Reviving Math Success: A Middle School Program for Boosting Student Achievement

I’m a data nerd.  I can stare at pages and pages of data for hours.  I graph it in different ways to look for patterns and trends.  I map it.  I rearrange it.  I compare it to other data sets.  This oddity led me to revamp NAREIT’s index to create the multiple components that are still used today.  This new data reporting method ultimately helped REITs get favored treatment in the Tax Reform Act of 1987 and propelled me to Wall Street.


My natural tendency is to use the data to support an explanation of my findings.  By nature, I constantly wonder about the data that is used to support assertions.  It took me 60 years to finally accept that most people just want to know my conclusions and not the data and analysis that guided me.

Today, news headlines sound alarms about declining math skills, especially for low-income students or students of color.  I have a very different perspective, that no one talks about.  The kids at the top have also fallen off a cliff.  The rate of decline is accelerating.  Even worse, the state of our teacher education and teaching pool does not offer a path to reverse this trend.


I started HEROES before standardized tests drove our educational system.  At that time, I primarily worked with children who were academically ready for college-level work by the time they were 12 or 14.  I worked with a few outliers who started as young as 8.  Most of the kids I worked with excelled in math and related fields although I worked with a few who were writers.  I organized events for hundreds of students who were able to actively participate in seminars taught by college faculty members and researchers.


When I founded HEROES Academy with my daughter, we initially offered courses that were extensions of these seminars.  But each year, we noticed that our applicants had weaker basic math and language arts skills.  These were students who hit the ceiling on all standardized tests offered at their schools, were identified as gifted and talented, and often had IQ test scores to verify their aptitude, but still had much weaker basic skills than students we worked with in the past.  Eventually, we realized that we had to provide math and language arts classes for them to have the skills necessary to actively participate in our programs.  I refuse to offer “edu-tainment” courses.  I won’t offer a fun “computer programming” course that is only teaching kids how to play with software that is repackaged as educational.  Our computer programming courses included classes like data structures that required math skills.


Initially, I thought that offering math classes would be easy.  Simply choose a textbook series and follow it.  It didn’t work that way though.  What I realized was that since the passage of the No Child Left Behind Act in 2001, math textbooks were written to prepare kids to score high on standardized tests instead of teaching them the logic that is the foundation of math.  College textbooks were an option, but college algebra and prealgebra textbooks are written for weak math students.  Art of Problem Solving was an interesting option that I considered and tried to use for a while.  But that series is designed to prepare kids for math competitions.  They provide wonderful enrichment math that is great for developing logical thinking and problem-solving skills, but they don’t provide a solid foundation on the basics.  They are written for students who already have a solid foundation of the basics.  The engineer in me concluded that the only solution to the problem was to write my curriculum from scratch.


For the last several years, I’ve been writing, and rewriting my curriculum.  I’ve used the Common Core as a checklist.  I’ve used my student’s questions and struggles as my guide. I feel that the grades 3 through 5 curriculum is complete enough to pass on to Miss Danielle.  This summer I began to reformat my material so that it can be used by other teachers or parents.  My focus is now on middle school math.  I realize that the current state of middle school math means that I need to structure these classes differently than I did in the past.

State of Middle School Math

Students who are currently in 5th grade were in 1st grade when the COVID shutdown occurred in March 2020.  They technically completed 1st and 2nd grade virtually and experienced the chaos of bouncing between in-person and virtual during 3rd grade.  I say technically completed 1st and 2nd grade because they “passed” those grades and were promoted to the next grade, but they didn’t really learn the content that they were supposed to learn in those grades.  They should now be finishing their arithmetic education and beginning the transition toward algebra.  But they don’t know the basics.  I find that they can perform calculations – at least the very top students that I meet can add, subtract, multiply, and divide.  The algorithms to perform those basic functions are easy enough to learn online and test with apps.  What they don’t know is what any of it means.  They can’t translate it to anything.  They can’t apply it to anything.  They can interpret it.  They can’t use unit squares to build a rectangle that represents 3 x 5.  They can’t translate 5 times three-eighths into five plates with three slices of pizza on each plate.  They don’t understand place value.  They don’t know why any of these algorithms work or what the result means.  They only know that if they see a particular group of symbols on a screen, they are supposed to do a specific task and type the result into the app.  Doing this trick right makes the adults happy.


This year, school districts can receive funding through the New Jersey Learning Acceleration Program: High-Impact Tutoring Grant for students in grades 3 and 4.  What about the kids in 5th grade or higher?  Are we, as a society willing to accept that these children are never going to learn the essential basics that they should have learned in earlier grades?  I don’t think we’re going to keep them in school for two additional years to make up for this learning loss.  It appears that we are going to pretend that the problem doesn’t exist and just give them a piece of paper in a few years that says they’ve earned a high school diploma without having the skills that the diploma is supposed to represent.

Why Accelerated Math is Critical

I was educated during the Cold War.  When I was a child, we were worried about the Soviets.  We knew that we needed to nurture our best and brightest so that we could compete.  My father fought in World War II, Korea and Vietnam.  He fought for values, not cheap trinkets out of Southeast Asia.  Our educational system was built around those values.  We understood that democracy required that voters were educated enough to understand the gravity of the power of their vote, to comprehend and analyze the political debate and weigh them against their own personal values.  We knew that we needed the masses to be able to read, write, perform basic math, and exercise reasoning skills.  We knew that we needed to identify a select few who would be able to address the challenges of the future.


I personally benefited from this environment.  I remember one day; my math teacher asked me to stay after class.  She showed me a piece of paper and explained that I earned the third-highest score in the district on some type of math test.  It didn’t register as a big deal to me at the time, but looking back at the historical enrollment records, I can see that more than 10,000 kids would have taken that test in my district.  She gave me an envelope with some paper in it to give to my mother.  She told me that it was to apply for a program at NASA Langley.  Being a good little girl, I gave the envelope to my mother.  Being an uneducated Japanese war bride, my mother obediently signed at the X’s and I returned it to school.  That paperwork, given to me by a teacher whose name I can’t even recall, changed my life.  It opened the door to Department of Defense funded educational program in math and science.  In high school, I worked for the school board as a computer programmer writing what today we would call educational software for elementary grade students.   That program was also funded by the Department of Defense.


We didn’t have regularly scheduled standardized tests that were reported to some government agency then.  We didn’t look at educating our children as a way for them to be able to afford more cheap trinkets manufactured in developing nations.  We understood that educating our best and brightest was essential to prepare for future challenges.

Today our world is facing multiple challenges that require the mobilization of the masses, inspired leadership, and skilled problem solvers.  AI is not going to develop the technology to address our challenges.  We need skilled scientists and engineers across a multitude of specialties.  Math is the language of economics, science, engineering, technology and so much more.  We need people who have the skills to not just use the math that exists today but to develop the mathematics that will be required in the future.  I recently got a copy of the dissertation of one of the earliest HEROES kids.  His math is beyond my ability to comprehend, but I draw great satisfaction in knowing that I had a small part in his journey.  Knowing that I helped one child become one of the mathematicians that the world needs gives meaning to my work.  But the world needs more of them.

The Post-Covid Challenge to Accelerated Math

Initially, I only worked with students who scored at the 95% or higher when compared to students at least two years older.  So, a 5th grader would have to score at the 95th percentile or higher for 7th grade.  Those tests aren’t widely available, especially for younger children.


Ideally, I would require IQ tests.  We do this for the micro-school, but it’s an unreasonable requirement for weekend classes.  The NWEA-MAP test that we use has not been recentered since COVID.  The only students with qualifying NWEA-MAP scores are those who had access to quality math instruction outside of their school.  The top students that I’ve met in the past year are about half a year behind compared to the standards outlined for their grades.  They’re getting the top grades in school.  They are getting the highest scores on NJSLA, but when given a test of the standards for their grade, they only know about half of what they should have learned in the previous grade.  That makes sense to me because it seems like the average student is more than a year behind.  In other words, what we are teaching in 5th grade math today is content that would have been taught in 4th grade pre-COVID.


Placement is not something that can be done on a simple linear scale.  You can get a test score that says you place at 4th grade 2 months, but that doesn’t mean that you know all 3rd-grade content and nothing beyond the 2nd month of 4th grade.  That’s just how a test report can report a score.  The reality is, that all the students I’ve met in the past year have extraordinary learning gaps going back at least two years.  They know some 5th-grade content – like how to perform long division.  But they have gaps in 3rd and 4th-grade content and even some gaps in material they should have learned in 2nd grade.  While the cohort can continue to limp along for a little while, eventually they are going to hit a brick wall.  They certainly are not going to be able to handle algebra and beyond.  They might be able to get an A in a class that will be called algebra, but they won’t be able to understand algebra as it would have been taught pre-COVID.

My Proposed Solution

One thing that the government does understand about remediating the COVID-19 learning loss is that students need individualized attention.  We can’t reteach all the content that was missed over 2 ½ years of disrupted education.  We need to identify each student’s specific learning gaps and fill in those gaps.


Unfortunately, the government is only willing to provide this service for 3rd and 4th-grade “students that have been disproportionately affected by the pandemic.”  The rest of us need to solve this problem ourselves.


The first step in solving a problem is to acknowledge that there is a problem.  If you are happy with your child’s grades and think that if they are doing better than the average child that’s ok, then you don’t have a problem.  If you think that it’s important that your child doesn’t just get good grades but is also proficient in math and has the math skills that will be needed in their future endeavors, then you need to assess math skills and not assume that good grades equate to competence.  Grades are comparative.  The top kids in the class get As.  If no one knows all the content, they don’t all fail.


Next, you need to clearly define the problem.  Your child needs a thorough skills assessment.  This has been more challenging than I expected, primarily because I normally test for advanced skills not remedial skills.  I now start with a straight-up arithmetic operations assessment.  Can the student add, subtract, multiply, and divide numbers within 1,000: whole numbers, fractions, mixed numbers,  decimals, integers, rational numbers, etc.  This gives me a starting point.  Once I determine the limits of their arithmetic operations, I test for application (word problems).  Here’s where I’m finding the big gap.  The difference between the ability to perform calculations and the ability to apply or interpret those calculations is often two years or more now.  It is a huge gap that I’ve never seen at such scale before.  Basic concepts are a little harder to assess by paper and pencil.  My approach is through discussion and the use of manipulatives.  However, the inability to apply or interpret the results of basic operations indicates an even earlier gap in the understanding of a basic concept.  The lack of understanding of the basic concept at one grade level is revealed by the inability to do word problems at the next grade level.

Working with these students is like renovating an old house.  You plan on starting one project, but once you start you find other critical structural defects and get sidelined into an “I can’t believe this house is still standing” project.  I have found that if a family is willing to accept that this is just a remnant of COVID-19 – that it doesn’t indicate that the child is lazy, stupid, or hopeless, that recovery is possible.


I’ve seen parents yell at their kids “How can you not know this?  You’re in — grade.  You should know this by now.” This isn’t helpful.  Children don’t just wake up and know the content because they’ve reached a certain age or grade.  They know things because they were taught them.  Because students lost instruction during COVID, they weren’t taught things that they would have normally been taught.


To achieve success, students require three essential components: a foundational level of intelligence, access to necessary resources, and a commitment to diligent effort. We, as parents and educators, have a responsibility to provide them with access to resources.


New Jersey law states that “school districts must establish a process to identify students as gifted and talented using multiple measures.”  Post-COVID achievement tests allow us to identify students who have had access to educational resources.  They can’t identify gifted math students who have learning gaps due to the lack of access to educational resources.  Parents and educators need to develop alternative means to identify these students.

HEROES Academy’s Contribution to the Solution

When I was younger, I wanted to save the world.  I’ve long since realized that what I can realistically effectively do is to make a positive impact on the lives of a few individuals.  HEROES Academy can’t address the needs of all the students impacted by COVID-19 learning losses.  But we can make our contribution to the effort.  We are doing this through three initiatives:

HEROES Microschool for Gifted and Talented Students

 The microschool provides individualized instruction that easily facilitates addressing learning gaps.  Every student has individual long-term and daily learning goals.  We can do this because enrollment is limited to eight students who must meet strict eligibility requirements including IQ tests.

Middle School Math Boot Camp

The Middle School Math Boot Camp is a new program to identify gifted math students currently in 5th, 6th, and 7th grade.  The Boot Camp will be limited to ten students and will meet from 9:00-11:00 on Sundays.  Students must have a minimum NWEA Reading Score of 225 to enroll in this class.  During the first few weeks of class, students will take assessments to determine their individualized curriculum.  Students will be required to study math minutes and math vocabulary and to complete other homework between classes.  The amount of work assigned to an individual student will be determined by the results of their assessment at the beginning of the year.  Students who consistently demonstrate dedication to learning the assigned material and a math aptitude that would qualify for accelerated math instruction may qualify for additional HEROES Academy programs through the Math Boot Camp.

Putting Our Curriculum Online

Math Curriculum for Gifted StudentsThe key to accelerated math is tailoring instruction to make sure each student fully understands each concept without wasting time on concepts that they have mastered but the class needs to work on.  HEROES Academy has developed its own curriculum to facilitate this individualization of instruction.  This summer we began reformatting some of our curriculum to make it available for other teachers and parents.  You may find our resources HERE.  We will continue to add more resources to this site.

Our small contribution to the solution isn’t going to change the world.  But I hope one day my students can look back at their time with me and say that I changed their lives, even in a small way.  

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