Part of standardized test preparation is not only knowing the content of the exam, but also being able to self-assess why you're getting a question incorrect.  In this blog post, one of our most experienced standardized test preparation tutors reviews how he buckets content knowledge when teaching standardized tests, and how it will help you improve your results in the future!

# "I didn’t know I knew it"

The first thing I look for when going over test results with my new students is when they missed a problem simply because they didn’t realize what the question was asking or were unsure how to use what they already knew. For example, here are the misinterpretations of math questions that one of my students experienced during her first take: On a problem about percent reduction, she didn’t notice the clue word, “about” in the question, and so she didn’t realize that she could round the given number into a value easier to reduce. On a problem about perimeter of two soccer fields, she didn’t know what “not adjacent” meant, i.e., that the two fields didn’t share a side and so had to be measured separately.

# "I almost knew it"

The next step is to cover content that feels partially but not completely familiar. One student knew how to do one-step algebraic equations, such as 2x = 8 but was unfamiliar with algebraic inequalities, such as 2x > 8. On a problem requiring translation of a complex English sentence into math, one of my students didn’t realize that “of” meant that he should multiply two numbers together. This is a perfect example of an “I know part of it” problem, because he knew how to calculate a percent of a number, e.g., 30% of 100, he knew how to find a fraction of a number, e.g., ¼ of 12, and he knew how to solve for x, e.g, 5x = 15. He found it overwhelming, however, to see all of this presented in a single question, particularly when asked to take a percent of a variable: “30% of ¼ x is equal to ⅓ of 27. What is the value of x?” Our approach was to translate the English into math in pieces, focusing first on the multiplication indicated by the first “of.”

# "Now I know it"

Entirely new content doesn’t have to be complex, either. A student might not know that zero multiplied by anything is zero. A simple intuitive explanation returns to the rows that I use when teaching multiplication. Four rows of eight chocolates in a chocolate box adds up to 32 chocolates. One row adds up to just eight, and zero rows of eight chocolates adds up to zero. Even learning the Pythagorean theorem for the first time isn’t particularly difficult for a student who know how to square numbers.

## Cycling through topics

Any given session will probably incorporate two or three of these content areas. The homework I assign focuses primarily on these mid-level, “almost knew it” topics, includes a quick review of the easiest topics, and provides a very circumscribed review of the topics learned for the first time during our session. It’s important to weave old content into subsequent sessions for review. High scores depend as much, if not more, on remembering what has been learned as on learning new content. Fortunately, a good book tends to have increasing levels of complexity within each topic area, e.g., one-step followed by two-step equations, which are followed by systems of equations. This allows the earlier skills to be drawn upon when solving increasingly complex problems in subsequent weeks. Rather than assign all the algebra content across three consecutive weeks, I’d choose to assign easier content across two or three areas after the first week and then move onto intermediate and ultimately advanced content in subsequent weeks. Students will likely perform at different levels across different content areas, and we can’t practice every area each week, but I find that consistent review of multiple areas helps keep students up to speed for test day.

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