division facts to be the most valuable development during the elementary grades.

Once students have learned the 9 Lines in early 3rd grade, the structured applications of the 9 Lines will directly support almost ALL the math content areas that follow including all multiplication and division applications for whole numbers, fractions, and decimals, primes and composites, factoring: whole numbers and prime factorization, finding greatest common factors and least common multiples, exponents, and most significantly, FRACTIONS, and this is only referring to grades 3, 4, and 5! 9 Lines applications also support the vast majority of math content from pre-algebra through calculus.

SUCCESS WITH FRACTIONS IS BASED ON 9 LINES APPLICATIONS, SO I CREATED THE 9 LINES STRUCTURE AND FORMAT SPECIFICALLY TO SUPPORT SUCCESSFUL FRACTIONS PROCESSING

Almost all fraction applications require automatic retrieval of the multiplication and division facts: the four operations with fractions, especially addition and subtraction with proper and mixed fractions with unlike denominators, lowest terms and equivalent fractions, transforming mixed and improper fractions, and comparing and ordering fractions. Over the five decades I have been an educator, there has been an 80% failure rate nationwide (Hard Lessons: Why Rational Number Arithmetic is So Hard for So Many People, Siegler and Lortie-Forgues, 2017) for fractions and a major contributing factor has been students’ lack of automaticity with the multiplication and division facts. A key representative example of the significant need for automatic retrieval of the multiplication and division facts for processing fractions is the ability to find the greatest common factor (GCF) of two products. The ability to find the GCF of two products in which the GCF is ≤ 9 accounts for nearly all fractions applications in the elementary grades, and I created and designed the 9 Lines structure and format specifically to maximize students’ mental ability to find the GCF of two products in which the GCF is ≤ 9. The most prominent and powerful application of finding the GCF of two products is in simplifying equivalent fractions to lowest terms and generating equivalent fractions; and in using the 9 Lines, students can mentally simplify or generate equivalent fractions immediately.

MAKING MATH REAL: FRACTIONS, DECIMALS, and ADVANCED PLACE VALUE IS SCHEDULED FOR THIS FALL…

Baseline readiness for pre-algebra is the comprehensive integration of the four operations for whole numbers, fractions, and decimals and automatic retrieval of the 400 math facts. This crucial fundamental for algebra readiness is the basis for the two biggest Making Math Real courses: The 4 Operations & the 400 Math Facts and Fractions, Decimals & Advanced Place Value. Both of these courses are primarily based on the 9 Lines applications, and whereas I have not made the 9 Lines Intensive course a mandatory prerequisite course for The 4 Operations & the 400 Math Facts and Fractions, Decimals & Advanced Place Value, perhaps I should have… All MMR participants who have completed the 9 Lines Intensive prior to these courses have the highest advantage in maximizing their learning experience in these two seminal courses.

Rather than making the 9 Lines Intensive a required prerequisite for The 4 Operations & the 400 Math Facts and Fractions, Decimals & Advanced Place Value, I have instead, encouraged all of you to complete the 9 Lines Intensive prior to taking these courses by consistently scheduling 9 Lines Intensive courses after the Overview course two times per year; and on the Recommended Course Sequence Guide, I have prominently placed the strongest recommendations for completing the 9 Lines Intensive prior to enrolling in The 4 Operations & the 400 Math Facts and Fractions, Decimals & Advanced Place Value.

#### …AND THE NEXT 9 LINES INTENSIVE IS SCHEDULED FOR THIS SUMMER, SO YOU CAN COMPLETE THE 9 LINES CLASS BEFORE THE FRACTIONS CLASS THIS FALL

The next Making Math Real: The 9 Lines Intensive is scheduled for June 20 – 28, 2022, and will not be offered again until February 2023; and the next Fractions, Decimals & Advanced Place Value class will not be offered again until Fall 2024. This summer’s Making Math Real: The 9 Lines Intensive is the best opportunity to take advantage of this optimal timing for maximizing your learning of MMR right now.

Don’t miss out!

Be well and stay healthy.

David Berg, E.T.
Founder & Director of the Making Math Real Institute
Creator of the Making Math Real Simultaneous Multisensory Structured Methods

# From the Desk of David Berg, E.T. – Special Summer Edition

#### “Uncertain Times”Algebra 1 Pop-Up Discounts

These are still extremely uncertain times. Since the onset of the COVID 19 Pandemic in 2020, Making Math Real, in the effort to keep providing our series of courses, has shifted from in-person classes to a distance learning format via Zoom; and now, in May 2022, we still have no stable understanding of the ongoing impact of the pandemic, as recently there has been a significant increase in new cases of COVID.

ALGEBRA 1 IS THE ESSENTIAL FOUNDATIONAL DEVELOPMENT FOR HIGH SCHOOL MATH

Despite the uncertainty of the times, it is always part of the vision and mission of the Making Math Real Institute to continue to maximize a positive impact on the delivery of math education, and in that spirit, we want to maximize the positive impact of the upcoming Making Math Real: Algebra 1 course starting on June 30 – August 5. Algebra 1 is the essential foundational development for high school math, especially for algebra 2, pre-calculus, and calculus. Just as Making Math Real: The 4 Operations & 400 Math Facts is the essential foundational course for elementary grades mathematics, so too, is algebra 1 equivalent in its foundational importance to the development of higher mathematics.

THE ALGEBRA 1 CLASS WILL NOT BE OFFERED AGAIN FOR YEARS TO COME

Therefore, we want to encourage all of you who are ready for the Making Math Real: Algebra 1 class, (meet all prerequisites – for a list of Algebra 1 prerequisites, click here) first-timers or repeaters, to benefit from this last chance for the Algebra 1 course that will not be available again for years to come.

## Unlimited 50% OffRepeat Discounts

In maximizing our effort to encourage all of you to benefit from the upcoming Algebra 1 class this June, we are offering two special “Uncertain Times Pop-Up Discounts”. The first discount is for MMR participants who are enrolling in Algebra 1 for the first time: 10% Off discount; and the second discount is for MMR Participants wishing to repeat the Algebra 1 class: unlimited 50% Off Repeat discounts!

This will be the last offering of Algebra 1 for years to come — Don’t miss out!

We hope the offer of these two “Uncertain Times Pop-Up Discounts” encourages you to benefit now rather than having to wait for years before the next Making Math Real: Algebra 1 course will be offered again.

Be well and stay healthy.

David Berg, E.T.
Founder & Director of the Making Math Real Institute
Creator of the Making Math Real Simultaneous Multisensory Structured Methods

# Looking Forward to the Next 25 Years – Part 7

#### Part 7:NEW 9 Lines In-ServiceThe 9 Lines: The Most Renown of the MMR Strategies

The 9 Lines Multiplication Fact Acquisition and Application Strategy is the most internationally renown of all the Making Math Real Simultaneous Multisensory Structured Methodologies K-12. It is extremely effective, powerful and develops the automatic retrieval and immediate application of the 100 multiplication and the 100 division facts. Automatic retrieval of the multiplication and division facts significantly reduces cognitive load within all problem solving related to multiplication and division involving whole numbers, fractions, decimals, polynomials, rationals, exponents, logarithms, etc. Therefore, once the 9 Lines Multiplication Fact Acquisition and Application Strategy has been introduced to students, it provides the necessary fact finding basis within the vast majority of problem solving content areas in mathematics from the time of its introduction (typically in early third grade) through calculus and beyond.

#### Delivering the 9 Lines Appears Deceptively Simple

As with all the Making Math Real Simultaneous Multisensory Structured Methodologies K-12 I have created, the 9 Lines has been engineered to provide maximum cognitive efficiency and power while requiring minimum cognitive load. This means all the multifaceted detail layers of structure embedded within its instruction are extremely specific and distilled; that any omissions, substitutions, changes in sequence, or other errors of commission will mitigate its power. However, from an uninformed perspective, the 9 Lines looks so simple, which is why so many, having witnessed its power and without proper instruction, delude themselves into believing, “I get it – I can do that.

Over the past 26 years I have spent countless hours (and funds) getting spurious versions of the 9 Lines in videos, instructional articles, games, materials, etc., removed. In every case these spurious versions of the 9 Lines were completely off-base, eliminating all the specifically engineered promptings, language, sequences, assessments, pacing, guided cognition, and engagement that activate symbol imaging the files of a multiplication table.

More Supervised Practice Is Needed

However, the aforementioned spurious versions are not the only versions of incorrect applications of the 9 Lines I have observed. There have been numerous and varying circumstances that have presented me with the opportunity to see how MMR practitioners who have completed the Making Math Real: The 9 Lines Intensive (even multiple times) are also committing significant errors in their deliveries to students. The error rate is exceedingly high, for which I take some responsibility because when the error rate is so high, even for participants who I know are serious and are trying to deliver the 9 Lines as best they can, it indicates that every 9 Lines course participant needs and deserves extra support beyond what a class can provide; and without this prescriptive support from me, I believe this problem is being exacerbated by MMR practitioners networking with one another as a way to seek support and recommendations on how to deliver the 9 Lines rather than checking in with me.

Prior to the COVID-19 Pandemic when all the 9 Lines classes were in-person, significant practice time within each 9 Lines course was required for all course participants, so I could address participants’ major errors both individually and collectively during the classes. However, even with my ability to correct errors during the course, all students need and deserve additional supervision to ensure they are delivering the 9 Lines correctly. But now with the distance learning version of the Making Math Real: The 9 Lines Intensive course, I no longer can include any class practice as was required in the in-person courses. This has created a serious concern. I need to find a way to provide direct support for all 9 Lines practitioners, whether 9 Lines course participants or MMR practitioners of recent or long-term practice.

#### NEW Clinical Support Service: The 9 Lines In-Service

As a new inclusion in Making Math Real’s services for clinical development, and as an adjunct option separate from the Making Math Real: The 9 Lines Intensive course, I am introducing a new clinical service, “The 9 Lines In-Service” available exclusively to MMR practitioners who have completed The 9 Lines Intensive course. The creation of this new clinical service is in direct response to requests from course participants during 9 Lines classes who have asked if they could send me a video of them doing a 9 Lines with a student(s) and get my feedback. This is a great idea, but there are numerous reasons why this request is untenable during a 9 Lines course, which include:

• The time required for me to review each video followed by my detailed feedback would be minimally two hours per participant
• There is no available time during a 9 Lines class for this feedback
• The nature of the individually prescriptive feedback is highly confidential and requires private and confidential sessions
• There may be indications of extra time needed to address corrections, which may also include new videos sent to me to verify correct 9 Lines delivery and/or provide further corrections/adjustments

#### Send Me a Video Recording of You Teaching the 9 Lines

To get started with the 9 Lines In-Service, I need to observe you teaching an authentic 9 Lines to to a student in a one-to-one setting or to a group of students in a classroom setting. It is required that the student(s) is actually imaging a new table and is not a volunteer who is pretending to image a table so you have the opportunity to practice delivering the 9 Lines. Authentic imaging is imperative because it is necessary to observe the student’s affective and cognitive behaviors that would indicate your delivery of the 9 Lines is having the specific and intended developmental impact of activating symbol imaging. Therefore, you will need to record your representative sample of teaching the 9 Lines on one of the following: Zoom, phone, iPad, computer, video camera, etc. Your recording must show everything the student does including the student’s face while responding to your prompts and everything the student writes during phases 2, 3, and 4. The recording also needs to include you so I can observe your prompts, gestures, pointing, tapping, etc. Therefore, the camera can be placed between your student and yourself in such a way as observing a tennis match at midcourt, including as full a view of both teacher and student(s) as possible.

Please understand that the recordings should not be edited in any way. Each video recording needs to show an authentic imaging experience from start to finish without any interruptions whatsoever. The video recordings are for clinical purposes only and are not about production values or professionally made videos. Please also understand that if the video recordings are not complete or do not appear to be authentic, real time documentations of your 9 Lines delivery, I will request a new video recording before we can continue forward with the 9 Lines In-Service.
The 9 Lines imaging recording must include all aspects of the four phases and four assessment points within the 9 Lines including generating a new table at the very beginning through phase 4 application practice. After I review your video recording, I will schedule a Zoom session with you in which we will watch your video recording together, stopping it as needed for me to provide you with comments and/or corrections and allowing you the time to take notes.

The 9 Lines In-Service is exclusively for those who have successfully completed the Making Math Real: The 9 Lines Intensive at any time, either recently or long ago. For those of you who wish to benefit from this new clinical service:

• To get the 9 Lines In-Service started and scheduled, pre-payment for two hours of my time, (the minimum time needed) will be required. This covers one hour for me to review the video recording and one more hour for me to meet with each participant via Zoom to discuss my feedback.
• Send a link to your video file (and password, if needed) to [email protected] of you doing a 9 Lines imaging through Phase 4 (application practice) with a student who is authentically imaging a new table, not a volunteer subject who already knows the table. If after reviewing the video, I believe more than one hour of intervention time is indicated, I will inform the participant of my estimate for the amount of additional time needed, and pre-payment for the additional time will be required prior to scheduling the intervention session(s) indicated. All videos will be held in the strictest confidentiality and will never be shown outside of the prescriptive relationship of the 9 Lines In-Service, unless the participants (student and teacher) wish to make the video public or agree in writing that permission to show the video has been granted. In addition, MMR will not keep or store any video recordings. Once the 9 Lines In-Service has been completed, all links and/or copies of each video recording will be deleted immediately. All video submissions that do not include a complete 9 Lines imaging, Phases 1-4, will not be acceptable, and I will request a new and comprehensive version. All extra time needed for viewing extra versions of video recordings will be charged at the hourly rate.
• On a case-by-case basis, I may determine that a second video demonstrating a corrected version of delivering the 9 Lines is needed to verify that appropriate corrections/adjustments have been made.

I understand that the prospect of being observed and possibly receiving feedback about errors in one’s earnest attempts to do the best one can, might make one feel vulnerable and intimidated. Please understand that the entire focus for the 9 Lines In-Service is to help support your work as a clinical professional, and is never intended to be any form of qualitative reflection on the ability, character, effort, personality, commitment, dedication or integrity of the practitioner. It is my sincerest intent and hope that all of you would feel safe within this coaching relationship and could benefit from my direct feedback and input.
As an investment in your own future as a clinical practitioner, I hope all 9 Lines practitioners may take advantage of this coaching opportunity to fine tune their ability to deliver the 9 Lines Multiplication Fact Acquisition and Application Strategy correctly.

Be well and stay healthy.

David Berg, E.T.
Founder & Director of the Making Math Real Institute
Creator of the Making Math Real Simultaneous Multisensory Structured Methods

# 25th Anniversary Special: WARNING! How to Find a Reputable MMR Practitioner

## 25th Anniversary Special: WARNING!How to Find a Reputable MMR Practitioner

As Making Math Real continues to increase its reputation and renown, so, too, are the increases in fraudulent misrepresentations of spurious “MMR practitioners”. It is of crucial importance that the public becomes aware of these false advertisements of “certified” and/or “trained” Making Math Real tutors. Please be on the lookout for these frauds as they can cause untold damage for your child. These frauds advertising “Certified MMR tutors” often misappropriate screenshots from MMR’s website that falsely imply they are officially connected to and approved by the MMRI, have never taken an MMR course, and are intending to take advantage of MMR’s worldwide reputation as being the “Gold Standard of Math Education”.

Please see representative fraudulent example below:

### How to Protect Yourselves: Contact MMR Immediately

Whenever seeking professional level services, especially for clinically provided services such as for MMR-based interventions, due diligence is required. It is essential that you thoroughly vet every possible MMR practitioner. For example, in the representative example above, a concerned parent contacted us directly to verify these spurious claims. We provided this parent with questions to ask the frauds, and as expected, they were unable to answer any of the questions and their lies were brought to light. THIS IS HOW YOU CAN PROTECT YOURSELVES: AT ANY AND ALL TIMES, PLEASE CONTACT US AT [email protected] TO VERIFY ANY CLAIMS MADE BY ANY PROSPECTIVE MMR PRACTITIONER, AND WE WILL PROVIDE YOU WITH EVERYTHING YOU NEED TO VET THE PROSPECTIVE MMR PRACTITIONER.

Please understand we cannot publish any of these vetting questions, as this would provide the frauds the opportunities to craft their nefarious and misleading responses.

### Warning Signs

Immediate red flags indicating fraudulent advertising are the inclusion of the words, “certified”, “trained”, “expert”, etc. Making Math Real upholds the strict policy for all course participants to abide by the Making Math Real Institute’s Terms and Conditions, which explicitly state that using the words “certified”, “trained”, “expert”, etc., in reference to one’s MMR practices is strictly prohibited. See the Making Math Real Institute’s Terms and Conditions here.

Another key identifier of potentially fraudulent advertising is the lack of the mandatory Making Math Real Disclaimer, which is required to be placed clearly and in direct connection with the name and background of the practitioner:

REQUIRED DISCLAIMER
Any individual, school, district, or business that lists the use of Making Math Real-based methods is required to include the following disclaimer directly alongside or directly beneath such listing(s):
_______________________, in utilizing Making Math Real® (MMR®) methods, is in no way affiliated with, a member of, or employed by the Making Math Real Institute (MMRI), and does not represent or reflect MMR® or David Berg in any way whatsoever. Neither the MMRI nor David Berg has trained, certified, licensed, monitored, endorsed, recommended, or sponsored _______________________. MMR® is a clinical methodology, not a program or a curriculum, and neither the MMRI nor David Berg monitors, endorses, or accounts for the quality of services provided by _______________________.

### For the First Time in the 25 Years of the Making Math Real Institute’s History, We Will Be Able to Make Referrals to Certified MMR Practitioners.

Up to this current time, the Making Math Real Institute has never conferred certification for any practitioner, and consequently, without having sufficient basis to recommend a practitioner with confidence, we have not made referrals to any practitioner. Starting this year, and through the onset of the Making Math Real Institute’s Lab School Mentorship Program (LSMP), the certification process in the Making Math Real Simultaneous Multisensory Structured Methods has begun, and the names of the Making Math Real certified practitioners will be listed on the Making Math Real Certified Practitioners page on the Making Math Real website. The only referrals given by the Institute for MMR practitioners will be exclusively for Making Math Real Certified Practitioners. Therefore, if you encounter any claims of “certified MMR tutors” please visit the Certified Practitioner’s page to verify the claim; and if the name(s) are not listed on the certification page, then do not use that person(s) to work with your child/student, and please, contact us to let us know the name(s) of the spurious MMR tutor(s).

### The Making Math Real Institute Relies On You!

All of you are our eyes on the world, and over the years many of you have reported to us suspicious or fraudulent activities you have encountered. We deeply appreciate these reports so we may deal with these transgressions directly and continue to decrease the number of misrepresentations and fraudulent claims made by spurious MMR practitioners.

### The Problem with the Word “Trained”

Making Math Real provides intensive and comprehensive professional development, and to date, we have worked with thousands of educators worldwide. In this capacity, we provide workshops, seminars and in-services that range from a 1-day introduction through a series of course work that spans over 700 hours of instruction. Since we have touched so many thousands of educators in such a wide range of formats, we cannot possibly account for each educator’s development and proficiency. And, unfortunately, there have been educators, who after only a 1-day introduction, have inappropriately advertised themselves as “Making Math Real trained.”

As stated above, the word “trained” in reference to MMR practitioners creates an image/sense that the practitioner has achieved a level of competency that can be misleading. Unless a practitioner has completed the Making Math Real Institute’s Lab School Mentorship Program, all they have received is course instruction. Completing a Making Math Real course does not imply that the MMR course participant having received the course instruction is capable of applying those methods with the clinical competency necessary for being successful with your child or student. Making Math Real is a clinical methodology, not a program or a curriculum, and therefore the effectiveness of its application is entirely based on the practitioner’s ability to be prescriptive to students’ processing indications and needs. Someone may have taken all the courses (the courses are not trainings), but this provides no basis for the individual’s ability to apply the methods to a variety of students with diverse processing styles effectively. Training includes both coursework and supervised practicums, not just classes alone.

The following is a crucial understanding for all parents: regardless of the reputation of the school or program, your child’s learning experience is only as good as the teacher in front of your child.

### How To Find a Quality Practitioner Who is Not Yet MMR Certified

Please remember, it is the teaching, not the program that will provide success for your child. The Making Math Real methods are the most comprehensive, systematic, and incrementalized in the world today. However, an educator who merely takes a class does not guarantee that educator’s ability to teach the Making Math Real Simultaneous Multisensory Structured Methods effectively.

### Questions To Ask the Professionals:

LD OnLine offers hundreds of expert-reviewed articles and resources for educators, parents, and others concerned about children and adults with learning disabilities and ADHD:

Stay safe and be well.

David Berg, E.T.
Founder & Director of the Making Math Real Institute
Creator of the Making Math Real Simultaneous Multisensory Structured Methods

# Looking Forward to the Next 25 Years – Part 6

#### Part 6:Personal Transformations: A Celebration and a Request

The entire reason I decided to go public with Making Math Real 25 years ago was to help effect positive changes in math education. Now, as part of celebrating 25 years of changing lives, I feel it is important to celebrate and acknowledge all the successful MMR participants who have provided so much positive educational service. Many of you over the years have expressed to me your personal transformations of growth and development as a result of helping others grow, develop, and achieve; and I believe the positive impact in changing your students’ lives and your personal transformations of growth and development are of equal value and benefit.

In celebration of those steadfast MMR practitioners, who in addition to changing the lives of their students, have also experienced their own personal transformations, I am sending out the request to share your stories of having experienced powerful, personal transformations as educators, clinicians, math learners, and as human beings. Your stories of personal transformation, like your stories of changing your students’ lives, will again provide invaluable inspiration and motivation for countless others seeking to help their children/students. Please feel free to remain anonymous as your stories need not include any identifying information (unless you want to). I hope to continue publishing your stories for years to come.

Next Up:
Introducing “Clinician’s Corner”

Clinician’s Corner will start out as a monthly online open discussion group via Zoom in which I will respond to questions/requests from MMR practitioners. The intended format of Clinician’s Corner is to encourage questions and support pertaining to the clinical aspects and applications of maintaining MMR-based interventions, specifically the development of practitioners’ abilities to engage their clinical observations and diagnostics of students’ affective and cognitive behaviors. Clinician’s Corner is structured and intended for intermediate through advanced practitioners who have completed a baseline of coursework and have been applying MMR-based methods for students at various levels and diverse processing styles.

So please stay tuned for the final installment of “Looking Forward to the Next 25 Years” for the full description of “Clinician’s Corner”, the exciting new inclusion in the Making Math Real Institute’s commitment to providing significant support in helping MMR practitioners maximize their development as clinical math educators.

Be well and stay healthy.

David Berg, E.T.
Founder & Director of the Making Math Real Institute
Creator of the Making Math Real Simultaneous Multisensory Structured Methods

# Looking Forward to the Next 25 Years – Part 5

#### Part 5:Making Math Real Build Your Own Group Consulatation Program

In looking forward to the next 25 years, the Making Math Real Institute (MMRI), in addition to continuing its focus on providing and expanding the 700 hours of seminars currently available, will present a new focus on providing significant support in helping MMR practitioners maximize their development as clinical math educators. I will be offering the following new structures to implement this new focus on the clinical development of MMR practitioners and all will be presented in a distance-learning format:

BUILD YOUR OWN GROUP CONSULTATION PROGRAM (BYOG)
Distance-Learning Format

The Making Math Real “Build Your Own Group” is a consultation-based program for groups of any size from individual participants to groups of any number. If forming a group of 2 or more participants, all group members must share a common baseline of completed courses, which will define the parameters of the content covered for each group.

“Office Hours”

The Build Your Own Group Consultation Program (BYOG) is like having access to a professor’s office hours during which participants can receive whatever support they need/want, in any and all aspects of learning and applying MMR for a current course, any previous courses (group participants have in common), or extensions of content from any courses (group participants have in common). During MMR courses, there are frequent, good questions from participants spanning a wide range of requested information, which reflect a desire for deeper clinical understanding, specialized instruction not included in the courses, practical applications of MMR in the classroom or private practice, how to provide and interpret initial assessments, etc.

These kinds of questions typically require more time to respond to than is available during a course, and the BYOG Consultation Program can provide the platform and structure to answer these questions prescriptively and comprehensively. Benefits of the group sessions include the possibility of receiving a wider span of content and information and in defraying costs per person for group sessions: the greater the number of participants, the less the cost per person.

Build Your Own Group Information and Policies

If forming a group, the group must appoint a liaison to work with the Office of the Institute to get the group approved and is responsible for organizing all aspects of scheduling session(s) and payment(s). All sessions must be prepaid by the liaison and MMR accepts credit cards, checks, and money orders for all sessions’ tuition. Pre-payment can be for any number of 1-hour sessions, and when available, sessions can be for 1 to up to 3-hours per session. All session fees are charged by the hourly rate set for individual participants, groups of 2 – 6, 7 – 12, 13, 14 – 17, and 18 – 48.

IMPORTANT NOTE: It is never appropriate for participants to receive new and unstructured content. For example, if one member of the group has completed the Making Math Real: Algebra II course and asks a question about algebra 2 content, and another member has only completed the Making Math Real: Overview and Making Math Real: 9 Lines Intensive, it is not appropriate for the latter member to receive the response to the algebra 2 question as the response would be completely dissociated from all the structure required to make it meaningful and applicable for students. Therefore, prospective group members must first organize themselves around common courses completed and common goals/questions. In addition, as a consultation-based program, the Making Math Real “Build Your Own Group” is not structured or intended to present a new MMR course, rather, it is structured to provide any and all information and extensions relevant to current or previous course work.

and group pricing rates: [email protected]

SCHEDULING AND REFUND POLICY: Once the desired number of sessions have been scheduled and pre-payment has been received, the dates will be officially reserved on my calendar. Any participant and/or group canceling registration at any time or for any reason, after payment has been received, will NOT receive a refund. If MMR receives the cancellation at least 2 business days in advance of the scheduled date, rescheduling of the session(s) is permitted. If MMR cancels any session(s), all payments received will be fully refunded and/or credited back.

Next Up: Your Stories of Personal Transformation as a Result of Learning and Teaching MMR

For a number of years now, some of you have shared stories of “Changing Lives” of your students and their families as a result of successful MMR-based interventions. These success stories are inspirational and motivational in their evidence-based authenticity that there are solutions to the problematic teaching and learning conditions/challenges so prevalent within math education. Your success stories have provided countless new MMR participants the inspiration and motivation to empower themselves to begin solving these problematic educational challenges, so please keep contributing any and all stories you are willing to share with the world.

Personal Transformations

The entire reason I decided to go public with Making Math Real 25 years ago was to help effect positive changes in math education. Now, as part of celebrating 25 years of changing lives, I feel it is important to celebrate and acknowledge all of the successful MMR participants who have provided so much positive educational service. So many of you over the years have expressed to me your personal transformations of growth and development as a result of helping others grow, develop, and achieve.

So please stay tuned for the next installment of “Looking Forward to the Next 25 Years” for the full description of my request to those of you to share your stories of having experienced powerful, personal transformations as educators, clinicians, math learners, and as human beings. Your stories of personal transformation will again provide invaluable inspiration and motivation for countless others seeking to help their children/students

Be well and stay healthy.

David Berg, E.T.
Founder & Director of the Making Math Real Institute
Creator of the Making Math Real Simultaneous Multisensory Structured Methods

# 25th Anniversary Special: The Problem with Word Problems – A Research Basis Part I

## 25th Anniversary Special: The Problem with Word Problems – A Research Basis Part I

Word problems, word problems, word problems – the most common requests I receive and the highest anxiety-causing mathematics – everybody gets so worked up about word problems!

Throughout all the courses and over all the 46 years I have been an educator, many of you have heard me discuss the problem with word problems. I talk about how and why word problems are an entirely different category of math development than all the K-12 Making Math Real Simultaneous Multisensory Structured Methods; and consequently, why the teaching of word problems must be entirely different than the teaching of numerically-based mathematics.

### The Strong Parallels Between Solving Word Problemsand Writing Expository Essays

In my discussions, I note the strong parallels between the extremely high-order cognitive demands of solving word problems and expository writing. Both are:

• High(est) order cognitive demands on the ability to generalize current knowledge to new connections and on multidimensional executive functions in support of extensive working memory applications that must encompass the open-ended problem solving and critical thinking required for a wide diversity of word problems or for expressing a wide diversity of essay styles and topics:

#### Activate (Synthesize) Complete Comprehension Picture

Word Problems

Activate a complete comprehension picture from the language of the word problem

Expository Writing

Activate a complete comprehension picture (idea) of the entire essay to be written

#### Translate Complete Comprehension Picture

Word Problems

Translate the complete comprehension picture from the language of the word problem into a mathematical comprehension picture

Translate the mathematical comprehension picture from the language of the word problem into a mathematical equation

Expository Writing

Translate (organize) the complete comprehension picture (idea) of the entire essay to be written into a general sequential order of paragraphs: introduction with thesis statement, body with supporting evidence, and conclusion

Translate the complete comprehension picture of the entire essay to be written into a specific sequential order in the form of a detailed outline, paragraph by paragraph

Word Problems

Activate the required mathematical abilities to solve the equation

Expository Writing

Activate the required written expression abilities to transform the detailed outline into complete sentences and paragraphs

#### Demands on Working Memory

Word Problems

Activate and sustain the complete comprehension picture of the word problem throughout problem solving and know the solution makes sense

Expository Writing

Activate and sustain the complete comprehension picture of the entire essay throughout the planning and writing process and know the thesis statement, supporting evidence, and conclusion make sense

#### Demands on Open-Ended Problem Solving and Critical Thinking:The Highest Order of Generalizability

Word Problems

Solving word problems encompasses all math content. Any and all math applications can be expressed in any word problem form. The ability to independently solve word problems in general requires students’ abilities to synthesize, generalize, and translate all their math learning from the language of the word problems to the mathematical comprehension picture and apply the mathematics to solve them.

Expository Writing

Solving the challenges of expository writing encompasses all conceivable content/information/ideas that can be expressed in the different types of expository essay styles. The ability to independently write expository essays in general requires students’ abilities to synthesize, generalize and translate their content knowledge/ideas using word finding, sentence construction, grammar, and mechanics into expository forms of written expression.

• Multi-year development (typically 10) starting in kindergarten is indicated for both with respective year-by-year incremental instruction leading to the independent ability to solve an extensive variety of word problems or to write the classic American 5-paragraph expository essay. The significant duration of the multi-year development is directly related to the ongoing developments of front to back connections in the brain, which support the high-order cognitive demands of critical thinking and open-ended problem solving. Front to back connections typically start developing later in life, often starting in early adolescence.
• Neither word problem development nor expository writing development can be taught by assignment. Both require specific and explicit sequential development and there are no shortcuts for either. Representative examples of “shortcuts” for word problems include “Key Words”, “the 5-Step Plan”, “Draw a Picture/Make a Diagram”, “Guess and Check”, “Work Backwards”, etc.; and for expository essays, “The Hamburger Model” and graphic organizers such as “Webs, Mind Maps, and Concept Maps”. Interventions for word problem development and for expository writing must first determine students’ current developmental level within each respective multi-year progression and begin the intervention at that point, Chronological age and current grade level of the student do not factor into where the developmental intervention begins.
• Solving word problems and writing expository essays are extremely valuable developments
• Solving word problems and writing expository essays have been and continue to be extremely challenging for students of all ages

### Request For a Research Basis to Explain Why Word Problems Can Be So Challenging

I requested my colleague, Nancy Knop, PhD, a classroom science teacher, an educational therapist (currently retired) and a research biologist, to write an article based on the most current research on math and language to provide a research basis from cognitive science and neurobiology to explain why word problems are such a problem for so many of us. Dr. Knop and I have collaborated in multiple capacities over the last 20 years including co-presenting at Learning & the Brain Conferences in San Francisco, Cambridge, and Washington D.C., and she has provided me with numerous and valuable research-based resources throughout this 20-year period.

### The Problem with Word Problems

One of the most frequent requests I continue to receive from educators and parents throughout the courses and in my private practice is how to deal with word problems. Perhaps since word problems can be so challenging for so many of us, word problems continue to be inappropriately included as part of the domain of numerically-based mathematics and therefore considered as the highest level of mathematical achievement, and consequently are given prominent emphasis on standardized tests, general math assessments, grade level expectations across all grades, and IEP goals and objectives. This is the problem and this is the principal purpose of this article: word problem development with its significant requirement on translating language to math makes it a separate educational development from the teaching of numerically-based mathematics; and therefore, cannot be used either as a way to teach numerically-based mathematics or as a way to assess numerically-based mathematics achievement. Word problems and numerically-based mathematics require separate and explicit instructional practices and separate assessments to serve as respective progress monitors and measures of achievement levels.

### Providing Some Relief: When Indicated, Remove the Inappropriate Inclusion of Word Problems from IEP Goals and Objectives and Student Study Plans

In addition to wanting to help people understand the unique nature of word problem development, another of the principal reasons I asked Dr. Knop to provide this research-based article is when indicated, to help families provide the necessary basis to schools and IEP teams to have the inclusion of word problems in IEP goals and objectives and student study plans removed. Schools and IEP teams who are unaware of the unique nature of word problem development and inappropriately include word problems, especially for students with reading and language-based learning disabilities, as the means to address the development of numerically-based mathematics have caused profound distress and damage to numerous students and their families for decades. It is my sincerest hope that Dr. Knop’s article, “Of Course You Hated Word Problems: Current Research in Cognitive Science and Neurobiology Explains Why”, can provide much needed relief for students who have been subjected to the contraindicated inclusion of word problems in their IEP goals and objectives and/or student study plans.

### Of Course You Hated Word Problems:Current Research in Cognitive Science and Neurobiology Explains WhyNancy Fike Knop PhD, ET/P

Abstract. Brain pathways for processing words and processing numbers do not completely overlap. Mathematical thinking has its own set of brain pathways. As a result, solving word problems requires translation between these symbolic languages, making the math more difficult, leading to anxiety and avoidance. Math learning requires systematic, incremental development from concrete to abstract understanding using numbers, not words. Learning to solve word problems is a separate, though important, process.

It’s perfectly natural to hate word problems. You couldn’t help it. Our brains are wired one way for quantity/number symbols and a different way for language/letter-word symbols (Almaric & Dehaene, 2018, Fuchs et al., 2016a). Having to dip in and out of language areas of your brain to use separate quantity areas makes math more difficult. It’s like feeling your way through a room with your eyes closed. You can use hearing and touch to figure out where things are, but sight is easier – different areas of the brain are involved. Why make it more difficult?

Specialists in the brain and learning talk about domain-general and domain-specific brain functions. The hippocampus (memory formation), deep in the middle of your brain, and the frontal lobes (planning and inhibition of irrelevant information) are domain-general: you use them for all kinds of learning and thinking. Areas on the top toward the back, the parietal lobes (quantity), and the temporal lobes, on the left side inside your temple (language) are more domain-specific. In other words, these areas are wired into pathways you developed for specific kinds of thinking and communicating (Battista et al., 2018). Seeing, hearing, and touch all have their own specialized brain areas, too.

You were born with a brain area and pathways already specialized for recognizing, estimating, and comparing quantity (amount, loudness, brightness) and a separate area and pathway for recognizing spoken language. Your senses send information to those specific areas for interpretation. As you learned to count and read, letter and number combinations were stored in your memory and new connections were formed, but they developed in different places, with different pathways. Both domain-specific areas and domain-general pathways are involved (Qin et al., 2014, Vogel & De Smedt 2021, Wu et al., 2017).

For reading, your knowledge grew from hearing and understanding language into decoding written words, then combinations of words, then sentences, then chapter books. You combined that with encoding: writing words, sentences, paragraphs. If you were fortunate, you learned to do creative and expository writing. The left temporal and frontal lobes developed important pathways for this.

What happened when word problems entered the picture? At first, maybe not so much. Perhaps you could translate adding apples and oranges to figure out the total quantity of fruit in the basket. But if that problem was a written problem, it was more difficult than one spoken to you, because you had to decode the letter/word symbols and translate into number and operation symbols: different languages. Any language-based learning issue just added to the difficulty (Fuchs & Fuchs 2002, Geary, 2011, Kennedy, 2020). As the information included got more and more complicated, it could become too difficult. Too many brain areas were involved in sorting it out and translating it. If you didn’t have automatic understanding of the math, understanding literally in your body, involving, seeing, touching, and hearing, or enough practice doing problems like this one, the word problem was a serious challenge. Written words put you back at square one, trying to translate.

Increasingly, students are asked to solve math problems and then to “explain your thinking” using words or written language. Solutions to math problems that show all the steps using numbers DO completely show thinking, in mathematical language. Restating solutions in words requires another translation step. Solutions to word problems should be expressed numerically, with terms labeled as necessary, e.g. ‘15 pieces of fruit total.” That is enough. Once solutions are shown mathematically, it is not necessary, and you should not be required, to write sentences explaining again everything you just explained mathematically.

The demands of solving word problems are very similar to the demands of expository writing. Both require major translation tasks. For word problems: 1) translate the language of the word problem into a big picture of understanding, 2) translate that big picture into its equivalent as an equation, 3) solve the equation. For expository writing: 1) translate the big picture of an idea into an organized sequence (outline), 2) translate the organized sequence into expository language (expository language is different then spoken language), 3) write the essay. It takes many years of laying groundwork and developing the concepts and skills involved (Berg, n.d.). You are fortunate if you are comfortable with either one.

Most of us are not comfortable with word problems and we were not comfortable with them in school. Now, research in cognitive science and neurobiology is yielding an explanation for our discomfort. Our math brain was not designed for words. We developed strategies for coping, but we didn’t develop fluent understanding. Or we hated word problems, developed math anxiety, and avoided any further math (Ashcroft & Moore, 2009, Choe et al., 2019). Alas, real life presents us with “word problems” every day: knowing what 20% off means, balancing checkbooks, understanding simple and compound interest, income and tax rates, or analyzing statistics for accurate interpretation.

Confidence and competence in word-problem solving depends on knowledge of arithmetic (Fuchs et al., 2016b). Although this is basic and essential, it is not enough. For spoken story problems or word problems presented in text, language and reading comprehension is also necessary (Fuchs et al., 2020). For anyone with a learning issue that involves reading, executive function, working memory, or number sense, no matter how gifted in other areas, word problems become even more challenging (Knop & Chou, 2020). This is why arithmetic problem solving and translation of word problems into mathematics must be taught separately and explicitly.

Development of the ability to address and solve word problems is important. It takes many carefully structured years of instruction to develop the ability to analyze, translate, solve and translate again to communicate solutions effectively in both numbers and words. Our brains do not process word problems the same way as mathematical problems presented numerically. Learning to solve word problems is an important adjunct, and it is necessary. But word problems should not be taught or assessed instead of or as the entryway to numerically based mathematics. There must be separate well-designed approaches and progress monitors to both; otherwise it is like trying to teach children to see with their ears.

Selected References
Amalric, M., & Dehaene, S. (2018). Cortical circuits for mathematical knowledge: Evidence for a major subdivision within the brain’s semantic networks. Philosophical Transactions of the Royal Society B, 373(1740). https://doi.org/10.1098/rstb.2016.0515

Ashcroft, M. H. & Moore, A. M. (2009). Mathematics anxiety and the affective drop in performance. Journal of Psychoeducational Assessment, 27(3), 197-205. https://doi.org/10.1177/0734282908330580

Battista, C., Evans, T. M., Ngoon, T. J., Chen, T., Chen, L., Kochalka, J., & Menon, V. (2018). Mechanisms of interactive specialization and emergence of functional brain circuits supporting cognitive development in children. npj Science of Learning, 3(1). https://doi.org/10.1038/s41539-017-0017-2

Berg, D. (n.d.). Learn how to close the gap in achievement and reach the full diversity of learners. Making Math Real Institute. https://www.makingmathreal.org/about

Choe, K. W., Jenifer, J. G., Rozek, C. S., Berman M. G., & Beilock, S. (2019). Calculated avoidance: Math anxiety predicts math avoidance in effort-based decision-making. Sci. Adv. (5): eeay 1062 doi: 10.1126/sciadv.aay1062

Fuchs L. S., Fuchs D. (2002). Mathematical problem-solving profiles of students with mathematics disabilities with and without comorbid reading disabilities. J. Learning Disabilities 35: 563-573. DOI: 10.1177/00222194020350060701

Fuchs, L. S., Geary, D. C., Fuchs, D., Compton, D. L., & Hamlett, C. L. (2016a). Pathways to third‐grade calculation versus word‐reading competence: Are they more alike or different? Child Development, 87(2), 558–567. https://doi.org/10.1111/cdev.12474

Fuchs, L. S., Gilbert, J. K., Powell, S .R., Cirino, P. T., Fuchs, D., Hamlett, C. L., Seethaler, P. M. & Tolar, T. M.,(2016b). The role of cognitive processes, foundational math skill, and calculation accuracy and fluency in word-problem solving versus pre-algebraic knowledge. Developmental Psychology 52: 2085-2098. doi:10:1037/dev0000227

Fuchs, L. S., Fuchs D., Seethaler, P. M. & Craddock C., (2020). Improving language comprehension to enhance word-problem solving. Read Writ Q 36(2): 142-156 https://doi.org/10.1080/10573569.2019.1666760

Geary, D. C. (2011). Consequences, characteristics, and causes of mathematical learning disabilities and persistent low achievement in mathematics. Journal of Developmental and Behavioral Pediatrics, 32(3), 250–263.

Kennedy, D. (2020) What’s math got to do with it? Math learning disabilities, dyslexia, and ADHD: Understanding the connections, remediating effectively. The Educational Therapist 41(1): 4-8.

Knop, N. F. & Chou, S. H. (2020). Giftedness and Math Difficulty. In C. M. Fugate, W. A. Behrens, & C. Boswell, (Eds.), Understanding Twice-Exceptional Learners, Connecting Research to Pratice (pp 183-216)Prufrock Academic Press.

Price, G. R., Mazzocco, M. M. M., & Ansari, D. (2013). Why mental arithmetic counts: Brain activation during single digit arithmetic predicts high school math scores. Journal of Neuroscience, 33
(1), 156–163. https://doi.org/10.1523/JNEUROSCI.2936-12.2013

Qin, S., Cho, S., Chen, T., Rosenberg-Lee, M., Geary, D. C., & Menon, V. (2014).Hippocampal-neocortical functional reorganization underlies children’s cognitive development. Nature Neuroscience, 17(9) 1263–1269. https://doi.org/10.1038/nn.3788

Vogel, S. E. & B. De Smedt (2021). Developmental brain dynamics of numerical and arithmetic abilities. npj Sci. Learn. 6(22): 1-11 https://doi.org/10.1038/s41539-021-00099-3

Wu, S. S., Chen, L., Battista, C., Smith Watts, A, K., Willcutt, E. G., & Menon, V. (2017, September). Distinct influences of affective and cognitive factors on children’s non-verbal and verbal mathematical abilities. Cognition, 166, 118–129. https://doi.org/10.1016/j.cognition.2017.05.016

About Nancy Fike Knop, Ph.D., ET/P
Nancy Fike Knop, Ph.D., ET/P is a recently retired educational therapist. She worked with children and adolescents as an ET for 20 years, providing prescriptive remediation for challenges and background gaps in math and other subjects. Dr. Knop taught science to grades 7-12 at Head Royce School in Oakland and served as Department Chair for five years. She holds a B.S. degree from the University of Connecticut, a Ph.D from UC Berkeley, and a graduate-level certificate in Educational Therapy from UC Berkeley Extension. Dr. Knop writes and speaks locally and nationally, interpreting primary research about the biology of learning including brain development, the neurobiology of math and language learning, the role of vision, the importance of gesture, and the essential nature of sleep and other environmental influences that relate to learning and learning differences.

### Please stay tuned for “The Problem with Word Problems – A ResearchBasis Part 2:The Problem with Teaching Word Problems”

Be well and stay healthy.

David Berg, E.T.
Founder & Director of the Making Math Real Institute
Creator of the Making Math Real Simultaneous Multisensory Structured Methods