In order to gain a high School diploma, students must possess a certain set of skills. Most people would agree. Whatever those skills are, schools have not been able to provide for the basic needs of many students. News agencies report...
"Only about a third of U.S. high school seniors are prepared for college-level coursework in math and reading. And while the performance of the country’s highest achievers is increasing in reading, the lowest-achieving students are performing worse than ever." (Camera, 2016)
"... we found another six high schools where one percent tested proficient. Add it up – in half the high schools in Baltimore City, 3804 students took the state test, 14 were proficient in math." (Papst, 2017)
These reports are not outliers, unfortunately.
So, what skills should students possess?
Beside possessing social, comprehension, and time management skills that allow for productive teaming, task acquisitioning, and goal attaining (respectively), there are specific skills unique to each discipline. I can only reflect on mathematics, since I have more than two decades of hands-on experience to use.
The following statements summarize what math skills every high school student should eventually possess. Every high school graduate should be able to say these statements with sincerity and confidence.
I can calculate tip, tax, and commission.
I can convert between percents, decimals, and fractions.
I can reduce, multiply, divide, add, and subtract fractions.
I can solve proportions.
I can use the order of operations on problems that contain two operations.
I can solve linear and quadratic equations with and/or without technology.
I can use a graphing calculator to graph functions, solve equations, change window settings, locate relative max/min points, find point(s) of intersection, and find zeros.
I can evaluate a function (to determine area, revenue, population, ...) given values of independent variables.
I can apply the Pythagorean Theorem.
I can demonstrate knowledge of at least 15 properties of plane geometry: properties of polygons (sides, angles, diagonals, categorization, ...), slopes (parallel/perpendicular lines), basic proofs, or SOH CAH TOA.
I can create a table and graph of a linear function both with and without technology.
I can utilize formulas from coordinate geometry (distance, midpoint, slope).
I can solve a system of equations with or without technology.
I can calculate probabilities of simple events (die roll, spinner, horse race, ...)
Again, these statements outline a minimum understanding of mathematics that students must possess to be able to cope with the technologically complicated word that exists. I would strongly urge students to learn far more if they plan on attending college and being successful in life.
Let it be known that I am fully aware that the categories above are not exactly perfect. For instance, local max/min points would fall within the domain of coordinate geometry, but the skills in these domains are not perfectly discrete. Regardless of how these skills are grouped, all students who leave high school with a diploma should have mastered these skills.
I also believe students should be exposed to skills and concepts beyond what is outlined for minimum proficiency. For instance, students should understand exponential growth (population with humans and bacteria) and decay (radioactivity). They should understand high energy physics via sinusoidal graphs, too. These and other skills are necessities for understanding science, politics, and the pressing issues of our time.
Getting back to minimum proficiency standards, such a skill list begs several other questions to be answered in subsequent posts, namely:
- How can a school institute minimum standards?
- Should exit tests be administered? If so, how?
- Can teachers simply embed these skills within existing curricula and demand mastery with them while also assessing higher skills?
- How far are you willing to take this idea as a teacher who either prepares students for high school or teaches high school students?
- How can you implement minimum standards as an administrator who is responsible for the education of all students (including students who receive special education) in your learning community?
- How can students be taught to take intrinsic ownership of meeting and exceeding the minimum standards?
- Why should a high school be responsible for teaching topics students should have learned at the junior high school level?
- How can minimum standards be adopted while also preparing other students to be proficient or advanced with the standards?
I will address these questions in future posts. I will also address the standards for proficiency and excellence, too.
Most important, math educators should feel comforted knowing that I have gathered several, free, online supports for students. The supports include instructional videos, interactive quizzes, and text lessons to help high school students meet and exceed minimum standards. Simply use the MATHguide link placed immediately below.
(Camera, 2016) High School Seniors Aren't College-Ready, USA News, Accessed on Dec 22nd, 2017 at: https://www.usnews.com/news/articles/2016-04-27/high-school-seniors-arent-college-ready-naep-data-show
(Papst, 2017) 13 Baltimore City High Schools, zero students proficient in math, Fox Baltimore News, Accessed on Dec 22nd, 2017 at: http://foxbaltimore.com/news/project-baltimore/13-baltimore-city-high-schools-zero-students-proficient-in-math