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Posts Tagged as "algebra"

Case Study: A Rising 8th Grader Masters Her Summer Math Packet

Friday, June 10th, 2022

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!!

Related posts:
The Rhyme and Reason of Making Mistakes
Five fun ways to help your kid learn math this summer
Case Study: An ADHD Student Raises Her Grade from a D to an A
Case Study: Regaining Love of Math

Posts Tagged as "algebra"

How to convert from standard form (Ax+By=C) to slope-intercept form (y=mx+b)

Tuesday, May 8th, 2012

Here are two examples worked out of how to convert from standard form (Ax+By=C) to slope-intercept form (y=mx+b).

This is something that you get asked to do a lot as you start to get more comfortable going back and forth between different equations of a line.

And another example, because it’s nice to see more than one example when you’re learning something new:

If what you see here resonates with how you like to learn, and you’re looking to work with someone one-on-one to really master math, then I invite you to apply for my super special one-on-one math tutoring programs.

Just click here to get started with your special application for my one-on-one math tutoring programs. Once your application is received, we’ll set up a special phone call to get clear if my approach would be a good fit for your child.

I’m excited to connect!

Sending you love,

Related posts:
I cried myself to sleep over my math homework
How to multiply binomials using a box
Case study: a rising 8th grader masters her summer math packet
How to multiply binomials using FOIL

Posts Tagged as "algebra"

Got the summer math packet blues? Try some Purplemath

Friday, July 15th, 2011

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!

Related Posts:
The best algebra book in the world?
I am SO EXCITED about Math U See!
Q&A with Danica McKellar, author of Hot X: Algebra Exposed!
Five fun ways to help your kids learn math this summer (online!)

Posts Tagged as "algebra"

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

Monday, June 13th, 2011

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 7th 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!

Related posts:

Case Study: An ADHD student raises her grade from a D to an A
Case Study: Confused by math instruction in a foreign language
Case Study: Regaining love of math

Posts Tagged as "algebra"

Wait … that’s where algebra comes from?

Tuesday, February 15th, 2011

A statue of mathematician al-Khwarizmi

Ben Blum-Smith has a great article up about how certain key mathematicians first explored and refined the concept of negative numbers.

In his article, Blum-Smith dives into original historical source texts (in translation) to explore how the historical process of developing negative numbers parallels how each of us comes to understand negative numbers when we encounter them for the first time.

One of my favorite parts was learning that the title of one of the texts, Kitab al-Jabr wa-l-Muqabala, aka The Compendium on Calculating by Completion and Reduction by Muhammad ibn Musa al-Khwarizmi, is the origin of the word “algebra.”

Al-Jabr = algebra. AICH!!! So AWESOME!!!

And the treatise’s author, al-Kwarizmi? That’s where the term “algorithm” comes from. SO COOL!!!!!

Posts Tagged as "algebra"

Guest Post Alert: Q&A with Danica McKellar about Hot X: Algebra Exposed!

Monday, November 8th, 2010


My interview with Danica McKellar about her latest math book for girls, Hot X: Algebra Exposed!, is now up over on the new GeekMom blog. Check it out!

McKellar, well-known for playing Winnie Cooper on “The Wonder Years,” went to college intending to study film, but signed up for math classes because her brain felt “mushy.” When solving equations felt like a “drug rush,” she became a math major and co-authored an original theorem.

Since then, McKellar has emerged as a unique math role model whose previous books, Math Doesn’t Suck and Kiss My Math, spread the message that brainy is beautiful, being good at math is just part of being fabulous, and math doesn’t have to be scary—all messages that are very close to my heart as a female math tutor.

Her latest book, Hot X: Algebra Exposed! is the first algebra book in the history of humankind to discuss both breakups and binomials. Step-by-step guidance on how to do algebra is interspersed with quizzes (“are you a perfectionist?”), stories from her own life about being an actress and a math major, and testimonials from women who use math in their careers, including a daredevil airshow pilot/astrophysics computing scientist.

Hot X Algebra Exposed

When I was in middle school and crying myself to sleep over my math homework, I would have been thrilled to have an algebra book that was this friendly, encouraging, and helpful. I’ve never seen another algebra text explicitly addressing the emotional aspects of learning math, which I know from experience are so important to girls. (And it’s not just me—one of my sixth-grade tutoring students saw the book in my apartment, picked it up and exclaimed, “This is perfect for me!”)

So click on over to the GeekMom blog to read about McKellar’s own experiences being terrified of math as a 7th grader and growing up to give math a PR overhaul.

(Many people conspired to make this interview possible: Elizabeth Keenan, Ken Denmead, Liz Jones-Dilworth, Josh Jones-Dilworth, Missy Mazzoli, and Jina Moore. Thank you all!!!)

*Looking for a girl math tutor? Call 617-888-0160 for an appointment with Rebecca Zook!

Related Posts:
My Favorite Math Teacher is a Woman
Be Yourself, Do What You Love, Wear What You Want
No More Girls Versus Boys

Posts Tagged as "algebra"

Failure is not the enemy

Wednesday, May 12th, 2010

A few years ago, I was tutoring a ninth grader who was struggling in her geometry class. Her teacher’s teaching style didn’t mesh with her own learning style, and she also had a lot of test anxiety, so even when she began to master the material, it wasn’t yet showing through on her tests.

As we worked together, I observed my student slowly replacing her overwhelmedness with genuine interest and enjoyment. She started tackling difficult proofs, and her eyes would light up with excitement and understanding when all the pieces fit together. We were a few months into the long-term project of slowly building up her understanding when her dad made a decision, without my input, to pull her out of her geometry class because she was “in danger of failing.”

Even though my student understood the material, she got so nervous on the tests that if you just looked at her test scores it looked like she couldn’t do geometry. But she could! She consistently did it perfectly, by herself, in our tutoring sessions! When we reviewed her tests, the material made sense to her once she was outside the testing environment. And I was confident that she could pull up her grades if we continued working together.

In the sessions before her dad switched her math classes, I asked my student what she wanted to do. She told me that her choice would be to switch to another geometry class at the same level, but just with a different teacher. But for whatever reason, she didn’t perceive this option as being available to her—I’m not sure if it was a scheduling issue, a political issue, convenience, parental pressure, or something else.

What her dad decided to do was switch her into a “problem solving” class. My student and I met one last time after she switched into this class. Her book made me want to cry—it was a bunch of reasoning problems about things like Corey the Camel carrying bananas across the desert. (I’m serious. It really had problems featuring Corey the Camel.) The material was basically elementary-school level—no algebra, no geometry. Just simple word problems. Maybe the geometry class was 15% too hard for her, but this “problem-solving” class was about 100% too easy for her.

After that session, I did something I’d never done before. I wrote an email to the dad, explaining as diplomatically as possible and at great length that I really didn’t think this new class was appropriate for his daughter. I explained how much his daughter loved working on Geometry and was learning a lot even if she wasn’t yet testing well. And I expressed my concern that this class would limit her in the future, since basic algebra and geometry were prerequisites for so many other disciplines.

I wrote, wouldn’t it be better for her to take geometry and learn some geometry, even if she got a “failing” grade, than for her to take a class where she would learn nothing at all?

Her father’s response was vituperative. How dare I suggest that he allow his child to “fail!” And I never saw either of them again. I honestly don’t know how I could have handled this differently, but my heart still breaks for that student.

In comparison, another student’s family handled the perceived threat of failure very differently. I was working with a ninth grader who was struggling with Algebra 2 because her elementary school had failed to teach her basics like long division (she was supposed to “figure it out for herself”.) I believe when we started working together she was failing the class.

I was extremely proud of how hard this student worked, and she finished the year with either a low B or a high C. At the end of the year, her algebra 2 teacher suggested that she consider voluntarily repeating the class, just to strengthen her skills before moving on to more advanced math.

My student chose to repeat the class, even though she felt at least a little bit embarrassed to be the only sophomore in that class full of freshmen (at least I figured this was the case since she joked about it). She chose to learn instead of to look good. And her parents supported her. I was so impressed with her integrity.

By the end of her second time through algebra 2, the material that had brought her to tears the previous year did not phase her at all. But I think about the other family,
and how they didn’t want to let their daughter fail. Did that student ever get another chance to love geometry? Was she stuck in remedial math classes for the rest of high school? What did she did she do for her math requirements in college? I wish I knew. I hope she got another chance, instead of internalizing a message that she “couldn’t do math.”

Why do we protect our kids from failure, even to the detriment of their own learning?

Related Posts:
I cried myself to sleep over my algebra homework
Algebra Tears
“I Think I See A Mathematician!”

Posts Tagged as "algebra"

How to multiply binomials using a box!

Wednesday, February 10th, 2010

Many people find this more visual and intuitive than FOILing.

I split the video into 8 brief parts. Each part features one practice problem, fully explained and demonstrated on the whiteboard.

If you, your family, or your friends would like to see me make an instructional video about a particular math topic or type of problem, leave a comment to nominate your math problem for its very own video!

And if you like the video, please feel free to click on the “heart” to show that you “heart” it. <3

#1 – Multiplying Binomials with the Box Method (alternative to FOILing) from Rebecca Zook on Vimeo.

Click on “more” for the other parts of the video — four more examples, extra practice problems for you to test your mastery of FOIL, and answers to the extra practice problems!


Posts Tagged as "algebra"

My Favorite Math Teacher Is A Woman

Thursday, January 14th, 2010

After my last post about how I used to cry myself to sleep over my math homework in middle school, one of my friends wanted to know, when did math start to make sense to me again?

Two words: Nancy Oliver.

My amazing ninth grade geometry teacher.

Nancy taught in a classroom where a former student had painted a colorful mural of the trig mnemonic “SOH CAH TOA” as a tribute to her on the back wall. In her room, I felt relaxed, focused, and safe. I had just spent three years of middle school algebra feeling panicked, utterly frustrated and incompetent in the math department. But with her instruction, I finally felt like math was something I was completely capable of doing.

How did she do it? Like any good teacher, she showed us what to do, and then gave us a chance to do it. At the beginning of each class, she’d demonstrate a new type of problem. Then, after answering our questions, she’d assign practice problems so we could practice what she’d just shown us. With her, even challenging proofs seemed like enjoyable puzzles to figure out. My brother and I still talk about what an amazing math teacher she was, over ten years after we took her class.

But when I reflected on my friend’s question, I realized something I’d never thought of before. Nancy Oliver, the only math teacher I had from 6th to 12th grade who was a woman, was also the only math teacher I had from 6th to 12th grade who really made sense to me. Coincidence?

Obviously there are some great male math teachers out there. I’ve worked with some of their students (Byron Parrish’s, at the Winsor School), I read their books and watched documentaries about them (Rafe Esquith), and I follow their blogs (Sam J. Shah). I was just never lucky enough to actually have one of them as a teacher myself! (Disclaimer: I also know from experience there are bad female math teachers out there.)

Maybe my personality and teaching/learning style was just more compatible with Nancy than with any of my other teachers. But it’s also possible that the fact that Nancy was a woman was a big part of why math finally started to make sense to me, a girl, when she was my teacher.

Maybe the secret ingredients were:

I felt completely comfortable asking her for help—more comfortable than I did with any other math teacher. I never, ever felt stupid or ashamed, no matter how confused I was. (In comparison, I often felt embarrassed asking my male teachers for help, even though I knew most of them wanted to be patient and kind with me.)

I understood her explanations. Nancy consistently explained things to me in a way that made sense to me. (I often felt discouraged even approaching my male math teachers for help. Not only did that mean I couldn’t figure it out by myself, but also, their explanations didn’t clear up my confusion as consistently as hers did.) It’s possible that Nancy approached math in a particular way as a woman that made it easier for me as a girl to understand her. Or, maybe she just had a larger repertoire of explanations than my male math teachers did.

She was a role model to me. Maybe I thought—even subconsciously—“if this awesome lady can do geometry, maybe I can too.”

Now that I’m a math tutor, I feel a special bond with many of my students who are girls. (I bond with my male students too, just over different things, like biking through Boston in the snow.) At first I thought that girly bonding—over the release of Mean Girls, or Betsey Johnson handbags shaped like strawberries, or mutual admiration for each other’s style—was just part of establishing rapport and helping my students feel comfortable. But now I wonder if maybe some girls just feel more comfortable with me as a role model because I’m female.

So, thank you, Nancy Oliver, for being my female math role model, and helping me turn everything around. I hope I can carry your torch!

Related Posts:
I cried myself to sleep over my math homework
On being yourself while doing math
Case study: regaining love of math
Case study: confused by math instruction in a foreign language

Posts Tagged as "algebra"

I cried myself to sleep over math homework

Monday, January 11th, 2010

Looking back at how I responded so insensitively to my student who cried during our tutoring session, I’m stunned by my in-the-moment lack of compassion. Because… I cried myself to sleep over my algebra homework throughout most of eighth grade! It’s still vivid in my mind: sitting on my twin bed with my algebra book in my childhood bedroom, with its pink hearts and flowers wallpaper, struggling to finish my homework and crying with sheer frustration.

I loved math as much as any other subject until I hit 6th grade and was introduced to pre-algebra for the first time. Isolating for a variable, balancing an equation, the order of operations—none of this made any sense to me. I would go to my teacher for help, and he would patiently try to explain it to me, but it still didn’t make any sense. I made the same mistakes over and over and over without gaining any understanding or insight.

I have absolutely no memories of seventh grade math, but eighth grade math burns in my memory: sitting in class, trying to do the problems, approaching my teacher’s desk, asking him to explain it to me, dutifully nodding even though I still really didn’t understand, returning to my desk, and feeling overtaken by numb despair.

I’m not sure if his explanations didn’t make sense to me because he always explained everything the same way, or if he had a variety of explanations but none of them clicked with my learning style. He was a sweet, patient man, but his explanations did not help me to learn.

Now that I’m a math tutor, when I remember all those eighth grade nights, crying myself to sleep over my algebra book, I ask myself, why didn’t I think of getting a tutor? I never thought about asking anyone but my math teacher for help. I didn’t ask my friends, I didn’t ask my parents, I didn’t ask other teachers. It never even crossed my mind to try to switch to another teacher, or get another book. Why?

Maybe I wasn’t aware that these options were available. Or maybe I felt somewhere deep inside that, as a student who had a passion for learning and a capable reputation, asking for a tutor would be an admission of defeat. Or maybe it seemed “easier” to think of those nights of algebra tears as isolated incidents instead of taking on the “larger project” of trying to find a better solution for myself.

But paradoxically, I think this experience made me a better tutor. Many of the students who come to me might be completely frustrated and far behind. Maybe they don’t have anyone else they can turn to for help. Maybe they’ve never found a textbook that works with their brain. Maybe they are crying themselves to sleep over their algebra homework. Just like I did.

Related Posts:
When Persistence Isn’t Enough
The Downside of Always Telling Students To Try Harder
The Downside of Always Telling Students To Try Harder (2)
Algebra Tears