Research and Findings from 87 Surveyed High School Math Teachers:
In April 2024, I asked countless teachers in the post covid-19 education system the burning question: What math resources do you WISH students knew BEFORE taking your course? In other words, what are the most prevalent post covid effects on their skill levels? Below you can find the summary and analysis from my engagement with 87 high school math educators across 6 teacher Facebook groups. I shared those group names at the end of this blog if you’re interested!
From this research, I have carefully crafted six 9 to 11-page pretests for each subject!
Take an unsurprising look at the staggering similarities across multiple subjects of skills lacking in our math education system in the post covid world:
| Skill Lacking | Rank | Courses |
|---|---|---|
| Factoring Polynomials Side note: It is not surprising that the 3rd ranked complaint in Calculus is students not knowing how to solve a trigonometric equation, in which factoring is a necessary component. | Top 3 | Algebra 2, Geometry & Precalculus |
| Operations with integers | Top 4 | Algebra 1, Algebra 2 & Precalculus |
| Solve a multi-step linear equation | Top 4 | Algebra 1, Algebra 2, Geometry & Precalculus |
| Operations of rational expressions | Top 7 | Precalculus, Calculus and Statistics & Probability |
| Operations with fractions Side note: This remains an issue in Precalculus as it’s ranked 13th . | Top 8 | Algebra 1, Algebra 2 & Geometry |
| Solve a system of linear equations | Top 9 | Algebra 1, Algebra 2 & Calculus |
| Order of operations | Top 10 | Algebra 1, Algebra 2, Geometry, Precalculus and Statistics & Probability |
| Identifying the type of function (linear, quadratic, exponential, periodic, etc.) | Top 15 | Algebra 2, Geometry, Precalculus & Calculus |
The math struggle is real! Here’s a compilation of skills, ranked from most to least common, that countless teachers have frequently reported their students are lacking in the post-COVID era:
Algebra 1:
- Order of operations
- Operations of integers & multiplication table
- Solve linear equations (one-step & multi-step)
- Fractions and decimals
- Knowing vocabulary such as coefficient, like-terms, constant
- Graph a line
- Decimal, percent, and fraction equivalence
- Word problems – setting up equations
- Calculate slope
- Solve a system of linear equations
- Write equations in slope-intercept form and point-slope form
- Understanding x and y intercepts
- Plot points in a cartesian plane
- Solve and graph inequalities
- Real numbers and understanding the number line
- Recognize what a function is, and what the independent (x) and dependent (y) variables mean
Algebra 2: [Scroll to the bottom of this blog post for the *free* pretest!]
- Factoring polynomials
- Operations with fractions
- Solve multi-step linear equations
- Integer operations & multiplication table
- Quadratic formula
- Order of operations
- Identifying parent functions. Which is linear? Quadratic? Etc.
- Multiplying fractions with also cross-simplifying (shortcut)
- Squaring a binomial
- Computations/evaluations with polynomials
- Operations with rational expressions
- Graphing
- Familiarity with the coordinate systems
- Solve a system of equations & inequalities
- Simplify radicals
- Complete the square
- Reading math notation
Geometry:
- Integer operations and multiplication table
- Plot points in a Cartesian Plane
- Factoring polynomials
- Solve linear equations
- Pythagorean Theorem
- Distance & Midpoint formulas
- Operations with fractions
- Order of operations
- Find area and perimeter of squares and rectangles
- Quadratic formula
- Location of quadrants
- Identifying parent functions. Which is linear? Quadratic? Etc.
- Calculate slope
- Recognize basic shapes
- Equation of a line in slope-intercept form
- Reading inequality symbols
- Triangle Sum Theorem
- Simplify radicals
- Applying a formula to solve or evaluate something
- Find the circumference and area of a circle
- Knowing the difference between points, side-lengths, angles, and planes
Precalculus:
- Factoring polynomials
- Operations of integers & rational expressions (no calculator)
- Manipulating rational expressions
- Solve a multi-step linear equation
- Logs and exponents manipulations
- Complete the square
- Find the domain and range
- Function composition
- Right triangle trigonometry
- Order of operations
- Quadratic formula
- Simplify radicals
- Operations of fractions
- Evaluate and graph various types of functions
- Identifying parent functions. Which is linear? Quadratic? Etc.
- Basic trigonometry
- Polynomial long division
Calculus:
- Unit circle knowledge and evaluations of trig functions
- Pythagorean identities
- Solve trigonometric equations
- Knowledge of sine, cosine, and tangent functions
- Identifying period, amplitude and phase shift
- Logarithms
- Operations of rational expressions
- Finding asymptotes of rational functions
- Solve a system of linear equations
- Identifying parent functions. Which is linear? Quadratic? Etc.
- One teacher even wished that students took physics before calculus to explain the WHY in calculus.
Statistics and Probability:
- Convert between fractions, decimals and percents
- Simplify and manipulating fractions
- Order of operations
- Basic common concepts, like number of cards in a deck, how many numbers in a standard die, which letters are vowels, etc..
- Middle school basic statistics: mean, median, mode, histogram, combination, permutation, etc.
- What is a complement
- Simplify factorials
- Background on identifying slope and y-intercept of a linear equation, and then interpreting what it means in the context of the problem. This is helpful when teaching correlations.
- One teacher even specifically requested for me to find a way to let students know that their chances of winning the Mega Million jackpot is extremely slim.
Facebook Groups Where I Gathered Research:
- Secondary Math Resources for Teachers
- Math Teachers Professional Learning Network
- STEM Teachers Group – Middle School and High School Educators
- Math Minded Teachers
- Math Teachers Honest Math Chat
- High School Math and/or Computer Science Teachers
Alright my friends, now it’s time for you to the reap the benefits of this research! Don’t miss out on my *FREE* 10-page Algebra 2 PRETEST with answers!
If you’re a teacher, click here.
If you’re a student, click here.
You can also catch me going over every problem on the Algebra 2 pretest below as a flipped-classroom experience!
