Rebecca Zook - Math Tutoring Online

When this student came to me this past June, she had been invited to take a placement test in the fall to see if she would place into an honors math class, and wanted help pacing herself on her summer math packet.

I just found out that she placed into honors, and she was so excited when she told me that she screamed on the phone! I am SO proud of her hard work and persistence!

Here’s how we made it happen:

Openness and Trust. Throughout our sessions together, this student was extremely transparent about what she did and didn’t understand. This was enormously helpful, especially because while we thought the summer math packet consisted of review only, it turned out that a ton of material was stuff that this student had never learned. Her willingness to tell me whether she was elated or frustrated–frequently with a self-deprecating sense of humor–helped us build camaraderie and also made our work together much more effective.

Which brings us to…Adjust as you go. When we realized that we had a lot of material to cover from scratch, instead of just reviewing, we adjusted the plan and decided to meet more frequently.

Break it down. The packet was extra-challenging because each page was like a tossed salad, blending problems from all different parts of the curriculum. While this is a great strategy to use when you’re reviewing material, it is not an effective way to learn something new.

So we backtracked, and my student learned one prerequisite skill at a time, practicing it thoroughly until it felt comfortable and automatic. Then, we combined these skills in more complex problems, gradually building up to problems as hard as the ones in the packet.

Practice outside of sessions. I also gave this student individualized worksheets that gave her a chance to practice and internalize the skills we were working on, with answer keys so she could check her work as she went (instead of waiting to talk to me and then finding out that she had practiced something the wrong way). This was especially important because it was the summer and she wasn’t getting a regular dose of math from a school math class.

Feedback on solo work. After building up her skills, my student worked independently on chunks of the packet at the time. This way she got comfortable with problem sets where different kinds of problems are juxtaposed on one page, just like they would presumably be on the placement test. Then, when we worked together, we would go over all of her work so she knew she was on the right track.

Which brings us to, “What did I do wrong?” At first, my student just seemed annoyed with herself when she made a mistake, but I really emphasized to her that it’s okay if you make a mistake as long as you take the time to ask yourself why and learn from it. Scrutinizing and learning from errors gradually went from being an irritating chore to just a routine and helpful part of the learning process.

Enthusiasm. More than any other student I’ve ever worked with, this one has a great appreciation for mathematics’ dramatic resonance and poetic potential. When she learned how to find the solution to a system, she said that that would be a great name for a band. Frequently she remarked that new concepts we were going over would make the premise for a great science fiction story.

Her gleeful excitement about the greater meaning of what she was learning seemed to help her take the tough stuff more in stride, because even the “annoying” math procedures were part of something that was exciting to her.

Parental backup. The best tutoring happens when everyone works together as a team, and this student’s mom was totally focused on the process of learning. She made sure that her daughter completed assignments in between sessions (especially important during the summer). She asked me thoughtful questions about the material and her daughter’s progress that showed me she herself was deeply engaged with her daughter’s math material.

Because she was so organized and also willing to re-learn math and ask questions about the parts she wasn’t sure about, she was also a great role model to her daughter. Her involvement and support was instrumental in her daughter’s success.

I was so thrilled to hear that this student had rocked her placement test and placed into honors! Hooray!

***Update: I just found out today (12/7/2011) that my student got an A for the trimester in her honors math course! I love it when students become completely self-sufficient and continue to succeed after they “graduate” from tutoring. Hooray!!

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Joost Elffers & Saxton Freymann‘s delightful Melon School Bus

Happy back to school! I wish you a magnificent return full of friendly classmates, excellent teachers, awesome games at recess and cupcakes in your lunchbox!

As we head back into the swing of things, many parents realize that they want to help their kid with math, but aren’t quite sure where to start.

Here are five tips you can use throughout the entire coming year — no matter what you’re working on or how old your kid is.

Here we go…

When your kid gets stuck, help them try something different. Math is cumulative; today’s most challenging questions are on material that eventually your kid will need to have down cold. So if they’re hitting some math turbulence, help them address the issue now instead of hoping it will just blow over. Read the book together. Go over their notes from class. Look up a YouTube tutorial. Encourage them to ask their teacher to explain it again. If what their teacher says doesn’t make sense, try explaining it to them yourself in different ways.

Experiment: does your kid effortlessly memorize song lyrics? Download Rockin’ the Standards’ math songs together or make up some new ones. Does your kid freeze up when faced with times tables flashcards, but love to build things? Try building multiplication facts using Legos or math blocks.

Slow can be fast. Sometimes kids need more time to digest or absorb information than is planned for in their classroom curriculum. Maybe their teacher expects them to memorize all of their times tables from 2s through the 12s by the end of the grade, and but they’re panicky and spotty about their 4s.

It’s okay. If your kid needs more time, just keep working on it together and be patient. It’s better to thoroughly learn one new multiplication fact a day than to try to cram stuff in their brain that’s not sticking because the pace is too fast.

Normalize error. Getting an answer wrong is just part of the natural learning process. So is getting an answer right. Neither situation calls for high drama. If a kid makes a mistake, say, “Okay, try again,” and ask them what’s the first thing they have to do. This tip comes from Doug Lemov’s great book, Teach Like a Champion.

If you notice your son or daughter beating themselves up over their mistakes, saying things like, “I’m such a bad kid since I got that answer wrong,” “I’m really not good at this,” or “I guess I’m just not a math person,” explain that everyone makes mistakes while they’re learning.

Systematic review helps. Incorporating review into your kid’s math routine will really help them retain what they’ve already learned. If your book includes mixed review that’s not assigned, encourage them to do a few review problems after they finish their homework. If their book doesn’t include review problems, do a “time capsule challenge” and quiz your kid on two or three random questions from previous chapters.

Make word problems routine. The reason why our kids study math is so they can solve real world problems. Yet word problems sometimes get a bad rap. While translating English into math is a separate skill that goes above and beyond simple computation, everyone can develop this ability.

If your kid’s math book includes word problems, invite them to do one a day just for fun, even if it’s not assigned for homework. You can get free word problem worksheets at teachnology.

You can also make up your own word problems together while running errands or at mealtimes. A lot of kids like to make up their own math problems, and it helps them feel like math is something that is part of them, that they can create, instead of something arbitrary that comes from a textbook.

Practicing this can be empowering and fun at the same time. When the math happiness bubbles up, be sure to enjoy it together.

If you have your own tips for a happy math year that you’d like to share, please leave a comment!

*If you’re visiting from the Math Teachers at Play Carnival hosted by Caroline Mukisa at Maths Insider, welcome! Here are some other posts you might find interesting:

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“It has been a long trip,” said Milo, climbing onto the couch where the princesses sat; “but we would have been here much sooner if I hadn’t made so many mistakes. I’m afraid it’s all my fault.”

“You must never feel bad about making mistakes,” explained Reason quietly, “as long as you take the trouble to learn from them. For you often learn more by being wrong for the right reasons than you do by being right for the wrong reasons.”

-Princess Reason in The Phantom Tollbooth by Norton Juster; illustration by Jules Feiffer

I’ve recently been working with a student who frequently beats herself up for making mistakes. Today I paraphrased this quote to her and explained that it’s okay to make mistakes as long as you learn something from them. She listened, but I wasn’t sure if it had sunk in.

Later in the session, *I* made a mistake, and I jokingly berated myself about it. She matter-of-factly responded: “it’s okay to make a mistake as long as you learn from it,” and smiled at me.

That’s when you know they get it. When they tell you what you told them.

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Trying to find a good English-speaking math tutor…in Mogadishu? An algebra tutor…in Algeria? A geometry tutor…in Guinea-Bissau?

Help is on the way! Today I’m guest posting about how to find a good tutor while you’re living abroad over at my colleague Becky Grappo’s blog, Educating Global Nomads.

As families around the world prepare to go back to school, I’m so happy that Becky Grappo has given this guest post a new home in cyberspace.

So check it out and leave a comment!

Also, if you are looking for someone to help solve your what-school-do-my-kids-attend-while-we-relocate-abroad problems, Becky Grappo is a great educational consultant who has worked with thousands of expat families.

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What an awesome way to remember what some of the essential functions look like!

Next time one of my students needs to remember what a function looks like, I’m gonna say, “Let’s DANCE!!”

*Via coeurdewhale at tumblr (I believe this is who created the image, but I’m not sure) and dong6241 at piccsy, a lovely site that showcases user-submitted images and has a great visual image search (blogger’s delight)!

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This goes out to all the kids who are working on summer math packets without having a textbook to refer to. If you need a good online math reference, I highly recommend Purplemath (one of my personal favorite math websites).

This site has a GREAT lessons index so you can quickly find the exact topic you need. The lessons (written-out explanations) are very thorough and easy to follow. They’re not written like a math book, but like having someone really smart and kind explain things to you in a conversation. The lessons do an excellent job of going over concepts AND steps, integrating the “what do I do?” with the “why it works!”

The site also features community forums sorted by level—starting with arithmetic and going all the way up to trigonometry. So if you have a math question, you can post it in the appropriate forum and get help from other community members. Elizabeth Stapel, the founder of purplemath, frequently responds to students’ posts in the forum herself!

Thank you, Elizabeth Stapel, for this totally user-friendly and expert site!

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When 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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Here’s a fun way to remember the formula for surface area of a cylinder—singing these lyrics set to the tune of Camptown Races (in the style of Foghorn Leghorn):

2 times pi times r times h; that’s the middle.
2 times pi times r times r; top and bottom, too.
Surface area!
Of a cylinder! It’s
2 times pi times r times h plus two times pi times r times r.

If you’re not sure about how to fit the lyrics with the Camptown Races melody, just listen to the intro of this sweet rendition on YouTube:

With this handy mneumonic device stuck in my head, I feel the urge to belt “Surface areAAAA! Of a cylinDERRRR!” while walking around my neighborhood and puttering around my kitchen!

Many thanks to Becky Brickell for sharing this great idea on the Texas Instruments Classroom Activities website!

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No classroom experience can meet every individual student’s needs at all times. Though teachers use a variety of approaches to reach different students and give them multiple chances to “get” the material, sometimes a student’s needs are so particular that a teacher just can’t address them in a crowded classroom.

Recommending a student work with a tutor can allow you to leverage your own expertise. You tell the tutor what you’ve noticed the kid needs to spend more time on. The tutor works with your student to help them internalize material and prepare for tests.

During the process, the tutor will share their observations about your student—information which may help you in your classroom interactions. And this kind of open and specific communication between you and the tutor will make a huge difference for your student.

Good tutors work with you as a team to accelerate and amplify what you’re already doing in your classroom. And while some teachers fear that a tutor will do their student’s work for them, a good tutor will encourage your student to take ownership of their work using specific, explicit strategies.

Here are some suggestions on when a teacher should recommend that a student get a tutor.

The student has major gaps in knowledge.

Maybe a student missed a couple years of math because they went to a bilingual school and were supposed to learn fractions in French. Maybe a student shows up in your Algebra 2 class having never learned long division because they went to a school where they were supposed to “figure it out themselves.”

When a student struggles with major gaps in material from previous grade levels that other students have down cold, a tutor can give a student the opportunity to really learn the foundational material.

Moreover, a student who might never admit to their official teacher how much they don’t know might feel comfortable sharing their problems with their tutor. The tutor can discreetly pass that information on to you, and you can use it to make the most of your classroom interactions with your student.

The student needs more one-on-one time.

If a student doesn’t have a lot of gaps in their prerequisite knowledge but they’re still struggling to keep up with the pace of the class, working with a tutor can be beneficial.

Tutoring can be a safe space for a student to ask more questions than they might want to admit they have in front of their peers. Also, one-on-one tutoring can allow your student time to drill or explore something as much as they need, instead of feeling like they have to “get it” right away.

More one-on-one time has another benefit. Often, when a student gets customized instruction from a tutor, they start to understand how they learn best and become more active learners both in and out of the classroom.

A student needs more differentiated instruction than can be provided in the classroom.

Maybe you already have a strong sense of your student’s learning style, but it’s hard to meet their needs in the classroom. Perhaps you’ve got a student with a diagnosed learning issue or disability, or a student who just marches to a completely different drummer. Maybe they need to experience the concepts in a way that wouldn’t make sense to anyone else in the class.

A good tutor can provide a completely differentiated learning experience, customizing their instruction to the individual student.

For example, a kid who feels pressured by flashcards might do a great job learning his multiplication facts by building squares and rectangles out of Legos. An ADHD kid who struggles to sit through a whole class period might thrive with a tutor who takes frequent breaks to shoot hoops. A dyslexic kid who’s overwhelmed by FOILing binomials might master the technique using a more visual box method.

When a tutor is successfully customizing your student’s learning experience, that student will be able to more effectively participate, contribute, and succeed in your classroom.

Tutoring boomerangs back to your classroom

An example: recently, I started working with a new tutoring student who, at the outset, was disinterested in learning math. But after a few weeks together, she started engaging more in her own learning. She spontaneously made up new lyrics to the tune of Michael Jackson’s “Beat It” to help herself remember that numbers that end in zero are even. A few weeks later, I heard that she was so engaged in trying to answer questions in math class that her teacher remarked, “I think I see a mathematician!”—referring to this same previously disengaged student!

The best kind of tutoring—the kind where you, your student, and the tutor are all communicating openly—can help kids transform. These students become more active self-advocates for their own learning. They participate more, engage more, and ask more questions in the classroom.

When a frustrated or overwhelmed student renews their love of math in part because of the tutoring experience you’ve helped them co-create, they’ll probably bring that new enthusiasm and confidence right back to your classroom.

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Just in time for Pi day, here’s a delightful musical interpretation of pi from Michael John Blake, using a piano, ukelele, autoharp, accordion, and bowed something-or-other, not to mention some totally sick handclaps!

I have already listened to this 3 times today. Maybe I should go listen to it another .14 times to bring the total to 3.14!!

If you’re not sure about this song, hang in there until around 2:33, where it really starts to rock.

Makes me want to make my own cover/dance music video of this song!!

Happy Pi Day, everyone! (Thanks to my Dad to bringing this video to my attention.)

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