December 1-2-3-4, 2021
I have a lot of empathy for teachers with everything that is going on in schools today. It was different when I first started teaching. I also have empathy for students who go unchallenged in many of today's classrooms.
TKA started in 2011 as a reaction against Common Core reform math and minimal guidance methods. I fused basic algebra ideas with standard arithmetic. I taught algebra ideas by explaining worked examples (models) with practice and feedback in class. The importance of traditional arithmetic was stressed, starting with automating single-digit math facts that supported the standard algorithms. It begins in 1st grade. (Note: The pandemic effect put kids behind. Unfortunately, it was a lost year for many students. For example, I was able to teach much more content to 4th graders a few years ago than 4th graders today. Elementary school classroom teachers are struggling to help kids catch up, but I think some arithmetic gaps will remain.)
Today, much of education is not about teaching kids to read, write, do arithmetic, or about achievement, merit, and excellence. Instead, schools have become a bastion of equity, diversity, identity, and inclusion. The liberal ideology is strongly supported by teacher unions, schools of education, federal and state education departments, school boards, and others, including the media. I believe education has gone down the rabbit hole, an abyss. Commonly, there seems to be an inverse relationship between excellent academics and equity. The "equity" reformers have been dumbing down the curriculum for decades. Equity has come to mean the same outcomes. The same outcomes are not possible unless content and standards are lowered substantially. Furthermore, kids are not the same in academic ability.
Reflections of an Education Contrarian: A Divergent View
I am an education contrarian. My views often diverge from mainstream education "group think" and orthodoxy. For example, I teach 4th graders real algebra. Also, by 1st or 2nd grade, students work with expressions and variables (symbols that represent a number), evaluate expressions, solve addition and subtraction equations (functions) use guess and check, and later inverses (3rd grade). Given an equation, the student builds a table of values (x - y) and extracts the (x,y) number pairs from the table to plot points in Q-I, even in 1st grade.
1st Grade Algebra: Teach Kids Algebra - TKA
In TKA the focus is on variables, order of operations, and functions.
Functions: Equation-Table-Graph y = x + x +2
|Functions In the 1st Grade (STEM Math)|
Equation, Table Building, & Point Plotting (Graph)
Algebra is about figuring out what you don't know from what you do know. (LT) That's why we study algebra! It's why I teach 1st graders functions (equations-tables-graphs) fused to the arithmetic they are learning. Ian Stewart points out, "Mathematics happens to require rather a lot of basic knowledge and technique." But, first, you have to know something in long-term memory: facts and procedures. Learning arithmetic or algebra well involves memorization, repetition, review, and practice-practice-practice. In short, hard work and persistence!
Note: I am teaching two 4th grade classes at the Title-1 urban school. Almost all students are minorities. I am a volunteer guest algebra teacher and give lessons two hours once a week. 12-1-21
Teach Above the Curriculum!
I am increasingly concerned about academic achievement in schools, especially mathematics and science. Kids can learn more in-depth, key math content earlier and faster. I challenge teachers to stretch beyond state standards and progressive reform math. Teachers of 2nd graders, for example, should teach above the 2nd-grade curriculum and dive into the middle of the 3rd-grade curriculum. Students in 2nd grade should memorize half of the multiplication facts and calculate with the standard algorithm.
One of the most debilitating trends in many progressive schools that teach reform math is their excessive emphasis on calculators. Many reform math programs expect students to use them starting in the elementary grades. Calculators enable students to do arithmetic without thinking about the numbers involved in a calculation. For this reason, it makes sense to use them, let's say, in a high school science class (chemistry and physics). But for elementary students, even middle school students, the main goal of math education is to get them to think about numbers and learn arithmetic--both factual and procedural knowledge.
In K-7, toss out calculators, most manipulatives, minimal guidance methods, and group work. Instead, explain worked examples (models) and give plenty of practice. Students should practice 30 problems a day, mostly review.
We need to train teachers better. They should be required to take a precalculus course in college, along with college-level chemistry and physics, even future 1st-grade teachers. Most educators will disagree. Still, K-8 teachers must know math and science because they teach math and science.
(1) Students can learn more mathematics than the current curriculum.
(2) Students can learn more math earlier than previously thought (e.g., the beginnings of multiplication and algebra in 1st grade).
(3) Students can learn more math faster.
Note: Teach Kids Algebra (TKA), my algebra program for grades 1 to 5, started in mid-January 2011 with two 1st-grade classes (7 Lessons), two 2nd-grade classes (7 Lessons), and one 3rd grade class (twice-a-week Lessons). The algebraic thinking lessons introduced true/false statements (=), variables, and the algebraic rule for substitution. Then, it quickly expanded to functions: equation-table-graph. TKA is STEM mathematics for very young children. Through the years, most students learned the algebra content with once-a-week, hour-long lessons. TKA in 4th-grade classes started late this school year (November 2021). TKA for 2nd grade will begin early next year.
- 1. Using Numbers,
- 2. Measuring,
- 3. Communicating (graphs), and
- 4. Using Time/Space Relationships (geometry).
In SAPA, 1st-grade students learned negative numbers. Today, there is nothing like it. However, some SAPA math topics are part of TKA, especially integers, linear functions, and graphing. Much of the math taught in SAPA was above the current curriculum.
Algebra is about figuring out what you don't know from what you do know. That's why we study algebra!
What has happened to math education in the US?
We chase after test scores instead of credible academic achievement and continue a sameness ideology via Common Core and most state standards. Teaching to the test is a flimsy curriculum and a lousy way to teach mathematics to novices. Also, we expect kids to do critical thinking without sufficient background knowledge in long-term memory, even though, according to cognitive science, factual knowledge in long-term memory must precede higher-thinking skills.
Minimal teacher-guided instruction, very popular in reform math, is ineffective and inefficient and contributes to substandard achievement, according to researchers Kirschner, Sweller, & Clark. Kids cannot solve math problems on a near-empty math tank (the long-term memory). For example, critical thinking will not help a student solve a trig problem without specific, prerequisite trig knowledge in long-term memory and practical experience working with similar trig problems.
Drills & Lessons
In 1895 the "Committee of 15," sanctioned by the National Education Association (NEA), made recommendations for elementary schools (grades 1-8). Arithmetic should be taught beginning in 1st grade with 60 minutes of oral drill daily plus five textbook lessons a week to prepare students for geometry and physics in 7th grade and algebra in 8th grade. These recommendations make good sense even today, but, unfortunately, the wisdom of old souls has been replaced by a progressive agenda of reforms and ideology that don't work (e.g., Common Core taught as reform math).
I read comments in other blogs that are opinions or off the mark. I often exclaimed, "What is this person talking about?" When I write about education, I write from things I have done in the classroom. I was not born when the Committee of 15 laid down its recommendation, but if you want kids to learn stuff, then the Committee of 15 was correct, daily drills in addition to five weekly lessons. When I was a classroom teacher, I often implemented daily practice with daily lessons.
The test of the morality of a society is what it does for its children. --Dietrich Bonhoeffer, Theologian