Math is About More Than Number Crunching as well as Formula Writing

I convey been participating inwards a majority report over at the Math Coach's Corner on this book.

It describes ix habits kids (and adults!) require to back upwards mathematical thinking. I was reading virtually habit iii which is identifying similarities too differences too recognizing patterns too I saw this quote:

“If identifying similarities too differences is basic to human idea too boosts pupil achievement, why, then, are nosotros nevertheless content to settle for let on crunching too formula writing every bit the dominant shape of instruction?”

This got me genuinely fired upwards too every bit I was leaving a comment over on the majority study, it turned into the story of my ain mathematical instruction too why I intend their needs to locomote a shift inwards teachers' focus from teaching kids how to do math to helping kids intend virtually math.

Here it is!

I was taught arithmetics inwards uncomplicated schoolhouse too didn't discovery it especially interesting but was ever quite proficient at it. When I intend virtually my ain instruction inwards math, it is amazing that I didn't completely loathe it. We used Addison Wesley trend textbooks too everything was taught every bit a procedure. Nothing was ever connected for us at all. In 5th score I think nosotros had a broad make of might levels inwards our classroom. The instructor allowed to a greater extent than or less other pupil too I to root from the dorsum of the 5th score text majority too run our agency forward. I don’t intend nosotros ever got whatever instructor time, nosotros simply did page afterwards page of rote practice. We fifty-fifty checked our ain run too graded our ain tests amongst the teacher’s edition. I idea it was a bully run a jeopardy hence but instantly it seems similar a recipe for disaster!

In middle schoolhouse too for algebra 1 too geometry, I was able to follow the procedures that had been taught too relied on my bully retentiveness to “plug too chug” my agency through these classes amongst splendid grades. Looking back, I run across that I didn’t genuinely empathise the math but I could do it. I was never taught to intend virtually the numbers I simply operated on them. It wasn’t until 10th score when I stepped into an Algebra 2 shape that I ever started getting the connections betwixt things. I had a fantastic instructor who helped me to run across connections too challenged me to alive upwards to my mathematical potential. Luckily I had the same instructor twice to a greater extent than earlier graduating from high schoolhouse too he genuinely helped foster my honey of mathematics.

As an undergraduate, I had a dual major inwards uncomplicated instruction too mathematics too took to a greater extent than or less really challenging math classes. I had the widest make of professors you lot tin perhaps imagine ranging from the really proficient to the completely inept. I had a dynamic, inspiring instructor for my combinatorial theory shape too to this twenty-four hours I acquire hence excited virtually combination problems too I honey doing them amongst my students. I also had to a greater extent than or less of the worst professors imaginable too I intend instantly looking dorsum it is because they couldn't or didn't connect what they were trying to learn me amongst what I already knew. I don’t know if they genuinely understood the connections themselves. I think i professor who taught a shape on groups too rings would convey the entire shape demonstrate upwards at his role during role hours because none of us could figure it out. Finally he told us all that if nosotros showed upwards for shape too tried our best, he would give us all a B.

It wasn’t until I began teaching too started working on my master’s score inwards K-8 math instruction that I in conclusion genuinely understood the connections inwards math. Being introduced to things similar the expanse model for multiplication too in conclusion getting that multi digit multiplication, fraction multiplication too polynomial multiplication are all connected past times this model changed the agency I persuasion math. Instead of a listing of disconnected procedures, I had a visual model that could assist me solve ANY multiplication problem. Through my master’s program, I also in conclusion got the connexion betwixt algebra too geometry. When I was inwards high schoolhouse they were taught every bit 2 dissimilar subjects but through the problems I worked on inwards this program, I got to run across that you lot tin solve many problems amongst algebra or geometry. I also learned that I tend to favor solving problems amongst algebra too genuinely had to opened upwards my hear upwards to run across how the same work could locomote solved amongst geometry. It made me a meliorate mathematician too a meliorate teacher.

When I intend virtually my ain math education, I tin run across why I learn the agency I do too why I am ever annoying my students amongst my sayings similar “think virtually the math, don’t simply do it!” I spent many, many years simply doing the math too was quite successful at it. However, I was missing the passion, agreement too beauty of mathematics. I could non solve novel problems. I could exclusively plug numbers into formulas. If I forgot a formula or a procedure, I had no agency to acquire dorsum too simulate it for myself. I convey a bully retentiveness hence I did good inwards full general because I tended to non forget. As my deeper agreement of mathematics developed, it helped shape me into the instructor I am today. I acquire the connections now. I know if my response makes sense. If I forget a formula or a procedure, I tin rely on other things that I know that are connected to it to assist me out. I honey aught to a greater extent than than jumping into solving a novel problem. I thrive on trying novel math too applying my novel cognition to what I convey learned inwards the past. I honey math.

I desire my students to experience virtually math the agency I do now. I desire them to convey the connections too locomote passionate virtually using what they know to solve novel problems. I don’t desire them to settle for beingness taught how to do it! I desire them to build their ain cognition too larn to intend instead of simply applying procedures. I am non willing to allow my students larn math the agency I did. I desire to a greater extent than for them. It is fourth dimension to halt teaching kids how to do math too root helping them larn to intend virtually math!

What do you lot brand math virtually to a greater extent than than let on crunching too formula writing?