Like many, my elementary school was fortunate enough to have a computer lab and it was always a mad scramble to get the best programs (on 5.5″ floppy discs, no less) to play at the time. But my father was also quite interested in computers and we have always had at least one computer in the household from when I was 6 years old and onward.

One of my most memorable educational computing experiences was, ironically, one of my most hated as well. My dad had picked up some programming skills and had brewed up, among other things, a math practice program that would generate random, single operation, arithmetic questions using numbers between 0 and 100. It would also time your progress and track your score. Much to my dismay, I had to complete 100 questions each day and print out my time and score to show my dad. My initial distaste for it began to fade as the constant practice helped my math speed and accuracy and it soon became a challenge to see how quickly and accurately I could complete the 100 questions. The practice and math foundation that it built continues to serve me well to this day.

Thinking back to this experience brings up a few questions though:

- Current pedagogical trends seem to focus less on rote memorization and drill, and more on creativity and analysis. However, all knowledge proficiency involves some amount of skill proficiency as well. But is it possible that the continued reduction in skills practice will become a detriment to student learning? Do educational trends like these cycle?
- Much of the success of my dad’s math program was built upon the speed and efficiency of the computer to reduce his workload (ie- thinking up questions, checking the answers, timing the session), and many current educational technologies do provide such conveniences (ie- online quizzes, tracking of grades, assignment submission). But when deciding on which technologies to implement into the classroom, how do we differentiate between ones that provide truly innovative learning experiences and ones that only provide convenience?

It is interesting to me that you have hit upon the controversy that is rampant in our school board regarding math instruction. It has been my experience over the years that although discovery and exploration in math is a good thing, students still require an understanding of basic math concepts before they can be confident to explore other ideas. I teach grade 7/8 and have had the assumption that the students coming into my class would have a good grasp of basic addition, subtraction, multiplication, and division facts, however, this assumption has largely been false, particularly when it comes to multiplication and division. My students do not have these at their fingertips and generally spend huge amounts of time figuring out basic concepts, rather than being able to focus on discovering new relationships or functions in mathematics. Due to appalling math scores on the EQAO tests the last few years, our board has taken a step back towards drills and rote learning. We are using Strings concepts and math practice to enable our students to have that skill proficiency to tackle the higher order thinking problems.

Anne

Hi Lawrence,

Your post makes me think about my experience with the game Number Munchers. Do you remember that game? You could decide which math concept (multiples, factors, primes) to play and points were awarded for speed and accuracy. Being someone who did well with math memorization I remember challenging myself to figure out prime numbers. I had not been taught the subject (and I can’t recall being specifically taught this concept in the classroom) and I had to figure out what prime numbers were through trial and error. Eventually I did come to have a good understanding of what prime numbers were because I was motivated to succeed in the game. Throughout the MET program I have come across the Video Game Model and other research related to this concept. Although I can see the argument for eliminating “drill and kill” focussed teaching, I do see how it can be beneficial for many students to practice repetition to develop memorization for basic facts. I incorporate mad minutes for basic facts into my primary math classroom to start to build that memorization. I have found that it extends well when introducing long addition and subtraction and then moving on to multiplication. Similar to you, I also worry that a reduction in skills practice will be detrimental to student learning and that is why I choose to include some of it in my teachings.

Allison

Allison, Thank you!!! As a Math 10 and Physics 11/12 teacher, I need my student to know their times tables inside and out. Those students that do not have them mastered, lack confidence. If you lack confidence in these courses, you greatly reduce your chance of success and anxiety can be crippling. Times tables are my litmus test, to be honest! Having a solid understanding does not guarantee success, but not having them will almost always guarantee failure. It is not that students are not allowed calculators, either. Perhaps an pathological analogy would work here? lack of confidence (disease)–> anxiety and lack of times tables (symptoms). Or would lack of times tables be the disease that present the symptoms of low confidence and anxiety? Hmmm… ~Dana

Hi Lawrence, In response to your first question, I believe that the pendulum has swung too far in some provinces regarding the elimination of rote memorization. (Why do Ministries go “all in” on certain educational fads?) I have yet to meet a successful senior physics student who does not have times tables memorized. I would bet that these are the students who have had them from elementary school, as well. Does EVERYONE have to take senior high math and physics? Probably not— the world would be a most boring place if we were all math and physics types! However, I still believe we are inadvertently instilling anxiety into our students who do not master the basics in elementary, due to rote memorization being shunned. Do we only do rote learning in a math class? I sincerely hope not! But there is a time and a place for it, IMO. I have had waaaaay too many tears flowing in my math class— typically amongst high achieving humanities students who just need to take the minimum amount of math to get into university. Socially promoting students until Grade 9 (in BC), does not help those with significant math challenges, either, but that is a different conversation*. ~Dana

(*I wonder if school districts could offer Summer School Math classes for Middle school students who were deficient in math. What a help and a confidence boost it would be for them to have that extra support!)

Hi Lawrence,

You have touched upon a couple concerns I have held for a while now. With inquiry-based learning at the forefront of best practice these days, it’s hard to find anyone defending rote memorization and drill in the math classroom these days. I am a huge supporter of online math platforms like Mathletics and Khan Academy and have found high levels of student engagement with these programs at the grade 6-8 level. I think it is safe to say that most of these programs are more convenient for the teacher and the student and but, yes, are some platforms more pedagogically sound? For instance, Khan Academy asks students to complete a set number of questions correctly (usually 5) in a row before moving on to the next skill. Mathletics asks students to complete 10 questions and the teacher decides what score is acceptable. Both models motivate students to progress through each skill in their own way but I wonder if one model is better supported by current pedagogical research?

Great questions Lawrence and ones that we will touch upon in Module B. I applaud your Dad for creating the program, and you for completing the problem sets set forth, Samia