The best way to teach math in the 21st century
Two different views on math instruction
Basketball and math both demand repeated drills to improve skills
By Phyllis Hunsinger
Math scores, as reflected on standardized tests in the United States, continue to be dreadfully low. The number of American students completing degrees in mathematics and engineering is at an all-time low. The above sentiments regularly appear in newspapers and in other publications. Without a doubt, there is reason for alarm.
Students today are as capable of mastering basic math concepts as they have ever been. However, the approach to teaching math is not as effective as it once was. As March Madness draws to a close this week, it occurs to me that if we coached basketball — which I did several times during my teaching career — in the same manner in which we teach math, there would be far fewer students interested in basketball.
Young people want to play with the basketball and actually expect to work and drill on the basics day in and day out. The rules of the game are introduced slowly, interspersed with continual drills of the basics. Players are taught techniques such as boxing out and breaking the press. They practice those techniques, as opposed to trying to “discover” how the processes came to be.
There are times when the “why” is important. Knowing how principles work can aid in long-term memory and understanding. But too often, modern math books spend an inordinate amount of time having students discover the theorems and algorithms for themselves.
Most basketball players are interested in how they can use the techniques in playing the game. They are rarely concerned with how the technique was first discovered. The same applies to math students.
By the end of the fourth grade, unless students can rapidly recite and write the basics of addition, subtraction, multiplication and division, they are ill-prepared to master other concepts, much like the basketball player who cannot effectively learn a lay-up without dribbling skills. The player must be able to dribble instinctively so the focus is on the basket. Students need to instinctively know the basic facts so they can focus on the solution and the problem solving needed to get there.
Students find it difficult to comprehend more complex math concepts often because they get too frustrated trying to solve the basic computations. This is especially evident watching students wading through statement (word or story) problems. Compare this to the player going down court for a lay-up: If the player has to concentrate totally on dribbling the ball, making the basket is going to be a much more difficult task.
Some years ago, the education gurus determined memorization to be a bad teaching method. However, there are many facts in life that need to be memorized: addresses, phone numbers, rules of English usage and basic math facts, to name just a few. When students are held accountable for mastery of the basics, progress in the subject is possible. As basketball players become more competent in the basics, they progress to varsity teams and beyond. The basketball coach knows to continually stress the basics. Math teachers would do well to copy that approach.
Coaches bring a lot of enthusiasm to the court. Likewise, math teachers need to bring a lot of enthusiasm to the classroom. Based on many years of teaching math, I thinks it’s time we return to tried-and-true methods that focus initially on math drills and memorization. That will build skills and enthusiasm among young math students.
Phyllis Hunsinger taught secondary math, coached basketball and was an administrator during a career in education that spanned 40 years.
Modern math requires more from students than ‘drill, drill, drill’
By Jody Mimmack and Bill Larsen
For too long it has been socially acceptable to admit “I’m just not good at math.” Change the word math to reading and it feels quite a bit different. Would it be acceptable for 80 percent of the population to openly admit, “I’m just not good at reading?” The answer is unequivocally “No.” Our 21st century economies require a dynamic, flexible workforce with people who understand and are able to apply mathematical concepts within the real world.
As you have read in this very newspaper, School District 51 students were not performing at high levels in the area of math. In response, in 2009 School District 51 selected a new math curriculum for all students, from kindergarten through 12th grade.
A team of teachers and specialists carefully studied a range of curricular options. The curriculum adopted was aligned from level to level and contained the critical 21st century skills addressed in the Colorado Academic Standards, as well as those found in recommendations from The National Council of Teachers of Mathematics. The math curriculum chosen by District 51 staff and adopted by the Board of Education best support student learning, making connections and transfer of knowledge to different settings beyond the K-12 school system.
Although most of us learned by the “drill, drill, drill” method, too few of us understood the why of math and too few could apply it to practical situations.
These traditional methods did not teach most students to problem solve or think critically, but rather taught students to memorize a specific formula or trick to solve a problem. The emphasis was on rote learning and practice.
Today, in addition to students needing to master mathematical concepts, the 21st century skills outlined in the Colorado Academic Standards also require students to master process skills such as critical thinking and reasoning, information literacy, collaboration, self-direction and invention. Because students are now expected to master concepts and processes, we also had to look at teaching students in a new way.
Because the research shows that learning with concrete experiences, modeling with representations and moving to the abstract produces higher levels of understanding in math — this is called the CRA model — we were timely in adoption of new math curriculum.
An example of the CRA model for the mathematical concept of fractions begins as early as kindergarten, with students understanding division and fractions through the sharing of materials into equal groups. By third grade, students should understand that “parts of a whole can be modeled and represented in different ways.” Fifth graders need to “formulate, represent and use formulas to add and subtract fractions with flexibility, accuracy and efficiency.” This understanding is extended to ratio and proportional thinking in middle school and eventually culminates in high school with algebraic thinking.
The new math curriculum is supporting math growth for District 51 students.
Before the math curriculum was implemented, our students were performing 1 percent below the state average.
Since the new curriculum has been taught, District 51 math growth scores have increased by 5 percent overall, exceeding the state average by 4 percent.
The Colorado Department of Education and District 51 are committed to graduating students who are “college or workforce ready” and the new math curriculum is just one of the ways we support this commitment.
Jody Mimmack is District 51’s Executive Director of Curriculum and Assessment. Bill Larsen is the Executive Director of High Schools. Liz Zitterkopf, Ann Conaway, Julie Schmalz and Nicole Wimsatt also contributed to this column.