Let’s T.I.N.K.E.R. DIVISION !!! — Blog Series #1
Make it or Break it …
After this I could either
LOVE or HATE MATHS !
The villain is…
LONG DIVISION ALGORITHM !!!
You get me or not, for my rhythm.
Coz I can’t see what’s happening…
what goes in, what stays out ?
what goes up and what goes down ?
how many groups, what’s in groups ?
what’s my left overs dude !
I wanna know, more than EQUAL DISTRIBUTION…
Please tell me what’s more than
REPEATED SUBTRACTION !!!
For I still struggle with Factors, Multiples & FRACTION !
Can we do more than CALCULATIONS ???
Division algorithms are nightmares for many young brains and the way they are taught without basics being clear, AFTER MULTIPLICATION, not with multiplication, as mere Division fact, not actually creating visual facts. These leave lot of loopholes for children for making further connection. Once they start regressing in Division concepts, immediate effects are visible in Factors, Multiples & FRACTION. Its not because of basics of Fractions, but the root cause is multiplication and division learnt partially or just for solving problems and doing CALCULATIONS.
Once multiplication is taught as Repeated Addition & Division as Repeated Subtraction, children might make connections when the numbers are smaller, perhaps in 2 digits, but as numbers grow either as dividend or divisor, they start taking back seat.
One very interesting fact which comes forward is “multiplication makes the number bigger” and “division makes the number smaller” because they are seen as extension of repeated addition & subtraction, respectively. THIS very concept en-rooted in minds thrash when children start doing FRACTIONS & NEGATIVE INTEGERS. What’s that ?
Multiplying fractions make number smaller and Division yields bigger number. Why is that so ? What actually is the process of multiplication & division irrespective of whether we are multiplying integers or fractions : Rationals or Real numbers to be precise.
First and foremost DEVELOP RESPECT for PLACE VALUE SYSTEM. One needs to understand, concepts of Carry overs, Borrowing, why do we add trailing Zeroes when we multiply by 10’s or add some XXX while using standard multiplication algorithm. What numbers are we pulling down when we divide and why ? Why do we tell children “If first number of dividend is smaller than divisor then use first 2 numbers ? ” This blog and upcoming ones will unlock the mysteries of simple but effective maths for young brains to develop thought process for DIVISION.
Consider the division problem: 24÷4 and 24÷6. What does this mean? What are we being asked to compute?
Traditional school curriculum teaches following strategies, at different stages of Division learning.
- Division as repeated subtraction: 24÷4 is asking for the number of times one needs to subtract four from twenty four to get to zero, whereas 24÷6 is asking for the number of times one needs to subtract six from twenty four to get to zero.
2. Division as finding groups: 24÷4 stands for how many groups of four can be found in a collection of twenty four, whereas 24÷6 stands for how many groups of six can be found in a collection of twenty four.
3. Division as distribution: 24÷4 is asking for how many star-stickers each child receives if twenty four star-stickers distributed equally among four children, whereas 24÷6 is asking for how many star-stickers each child receives if twenty four star-stickers distributed equally among six children.
4. Division as reverse multiplication: 24÷4 is same as : What times four gives the answer twenty four? 24÷6 is same as : What times six gives the answer twenty four?
5. Division as multiplication of fractions: 24÷4 is actually a one-fourth of twenty four, whereas 24÷6 is actually a one-sixth of twenty four.
6. Division as contained in : This is my personal favorite to think of the phrase CONTAINED IN. This helps me extend the division’s thought process to larger numbers, fractions and negative integers. It connects to PLACE VALUE SYSTEM appropriate. This also helps in connecting to multiples & factors, highest common factors & least common multiples (HCF-LCM).
6. Division as long division algorithm : And now compare the above to this.
How any child on earth could start relating division to this above shot, if he/she hasn’t rote learned and deep rooted memorized that 6 x 4 = 24 and(or) 4 x 6 = 24. Even then probability is less, one could !
Let’s extend the above methods with traditional algorithm first and see how it fits in child’s mind for larger numbers, as this can never be memorized like the smaller numbers, one ACTUALLY NEEDS TO KNOW WHAT IS HAPPENING & WHY ???
and these are calculated & solved like following traditional long division algorithms…
If these calculations remind of childhood division classes and its effects and non-usefulness, then we certainly need to stop teaching division this way. Let’s make the process more intuitive , connected, sensible, and which resonates with child’s mind !
More in this series …
PS : If you like to hook up to make division simpler, follow me and clap if you like the write up. Do leave your comments, if you have any queries, word of appreciation, memories related to your division classes !
