## Case Study: A Seventh Grader goes From “I don’t get it” to getting 100 percents

Monday, June 13th, 2011When this seventh-grader started math tutoring, she felt like she didn’t always “get” math, and the curriculum at her school wasn’t always totally connecting with her brain.

After about eight weeks together, she earned a 100% on a test, and her teacher sent her parents a note that she was doing really well and really seemed to be understanding the concepts in class. After about six months of tutoring together, she just finished up the school year making more 100% percents on her tests!

Here’s how we did it:

** Fill in the gaps. **Algebra builds on everything that comes before, and a lot of 7^{th} graders struggle with algebra because they still feel shaky about decimals, fractions, and other prerequisites. Whenever we found a gap – like when she told me she’d rather convert fractions to decimals whenever possible – we’d go back to where it started to get murky and then work step-by-step through many practice problems until she had mastered the material and filled in the gap. She also learned fun songs for all of the times tables to feel more secure with those foundational math facts.

**Customize: make it visual. ** This student seemed to get a lot out of **seeing** the math. When we went over decimals, we used grids to show how multiple decimals can add up to wholes. When reviewing fractions, we would divide a square into parts to make the concept visual and concrete. When her class started working on adding and subtracting negative numbers, we spent a lot of time using a number line to practice this. Making it visual made the material less abstract and more clear (and also more fun).

**Practice.** Everyone needs to practice challenging material until you internalize it. When she had questions about the material from class, we’d do lots of extra practice problems I’d make up for her on the spot.

For example, when she started working on order of operations problems, I’d create progressively more elaborate order of operations problems for her to practice. This way all the steps became automatic—no more second-guessing or feeling confused.

**Extend.** If we had extra time, we’d do more problems based on what she was doing in class, but take it to the next level. I frequently asked her to create her own problems and was delighted to see that a lot of the time, the problems she made up were harder than the ones I made up for her – because she wanted to make it even more interesting!

I believe creating her own problems helped her feel like math was something that belonged to her, something that she could create, instead of a bunch of impersonal, arbitrary problems from a textbook.

**Preview. ** This same principle of taking it to the next level meant that sometimes, instead of encountering a challenging new concept for the first time in class, we got to introduce it and explore it one-on-one. Then, once it came up in class, this same student who used to feel like she “didn’t get it” knew exactly what was going on.

**Immediate feedback. ** Throughout our work together, she got immediate feedback on whether or not she was doing the problems correctly. This nipped potentially bad habits in the bud and also meant that she could learn the material right the first time without feeling disoriented.

Immediate feedback also meant that when she started to feel frustrated, we would talk about it, take a big deep yoga breath, and clear the air, which made her effort much more productive.

Working with this student was a great pleasure because she did such a good job of communicating what she wanted to work on and what she did and didn’t understand. Because of her hard work, persistence, and open mind, she finished her year earning 100 percents!

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Hi Rebecca,

Love this post!

I love the way that you’ve shown how “slow and steady” can win the race. Going back and filling in the gaps is something that parents, teachers and tutors are often so reluctant to do – but it’s oh-so important. Math is like a tall building – it needs strong foundations!

I also love that your student created harder questions for herself – she obviously felt comfortable challenging herself as a result of the careful groundwork you’d both laid.

Thanks for sharing this – it’s an inspiration to parents, teachers and tutors alike!

Thank you so much, Caroline! I’m sorry I didn’t reply to your thoughtful comment sooner. For some reason it went to my spam folder but now it is properly categorized! Yay for slow and steady! I think going back and filling in the gaps is fun. 🙂

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