Literacy in Math Education – NOT an Oxymoron

In my last post I talked about the use of a pre-assessment in my unit plan teaching percents in context.  The other piece of that unit that was new for me was the infusion of literacy techniques.  After taking a wonderful class by Carol Manocchi at Fordham, I became a literacy convert.

What Is Literacy?

Literacy is much more than the ability to read and write.  When I first started teaching I believed being literate just meant having decoding and comprehension skills.  Students at a low level would be stuck decoding words.  Students at a higher level would be able to read and understand, provided they weren’t hindered with unfamiliar vocabulary.  Thus my view was a blend of emergent and functional literacy, a murky picture at best.

These days I have a much richer understanding.  For one, literacy is impossibly entangled with the specific subject being considered.  One can enjoy Harry Potter or The Hunger Games with a shallow level of functional literacy, but reading the New York Times or The Economist demands a degree of cultural literacy.  Likewise, someone who has access to a range of American cultural allusions may find himself lost while reading a major Spanish newspaper, even if he is fluent in Spanish.  So literacy is not a unitary skill that is acquired and transferred effortlessly across disciplines.

Literacy is the ability to read and understand what others have written, along with the ability to write as a means of recording information and for communicating with others.  Using this definition with regard to a specific discipline yields the idea of content literacy.  As a teacher of mathematics, I am interested in developing students who have content literacy in mathematics.  This ability is predicated on 1) general literacy skills, 2) prior mathematical knowledge, and 3) math-specific literacy (such as familiarity with the notation used in Algebra).

I began to realize more and more the truth that content literacy is not content knowledge during my student teaching this semester.  In eighth grade the most advanced math students are typically those with strong numerical fluency, which allows them to learn procedures and notice patterns while their less savvy classmates are bogged down by the computations.  However, if I were to ask my advanced students to justify their procedures or describe a pattern, they were often unable to do so.  I don’t mean that they lacked the vocabulary, like numerator or quotient or distributive property—use of correct terminology is icing on the cake.  They could not articulate why two different procedures yield the same result.  For example, calculating 7% tax and adding it to the bill versus just multiplying the bill by 107%.  And so it was that I set out to encourage meaning making in math class.

Literacy in Action

My first step was to create a need in students by showing them there were things they could not do and then tell them that I would teach them what they needed to know.  I designed a pre-assessment that included basic mathematical tasks as well as asking them to write how they would explain an idea to a sixth grader.  When we anonymously reviewed the class’s responses, I pointed out that even students who were able to perform the skill were unable to explain it to someone else.  I told them that I would teach them how and help them get better at communicating.

Rather than give the standard lecture (this is how you do X, now let’s all do X, now you do X), I had students read a short bit of text I’d created explaining the idea.  Beforehand, I introduced the concept of marginalia in order to get them engaged in self-cognition as they read.  (Many students read the page without making any marks, which I can only assume meant the words washed over them with little understanding.)  Then I asked them to write how they would do X.  I was surprised by the difficulty students had with what I thought was essentially an exercise in copying.  Just rewrite my explanation with different numbers, right?  Wrong.  A majority of the class was unable to answer the prompt.  So what that told me was that students needed more support in constructing, verifying, and extending meaning as they read.

We did several of this type of lesson throughout the unit, and students gradually improved.  I experimented with prompts; here are a few:

  • Explain how you would do X.
  • Why did both methods end up with the same result?
  • Write what you learned about X from the reading.  Include what makes sense and what you continue to ponder.
  • How would you explain this idea to a classmate?
  • Describe what you noticed from the previous problems.
  • Why do some businesses pay employees with commission?  What are the advantages and disadvantages?

I expected students to balk at this sort of difficult metacognitive, especially when many have conceptualized math as memorizing what to do.  But an anonymous survey a couple weeks in found the majority of students really enjoyed the reading and writing.  I guess it levels the playing field for those who don’t have strong numerical fluency, because we are discussing ideas and not just blindly computing.

Mathematical Discussions & Sentence Stems

Since writing is a time-consuming activity, I also wanted to introduce mathematical discussions for shortest bursts of reasoning.  Much of the time in math classes I’ve observed (and my own as well), the teacher asks a question with one correct answer.  If I were to teach content literacy, students should be able to explain their reasoning, not just produce the correct answer.  So I turned to Zweirs’ Building Academic Language to build a framework for classroom discussions.  It declares that classroom talk is a tool for working with information such that it becomes knowledge and understanding.

The first thing to consider was the balance between closed (or display) questions and open-ended questions.  Display questions, while suitable for activating prior knowledge or displaying what students know, rarely lead to deep discussions.  Zwiers provides four main categories of open-ended question:

  1. Personalizing: thoughts, feelings, opinions, interpretations
  2. Justifying: Why do you think?  What evidence do you have?
  3. Clarifying: What do you mean by…? How do you define…?
  4. Elaborating: ask for more, but may confuse students by sending positive and negative feedback in response to answers

Despite all this, he suggests questions are overused in classroom discussions and often still lead to a teacher-centered pseudo-discussion.

For that reason, I designed a series of four posters with sentence stems for agreeing, disagreeing, observing, and questioning.  Then I created a homework assignment that asked students to solve a problem and write up notes that would help them explain what they did to a classmate the next day.  Before the discussion I had students turn and talk with partners for 2 minutes sharing their answer and how they got it.  Then I said that I noticed many different answers as I walked around checking homework and wanted to have a class discussion about the problem.  I introduced the sentence stems I expected students to use and modeled along with some examples of how not to participate.  And then students discussed, with me merely moderating who was talking.  Occasionally I had to ask students to write down their ideas so that we could come back to them in order to allow each thought to reach its conclusion.  Within 15 minutes we had come to consensus and I sensed there was a high level of understanding from the engagement and what students were saying.  Towards the end I began cold calling students to explain whether they agreed or disagreed with what someone had said, which aided me in checking for understanding and holding everyone accountable for participating.

Even more so than with reading and writing about mathematics, students universally enjoyed our mathematical discussions, and I have been infusing them into class whenever possible.  I have been quite pleased myself with the development of students’ reasoning skills and ability to justify their answers.

Next Steps…

In the future I will focus more on the challenges I faced incorporating literacy into a mathematics curriculum.  At times it felt like I was devoting a lot of the class period to teach through literacy-based instruction what could be direct taught in a fraction of the time.  Asking middle school students to struggle with text and then write their understanding appeared to bear very little fruit at first.  In the future I will slowly introduce the idea of gaining knowledge through text by having students first read about something they are already familiar with.  After they have been successful with that several times, they can begin to use text to study new mathematical concepts.

I also struggle to find a way to consistently include literacy-based components, especially with topics like simplifying algebraic expressions.  There are more mathematical discussions happening, but I find it difficult to find time writing about a skill that they still haven’t mastered.  I think literacy has worked best when the writing was assigned towards the end of the unit.  Discussion may help sort out what to do as students are learning a new skill, but writing in particular forces us to (re-)organize our thoughts in a way that they become crystallized.  I think this may be one of the keys to long-term knowledge retention.  This is perhaps the biggest bane of math teachers, finding students who learned something last year, but have no recollection of what to do now.  Sometimes it doesn’t even take a year—they can’t remember the skills they learned last month.  Taking the time to incorporate literacy strategies to solidify students’ knowledge would be time well spent.

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Using Pre-Assessments in a Unit on Percent

My first year of teaching I was both blessed and cursed by a lack of curriculum.  The previous 8th grade math teacher had left a collection of NY state test questions from the past several years.  But even as an unsophisticated first year teacher, I realized this was a far cry from a well-planned curriculum.  And so I spent about hours and hours every unit scouring the internet for different ways to teach a concept, interesting problems, and standards-driven activities.  This constant quest for good resources has dramatically accelerated my growth as a teacher and is a continual supply of professional development.Now that I have surveyed the landscape, I feel ready to give back to the community.  My initial contribution is a unit on percents that I planned while student teaching in an 8th grade classroom.  There are several features I’d like to highlight that I think were valuable.  In this post I will discuss the use of a pre-assessment.

This was the first time I gave a pre-assessment.  In the past I didn’t gave much thought to prerequisite skills and understanding.  By giving a pre-assessment, I forced myself to consider what students needed to know to learn the new material.  I also sent students the message that I was serious about helping them be successful, and not just blindly following some curriculum.

Following the pre-assessment I collected student work and used the document camera at the front of the room to briefly flip through student responses.  It’s important that this process is anonymous, as the point is to display the range of ideas and not single out students for their mistakes.  The teacher may also want to slip in his or her own work to make a particular point (whether it’s a common misunderstanding, a correct solution, or a controversial answer).  For example, this student’s solution prompted an interesting discussion.

After giving a pre-assessment it’s important to put the data to use.  I found that students had a lot of trouble multiplying decimals and converting between fractions, decimals, and percents.  So I planned a station activity the next day where students could practice two skills.  Each station was led by a teacher or pair of students who had demonstrated mastery of that particular skill.  In this particular instance I allowed students to decide which skill to practice, but you could also assign groups.

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Any landing you can walk away from…

It’s been over a year since I’ve written about my foray into education, so I’m well overdue. Quick synopsis: overconfident first year teacher + weak classroom management + poor support = failure. Want the full details? Read on.
In the fall of 2010, I began my first year teaching 7th and 8th grade math at a charter school in the Bronx. I taught all three sections of 8th grade and one section of 7th grade 5 days / week, and I also was assigned the advanced 7th grade section that met 2 days / week. There wasn’t any curriculum in place; the 8th grade teachers from the previous two years had left binders of little more than problem sets pulled from past state tests. But Teach for America (TFA) had taught me strong backwards planning skills for designing curriculum, and I double majored in math in college. The freedom to design my class from scratch was thrilling. The literature about math education suggested students were frequently taught by people who themselves had limited understanding of the subject. In the search for better test scores teachers would give students tricks and formulas to memorize. I was eager to teach students to think critically and reason.
I still remember the night before the first day of school, too excited and nervous to sleep. The last time I had the problem was Christmas Eve half a lifetime ago. We spent the first week solving interesting problems and getting to know each other. I introduced our Big Goal–80% mastery on standards–and followed the TFA guidebook on an investment plan. The problem was that my students certainly didn’t care about the assortment of NY standards that would be tested on the state test. And my personal goals were to change lives, have meaningful discussions, and rekindle curiosity.
Classroom management was a challenge once the newness of school wore off. I conflated my early success with students’ timidity as they test boundaries and learn the lay of the land.  When push came to shove, I didn’t do enough to manage the disruptive students and hold the class to high standards.  My desire to keep everyone in class rather than send them to the Dean’s office–a technique other first year teachers routinely employed–left me looking soft.  In the end, all my strong rapport meant was that students saw me as more of a friend than an authority figure.  If I were still teaching in that school today, I feel confident I could manage the students and teach them twice as much.
I guess what frustrates me the most is that new teachers must be seen as an investment.  Rare is the first year teacher who outperforms veteran teachers his or her first year.   Instead, schools should see neophytes as a precious resource that must be refined to realize their full value.  They must receive support and mentoring that focuses on what that teacher needs most.  In return, new teachers bring enthusiasm and a fresh perspective.
From my point of view, I worked incredibly hard my first year, to the detriment of every other aspect of my life.  I designed two curricula from scratch, provided extra help during preps and after school, volunteered for optional retreats, and strove to build parent involvement.  I sought to be a role model for my students.  That my charter school and TFA would dismiss me–a career changer who left a higher paying job to teach–shows a lack of good faith.  I will become a master teacher without their support.  I will do what I set out to do in spite of their short-sighted decision.

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My first full week was amazing!

My 7th and 8th graders are a bit tougher sells than the elementary schoolers in the TFA weekly newsletter stories, but I already love them to death. I feel like I’m slowly building up great buy-in from these kids. The investment and management components seem so closely correlated to me, and I’m feel successful in a way I never did with my summer school students during Institute.
 
The students are also enjoying the lessons, and the reflective writing I’ve had them do has really impressed me. Teaching the same lesson multiple times in a row is another big difference from Institute. For me, it lets me see progress in an easily measurable way. (It’s so good that I would seriously suggest changing Institute to 2 lessons taught 2x a week rather than 4 taught 1x. It would also relieve some of the lesson plan load, which for me felt like it received a bit too much of my attention. The time spent lesson planning ate into sleep, which hurt my delivery for sure the next day.) I find that with repetition my lessons get tighter, the delivery gets better, the kids are more engaged and on-task. Fortunately–and fortuitously?–my classes rotate throughout the week so each one gets me at my best at some point.
 
Learning the names of 105 students is no small task, either! I’ve got the difficult students and the advanced students–sometimes one in the same–but those quiet, well-behaved middle ones blend together. “Aliyah? Wait, Alyssa?” I need to take more lunch duties so I can rehearse with the senior teachers.
 
Missing piece: classroom jobs. I need to put something together with job descriptions and applications. I think I have enough buy-in that the kids would want to interview. I’ll let you know how it turns out…

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Survey Says…

I’ve only had them a day and a half, and I already love my students. They have such personalities, they’re eager to do the right thing, and I have been impressed with their fledgling awareness. The first homework assignment was a student survey with 26 questions designed to provide a picture of my students’ homes, families, interests, desires, and perceptions of themselves and school. Here are some anonymous responses that are especially telling:

(note: student responses are transcribed as precisely as possible)
Q: School would be better if…
A: I was smart!
A: the water fountain was kool-aid
A: it was purple
A: we was not sharing a school
A: students could teach the class
A: we had no metal detectors
I don’t know that I can do much about most of those, but my seating chart is grouped heterogeneously…
 
Q: When I grow up, I want to be a/an…
A: model or judge
A: dancer or doctor
A: singer or a lawyer
A: policemen / basketball
Goes to show there are some dichotomies students don’t subscribe to!
Q: If I had three wishes, I would wish for …
A: to have all games, 1 billion dollars, & a family
A: my brothers to still live, have unlimited wishes, ma dad to have better job!
A: to be rich and have a great husband and 3 kids.
A: to be rich, have own army, have own town
A: easier puberty for girls, everyone not to steal, cheat, lye or fight and get money easier.
A: 1. help in school 2. money 3. candy
A: study or swim saftley with a shark go to Spain have good life.
A: Life to be more easier, to not have school, and for Love to not exist!
A: my cousin back, the new iPod 4g, and a dog
A: fairy godmother, castle, wings
A: money, more money, my own shoe company
Hilarious, heart-breaking, head-scratching…
The most common responses involved a big house, lots of money, and more wishes.
Q: What is one thing every teacher should know about you?
A: Ima Libra so I am psycho so when Im mad don’t mind me.
A: I am a math GENIUS and this year I want to be challenged.
A: That I dont like to participate
A: I like to cheer people up ^=D
A: I’m sneaky
A: I would the best student if you make the lesson interesting
A: that I try hard
A: I’m lazy
If you wondered why I can’t help but love these kids…
Q: What is one thing you would like to know about me?
A: why did you become a math teacher?
A: how you discipline students
A: are you a fun person?
A: was 8th grade easy for you?
A: do you get frustrated quickly?
A: what do you like to do?
A: what is your greatest accomplishment?
A: why did we have to do this sevrvy?
A: are you famous?
A: what should I know about you?
A: Everything about you
A: Where you come from
A: what is your 1st name?
A: what kind of student was he in school?
I’m planning to give each student who asked a question of me a hand-written response. I think investment is just another word for rapport. And routines & rapport are my main focus for the first week and a half. Plus some interesting math puzzles!
 
The responses from this survey were above and beyond what I expected. I want to do another student survey for winter break. I’m already planning the questions! Submit any suggestions in the comments.

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Barclay and the Technicolor Poster

Today I went down to Barclay (Teacher) Supply Store in Brooklyn to pick up some odds and ends for the classroom. Tomorrow is the first day of school, and I still don’t have student trackers up on the wall. Wendy Kopp would lose her mind if she found out. How will I get the students invested in their academic success if they don’t have a public tracking system with glittery stickers?

(Side note: think what you will, even too-cool-for-middle-school students will go to unbelievable lengths for the sticker that they publicly dismiss as childish.)
So I ventured into Brooklyn and found myself descending into the bowels of Barclay, a basement warehouse of pens, pencils, tape, paper, folders, post-its, workbooks, and more. But the unbelievable assortment of posters they carried blew me away. From elementary to high school, science to social studies, secular to Jesus-themed, they had a poster for just about everyone.
Except, it seems, me. I quite liked many of the posters my peers had made during summer school with facts about rocks or how to write a good essay. These posters were handmade, drawn on giant sheets of chart paper, and colored with fat-tipped markers. They were clean, bright, and clearly summarized their key points.
The posters in the store, perhaps with the exception of the elementary school ones, did not. Written by someone who long ago forgot what it’s like to learn something, the abominations I saw looked as though a rainbow had thrown up on them. When did white space become a bad thing? It’s like Debussy says about music: “Music is the silence between the notes.” These posters were so busy that even if I wanted to gather information from them, I would be constantly distracted by pictures of rulers or happy faces or apples. A few really dated posters had pictures of a computer with a CRT monitor and 3.5″ floppy disks. For a brief second I was tempted to deck out my classroom with an 80s theme just to see what the kids would do, but then I came to my senses.
I searched and searched for posters I would feel good to hang in my classroom. I went through PEMDAS & how to solve word problems (ironically, too wordy). I looked at measurement conversions and the quadratic formula. Finally I found a set of 4 that describe big ideas in mathematics: the concept of 0, the Pythagorean Theorem, pi, and the Sieve of Eratosthenes. Perfect! They fulfill all my criteria for a good poster:
– Interesting content
– Presented well (layout and conceptually)
– Good use of color & white space
– Large enough to see from a distance
and, finally
– Good font choice
For anyone who has not questioned a business’s font selection or wonders what the difference is between serif and sans serif… well, I have one recommendation.
Watch Helvetica. It will forever change the way you look at printed text. Seriously.

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The Uncensored Thoughts of a Student Teacher

I should be lesson planning for the first week of school. It’s a little over a week away, and I’m starting to feel anxious about it. But instead I find myself wanting to crystallize some thoughts I have about Teach for America. Writing them down, just like talking to myself, helps me to logically sequence everything. So even if you weren’t here reading these words, I would still find the exercise useful. But–if we’re lucky–I can have my cake and you can eat it, too.
 
Teach for America (hence, “TFA”) traditionally recruits a swarm of bright-eyed, bushy-tailed college grads. Freshly minted, they decide to jump back in to the world of education they have just left, albeit on the other side of the red pen. So it is understandable, dare I say predictable, that the people who join the corps come with a wide range of thoughts and thoughtfulness about pedagogy and motivations are for joining.
 
Thus TFA comes equipped with a delicious flavor of Kool-Aid that has been specially fortified with all your daily vitamins and minerals. I’ve been drinking this stuff for months, though, so the first couple of weeks at Institute were monotonous. In predictable bullet point format, here we go:
 
  • You must have high expectations for all of your students and truly believe that all of them can and will succeed. Yes, this seems self-evident to me. People rise or fall to meet expectations. Give someone a week or a month to do something and that’s how long it will take. Or, more broadly, consider the question of free will. The only reasonable stance to take is that free will exists. If it does, and you’re right, then you will behave appropriately. If it doesn’t, and you’re wrong, you were still holding a belief that coerced your non-free will to act in the most potentially useful way possible. So set big goals, “ambitious yet feasible,” and truly believe that students will achieve them.
  • The Academic Impact Model posits that Student Achievement is predicated on Student Actions, which are predicated on Teacher Actions, which are predicated on Teacher Knowledge, Skills, and Mindsets. Again, YES, obviously, how could they not? Clearly there will be external influences, but the most powerful and successful teacher will ensure his influence is the most potent. He will battle against negative influences with the knowledge of what is really at stake, and with a degree of conviction most students will not yet possess. It is the teacher’s job to model that disciplined attitude and effort can achieve whatever it is one desires. And it is the teacher’s burden to realize he is responsible not just for a student’s success but also a student’s failure.
  • Once you have a goal in mind, backwards plan to ensure all your efforts will align with and lead to achieving that goal. This insight gets to the heart of TFA’s affinity for data. It is introduced to warn new teachers against the dangers of “activity-based” lessons, where the kids are having a great time but not really mastering the intended objective. For example, we could play blackjack in math class, but if we haven’t sufficiently worked out probabilities the strategy would be lost on students. But backwards planning goes deeper than that, too. It means starting with the goal in mind, knowing how you’ll assess that you’ve met that goal, and then breaking the goal into small chunks, each of which can itself be backwards planned.
 
These are just a few of the concepts that have been inculcated into corps members from the first days of Institute and run through the heart of most training I’ve since received. I wish I could go around the country giving all teachers a quick Check for Understanding to ensure they’re drinking the Kool-Aid. With schools already started or starting soon, it’s imperative students have thoughtful teachers who believe in and assume responsibility for them.
 
Back to the lesson planning!
 

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