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Pineapples Don’t Have Sleeves – New York 8th Grade ELA Exam

If you’re confused by the title of this post, don’t worry.  You’re not alone.  The 8th grade New York ELA exam last month included a passage entitled “The Hare and the Pineapple,” a nonsensical story patterned after Aesop’s well-known version.  See here for a copy of the story and associated questions.  In the middle school where I teach, students were equal parts baffled and annoyed.  When the wider public caught wind, the ensuing uproar was dubbed “Pineapplegate.”  Pearson, the maker of the NY state test, had this to say in defense of the passage.As a teacher who already has concerns about widespread standardized testing starting in third grade, I take issue with the whole thing on a number of levels.  First, even I had trouble deciding what the “correct” answer was for several of the questions.  I earned a perfect score on the ACT.  I actually enjoy taking standardized tests.  So when I’m baffled by a question on an 8th grade English test, I assume it’s not me.  It’s the test.

Second, I wonder what sort of accountability Pearson has for their testing materials.  Considering the company just won a $32.1 million contract to provide testing materials for the next several years, it seems that they should provide quality assurance measures.  Perhaps Pearson should pay a $100,000 penalty for each question that needs to be thrown out.  There were several in this year’s math & ELA exams.  (For example, this 5th grade math question was thrown out after teachers realized it was impossible for students to solve.)

Finally, how can we make standardized tests more useful for students and teachers?  As a student, I just see a summarized score of 1 through 4.  For example, what would a “3” really tell me?  Research tells us feedback must be timely to be useful.  Currently the standardized test results come back too late to be useful for students or teachers.  The full breakdown of student results by standard don’t arrive until well after the end of the school year.  And even then, teachers don’t have access to the original questions.  I understand that norm-referenced tests need large samples of data and are often field-tested for validity.  But more transparency would be wholly appropriate and ease concerns of all parties involved.  (Except perhaps the testing company.)

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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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