Math Unmuddled: Early Algebra

A good grasp of basic Mathematics is important in today’s world, irrespective of the career one chooses to pursue. While Math is typically associated with Science and Engineering, it is hard to think of any line of work that does not involve an understanding of school-level Math (at least till grade 10). Unfortunately, many students struggle with the subject and even develop a fear of Math. The most common reason for this is that they attempt to remember many disconnected rules and procedures, and this makes Math seem more difficult than it is.

The GenWise team has seen many instances of this in their experience. For example, we have asked grade 2/3 students to perform a division like 391/17. After they answer this correctly and say ‘23”, we ask them to multiply 23 by 17. We find that there are always some students who start performing this multiplication instead of immediately seeing that the answer has to be 391 (because multiplication is the inverse of division). When underlying concepts such as these are understood, there is ‘less to remember’ and Math becomes simple and unmuddled. The ‘Math Unmuddled’ series takes up topics that pose common difficulties for children and clarifies these to build strong conceptual foundations.

This course demystifies basic Algebra, which puts off many children (and some adults too!). When students are introduced to Algebra, they often think of it as a subject that is unrelated to any Math they have done in the past. What these students may not realize is that they have been thinking algebraically for quite some time—recognizing and describing patterns, using inverse operations, and finding unknown values. Here are some examples:

• 6 divided by what gives 3?
• I have Rs. 20/- rupees and the slab of chocolate I want costs Rs. 45. How much money do I need before I can buy the chocolate?
• When I add three odd numbers, why do I always get an odd number?

Students struggle with Algebra also because of some specific gaps. One such is that students understand the “=” sign as meaning “carry out the operation”.

Consider this question:

8 + 4 =____ + 5

In a study of 145 sixth-grade students, 84% of them gave the solution "12." Another 14 percent gave the solution as "17." They had not learned that the equal sign expresses a relationship between the numbers on each side of the equal sign.

Yet another issue is the difference between when there is only one variable and when there are two related variables.

Consider  x+3 = 5.

X = 2 is the only “correct” answer here.

In x + y = 7,

x equals 5 when y equals 2.

But x and y could literally have infinite combinations of values which would all be “correct.”

Still another bottleneck is when they have not mastered integer operations. That can make it doubly difficult.

All in all, when students have not been provided with the scaffolding required in the early stages of formally meeting Algebra, it can seem to be meaningless rather than a beautiful notation to better understand and represent our world. They find questions such as the below, to be challenging:

The minimum fare for the cab I use is Rs. 50/ and the fare doesn’t change for the first two km. Then on, the rate is Rs. 20/- per km. How much do I have to pay if I travel

• 1 km? 2 km? 3 km? 4 km? 5 km?
• For some unknown number of km, say, n, can I predict how much I will have to pay?

Note:

The course is not a substitute for learning the topic in school. It is assumed that students already have some familiarity with the topic. Also, in the limited time available in this course, it is not possible to focus on practice. Students must internalize what they learn in the course through subsequent practice, under the guidance of a teacher or a parent.

References:

• https://multiplex.videohall.com/presentations/1196 (Part of The Impact of a Teacher-Led Early Algebra Intervention on Children’s Algebra-Readiness for Middle School (2014-2018),
• http://algebra.wceruw.org/index.html
• https://sedl.org/pubs/sedl-letter/v15n01/5.html
• https://apasseducation.com/education-blog/4-misconceptions-students-have-algebra/