At least 5 times a week, someone will share that their son or daughter is a poor test taker. We all know people who ace the test with no effort but much can be gained by focused studying and commitment and I do not just mean test scores!
Tests may not always show knowledge and skills — that 7 in Physics was tough freshman year (yes out of 100!) but I learned so much about attention to detail and focus. How many times do we see 2^3 (2 to the 3rd) = 6 rather than 8? I call these “fuzzy errors”. People can improve their test scores and their attention to detail by answering the exact question and noticing the finer points of what they are being asked.
How did I learn to do this? The hard way — btw, my next score in Physics was exciting because it was double digit — 11! (because class avg was so low, I still managed a C in the class).
Yikes!!! She saw that superscripted exponent as just a plain vanilla x. How often do students not answer the exact question but something super wicked close? Scores do not always reflect student knowledge and skills due to these “fuzzy errors”.
People can improve their Math skills and scores by paying attention to the details to reduce fuzzy errors. I learned this the hard way in engineering school: a little m means milli or thousandth .001 buta big M means mega or million so if you write a M when you mean m your answer is off by a billionfold — that’s a BIG fuzzy error!
For lesson planning, multiple choice with “good wrong answers” can be used for instruction so that students see common errors and misunderstandings and get less fuzzy. Quantitative Comparison questions are amazing for this — they were sadly deleted from the SAT in 2005 but still alive on the GRE QC questions.
During exams, I walk around with a crayon or highlighter and make visual comments on student papers to point out details such as a missed negative sign (I obviously missed the above during the College Algebra final!!). This helps students to improve their metacognition and attention to detail which strengthens student skills, scores, confidence and enjoyment of Math.