Sunday, November 02, 2014

English-Math Synergy Helps Students Overcome Math Fear

Community college students generally dislike math word problems. The difficulty is particularly pronounced in introductory algebra, intermediate algebra, and introductory statistics courses. Students often cannot make sense of what the question is asking them to solve. It frequently comes down to a difficulty with the English language. The challenge is not restricted to ESL students but to native speakers as well. Students can solve algebraic problems if they are expressed in straightforward mathematical notations but if the same problem is expressed in words, they are lost.

Consider the following:
Solve for x in the equation
x – 0.2x = 320
Students find it easy to solve:
0.8x = 320
Dividing both sides by 0.8, x = 400

Now consider the problem: After a 20% reduction, you purchase a camera for $320. What was the camera’s price before the reduction?

Suddenly this problem looks strange and difficult. There is that 20 percent reduction. There is that word ‘before.’ How exactly do they translate into mathematical notation?

Consider another problem: Solve for x and y.
x + y = 146
x = y + 12

Again, this appears to be an easy problem to solve.
Substitute the value of x from the second equation into the first:
y + 12 + y = 146
2y + 12 = 146
2y = 134
Dividing both sides by 2 give y = 67
Thus, x= y + 12 = 67 + 12 = 79

However, suppose the problem is presented like this:
In two consecutive games, the college basketball team scored a total of 146 points. The team scored 12 more points in the first game than in the second. How many points did the team score in each of the two games?

It is the same problem but writing down the two equations, in which x = points scored in the first game and y = points scored in the second game, pose a problem for many students.

Finally, consider this problem:
Solve for x and y:
x + y = 16000
0.06x + 0.08y = 1180

Students can substitute the value of x from the first equation into the second and solve for y and then solve for x.
0.06(16000-y) + 0.08y = 1180
Solving for y gives y = 11000. Hence, x = 5000.

However, suppose the problem is stated this way:
You invest part of $16,000 at 6% interest and the remainder at 8% interest. If the annual yearly interest from these investments is $1180, find the amount invested at each rate.
Again, creating a set of linear equations to answer the question seems as remote as the moon, visible but beyond reach.

It may be helpful for math and English teachers to compile a list of words and their meanings in everyday context and in the context of mathematics, as well as a list of mathematical phrases and their translation into mathematical notations. By working together, math and English faculty can help students overcome their fear of math word problems, enrich their vocabulary and enhance their critical reading and writing skills.

The larger goal is to help them see the connection between Math and English. It is through such interdisciplinary connections that students can discover new insights and make new connections of their own.

A partial list of words may include:
constant, variable, ratio, proportion, fraction, slope, factor, rational, irrational, commutative, percent, percentile, integer, decimal, compound, absolute, perimeter, area, volume, coefficient, term, monomial, binomial, trinomial, polynomial, simplify, evaluate, solve, equation, inequality, linear, non-linear, base, power, exponent, exponential, hypotenuse, numerical, numeracy, innumeracy, round-off, round-up, sequence, series, intersect, intercept, radical, elliptical, radius, circumference, circular, parabola, parabolic, ellipse, elliptical, quadratic, imaginary, complex, conjugate, matrix, unknown, vertex, model, prime, square, cubic, parallel, horizontal, vertical, grouping, precision, accuracy, dependent, independent, function, one-to-one, one-to-many, many-to-one, domain, range, average, mean, median, probability, hypothesis, regression, correlation …

Fragments may include:
at least one, at most 4, ratio of a to b, x split into k equal parts, golden rectangle, golden ratio, margin of error, confidence level, significance level, confidence interval …

Serendipity occurs at the intersection of disciplines. It is something that has been missing in America’s schools for far too long. The time has come to address this urgent issue. A first step will be to create synergy between English and math teachers. There is plenty of data that show how student performance in solving math word problems increase when they are clear about the precise meaning of words as they are used in their everyday context and in mathematical context.

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