## MATH FACTS: The Foundation of Mathematical Success

One of the greatest predictors of academic success is a student’s ability to master the four operations of math facts. However, it is common for most American schools to breeze over fact fluency, setting mastery standards as scoring an 80% on a written test, or even assuming a child has been working at home to achieve mastery instead of working on it in school.

A child has reached mastery if he is able to answer the equation in under two seconds without needing to count or perform any other computational strategies. With developments in technology, studies have been able to look at the brain while students work through equations. The data has shown that a student’s working memory, the ability to hold information for processing, is directly linked to success in arithmetic while a deficit in visuo-spatial working memory is a marker for learning disabilities.

What does this mean? Simply showing an equation and eliciting a response is not going to develop true mastery. In fact, this is just re-enforcing a lazy imagery, or imagination. This might be noticeable when a student is able to do well on a multiplication test, but then slows down when working on a mixed-operations worksheet or performing calculations during a word problem.

How do we develop a child’s visuo-spatial working memory? Just as we only get better at sports by practicing frequently, we will only get a stronger imagery through frequent, appropriate practice. However, not all practice is equal. In fact, practicing incorrectly will just perpetuate the problem. When we work with students, we ensure a multifaceted approach, which trains the student’s brain to look at number relationships using different strategies.

It is never too late for remediation. Simply put, the capabilities of the human brain can be described as miraculous. Research has shown that with one year of explicit tutoring, a child’s brain will physically grow and if a child does not develop math fact fluency, it could potentially lead to an inorganic learning disability.  We are all very different and our brains are shaped by our life experiences, the foods we eat, and daily stress, but this just means that instruction needs to be tailored for the student’s exact needs in order to maximize results.

Tips and Tricks:

• NEVER EVER EVER USE FINGERS FOR COMPUTATION. If the child is just learning to add or subtract, use beans or counters.
• Don’t go through flashcards mindlessly. Make sure you go through the pile once while the child is able to see the equations and then hide the cards and say the equations. If there are some that don’t seem to be “sticking”, put those in the mix more frequently.
• Play games, all types of games. Games encourage a student to move faster, which will encourage mental math.
• If they are not making progress with equations from imagery (visualizing the equation), have them write the equation, either with pencil and paper or with their finger on the table in front of them,  and have them look at what they wrote while saying the full equation and answer.

References:

Boyd, P., & Ash, A. (2018).  Mastery mathematics: Changing teacher beliefs around in-class grouping and mindset. Teaching and Teacher Education, 75, 214-223.

Burns, M.K., Ysseldyke, J., Nelson P.M., & Kanive R. (2014). Number of repetitions required to retain single-digit multiplication math facts for elementary students. School Psychology  Quarterly, 30 (10).

Menon, V. (2016). Working memory in children’s math learning and its disruption in dyscalculia.  Current Opinion in Behavioral Sciences. 10, 125-132.

Rosenberg-Lee, M., Barth, M., & Menon, V. (2011). What difference does a year of schooling make? Maturation of brain response and connectivity between 2nd and 3rd grades during arithmetic problem solving. Neuroimage. 57, 796-808.

Skarr, A., Zielinski, K., Ruwe, K., Sharp, H., Williams, R.L., & McLaughlin, T.F. (2014). The effects of direct instruction flashcard and math racetrack procedures on mastery of basic multiplication facts by three elementary school students. Education and the Treatment of Children. 37(1), 77-93.

## SAT/ACT Foundations

### Who is it for?

High school upperclassmen looking to solidify content areas in order to improve test scores.

### How it helps:

Students will gain a deeper understanding of content areas in order to better prepare them for the variety of questions found on the tests.

### What it includes:

• First semester is focused on direct instruction in all math content found on the SAT and ACT tests. Check for understanding and additional practice is provided as needed.
• Second semester is focused on test prep and test taking strategies for all sections of the SAT or ACT test. **Instruction is tailored to each student depending on their test of choice.

## 7th and 8th Grade Study Skills

### Who is it for?

Current 7th and 8th grade students who are looking to strengthen executive functions to improve study and work strategies.

### How it helps:

This class fosters independence, helping students learn how to plan their week, study efficiently, and manage their time. Students are able to complete their homework with the guidance of an executive function coach.

### What it includes:

• Organization of binder, backpack, and academic planner.
• Creation of weekly study plans.
• Tracking grades to look for patterns that can help improve study strategies.
• Practice of concepts and methods needed to increase study efficiency and improve critical thinking.
• Application of work and study strategies to homework, essays, projects, and assessments.

## 5th and 6th Grade Study Skills

### Who is it for?

Current 5th and 6th grade students who are looking to strengthen executive functions to improve study and work strategies.

### How it helps:

This class fosters independence, helping students learn how to plan their week, study efficiently, and manage their time. Students are able to complete their homework with the guidance of an executive function coach.

### What it includes:

• Organization of binder, backpack, and academic planner.
• Creation of weekly study plans.
• Tracking grades to look for patterns that can help improve study strategies.
• Practice of concepts and methods needed to increase study efficiency and improve critical thinking.
• Application of work and study strategies to homework, essays, projects, and assessments.

## High School Study Skills

### Who is it for?

Current high school students who are looking to strengthen executive functions to improve study and work strategies.

### How it Helps:

This class fosters independence, helping students learn how to plan their week, study efficiently, and manage their time. Students are able to complete their homework with the guidance of an executive function coach.

### What it includes:

• Organization of binder, backpack, and academic planner.
• Creation of weekly study plans.
• Tracking grades to look for patterns that can help improve study strategies.
• Practice of concepts and methods needed to increase study efficiency and improve critical thinking.
• Application of work and study strategies to homework, essays, projects, and assessments.

## 7th and 8th Grade Thesis Writing

### Who is it for?

Current seventh and eighth graders looking to advance their expository writing skills and reading comprehension in preparation for high school and beyond.

### How it helps:

Students learn how to become independent writers using strategies to organize, revise, and edit their writing.

### What it includes:

• Annotate a text to find evidence for an essay.
• Use visualization strategies to enhance reading comprehension.
• Learning how to answer an essay prompt and brainstorm ideas.
• Outline a 5+ paragraph essay with topic sentences and supporting details.
• Identify and write a thesis statement.
• Find evidence to support ideas.
• Use a thesaurus to improve word choice.
• Revise a rough draft for better clarity.
• Apply capitalization and punctuation rules while writing and editing

### Who is it for?

Current fifth and six grade students looking to supplement their school instruction and strengthen skills in reading, writing, and math.

### How it helps:

The small group setting includes custom lesson plans for each student and helps students improve work endurance, task initiation/engagement, and self-advocacy while mastering foundational skills.

### What it includes:

• Application of English rules for spelling
• Application of capitalization and punctuation rules while writing and editing
• Sentence combining
• Paragraph writing: outlining, topic sentences, supporting details
• Reading/Listening comprehension strategies with higher order thinking questions
• Greek and Latin roots
• Mental math strategies for addition, subtraction, and multiplication
• Math concepts including, but not limited to:
• Decimals
• Fractions
• Percent (if applicable)
• Area and perimeter
• Order of operations
• Word problems

### Who is it for?

Current third and fourth grade students looking to supplement their school instruction and strengthen skills in reading, writing, and math.

### How it helps:

The small group setting includes custom lesson plans for each student and helps students improve work endurance, task initiation/engagement, and self-advocacy while mastering foundational skills.

### What it includes:

• Handwriting: Proper letter formation for cursive
• Application of English rules for reading and writing
• Application of capitalization and punctuation rules while writing and editing
• Sentence and paragraph writing
• Mental math strategies for addition, subtraction, multiplication, and division (if applicable)
• Math content including, but not limited to:
• Place value
• Decimals
• Fractions
• Word problems

### Who is it for?

Current first and second grade students looking to supplement their school instruction and strengthen foundational skills in reading, writing, and math.

### How it helps:

The small group setting includes custom lesson plans for each student and helps students improve work endurance, task initiation/engagement, and self-advocacy while mastering foundational skills

### What it includes

• Proper pencil grip and letter formation for manuscript writing
• 71 Orton Phonograms: read and spell
• Application of English rules for reading and writing
• Sentence writing
• Reading/Listening comprehension development with visualization strategies
• Mental math strategies (addition, subtraction, multiplication)
• Math content including, but not limited to:
• Place value
• Telling time
• Identifying coins/bills and working with money

### Who is it for?

Current kindergartners who are looking to supplement their school instruction and strengthen foundational skills in reading, writing, and arithmetic.

### How it helps:

The small group setting helps students improve work endurance, task initiation/engagement, and self-advocacy while mastering foundational skills

### What it includes:

• Correct pencil grip and letter formation
• Fine motor development
• Phonemic awareness activities
• Practice the 71 Orton phonograms for reading and spelling
• Application of English rules while reading and writing
• Listening comprehension
• Oral directions
• Number identification
• Finding and creating patterns
• Comparing quantities
• Place value