Reading Aloud in Math Class

So I’ve been informally experimenting with the effect of reading aloud in math class.

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Many years ago, I noticed that when a student couldn’t get started on a task on their own, they’d raise their hand and claim “I don’t know what to do.”  I would ask, “Well, what did the problem say?”  The student would then answer, “I don’t know.”  My next step would then be to read the problem aloud and ask “What do you think you’re supposed to do?”  The student would respond to this question…and most often with the correct response.

I didn’t need to ask the students any questions related to the math at hand.  They just needed to hear the problem aloud.

I started to pay attention to this back and forth that I would have with countless numbers of students.  And then began to explore the question-what if they read aloud to themselves???

An eight grade honors level student came to find me because she couldn’t figure out a problem she had on an assignment.  I said read the problem.  She said “I already did.”  I asked her to read it aloud to me.  I could see the lightbulb go off when she finished and she asked “Am I supposed to _______?” And she was correct!

Two nights ago, my fourth grader that was accepted into the STEM program in our district, was working on an online assignment in the other room.  He came out to my husband and I and asked for help because he was stuck.  He sat down next to my husband and began reading the problem out loud to him.  As soon as he finished, he said, “Oh, never mind! I know what to do.”

I’ve noticed that I will often put my fingers on my ears and read-aloud in a whisper if I’m trying to double check the words that I’ve written.  It’s helpful to hear myself.  How can we explore this more with students?  How can we incorporate this in our classrooms?

I did a quick search attempting to find research on this topic.  I noted this article about reading aloud for English language learners.  But what was interesting was this:

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I’m interested in researching this further and would definitely love to know if anyone has had similar experiences with their students.

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Learning from a 5th Grade Math Team

When my oldest child entered kindergarten I wanted a way to volunteer my time at the school, so I began coaching the 5th grade math team.  I saw this as an opportunity to better understand the math that elementary students bring with them to middle school. The elementary school that my children attend is a feeder school to my middle school.

I used the set of resources provided by the school system to train my mathletes that year. One problem I tasked them with was titled Kicking Tees below:

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I didn’t attempt this problem before giving it to the students that day.  I watched as they solved it…easily handling #1, skipping #2, and then answering #3.  In my mind I thought, “Wow! I’d create an equation to solve #2…how would a 5th grader figure this out?”

I can’t be too dissimilar from other secondary certified teachers, where an algebraic approach is the first that comes to mind.  It took me a few moments to think about using a table, or simply guessing and testing given the boundaries offered by the answers to #1 and #3.

This was a revelation for me though…That students might have skills to approach problems in which I’d use a more sophisticated method.

I was curious about what a 7th grade Algebra class in the midst of learning about systems of equations might do with this problem.

They did the EXACT same thing that the 5th graders did~they skipped #2!

This began my thinking about the intersection between the teaching of content, skill, and strategy.  And the connection between elementary math and algebraic thinking.

I used this problem solving experiment to talk with the 7th grade students about math learning and about the connection between arithmetic and algebra.

For teachers, this highlights the importance of horizontal content knowledge

“a kind of mathematical ‘peripheral vision’ needed in teaching, a view of the larger mathematical landscape that teaching requires”

“According to Ball and Bass (2009), HCK is an awareness of where and how the mathematics being taught fits into the structures and hierarchies of shared collective mathematical knowledge. This awareness serves both to engage students and to provide meaning to the present mathematical experience”

Further, this article reports

“The teachers in our study seemed to be more concerned about the mathematical content at the level they were teaching than the broader (more advanced) mathematical context—which can be referred to as the mathematical horizon”


It’s become incredibly important for me in the work that I do with teachers, to help them see how the math that they are teaching fits into the learning the students do across a mathematical spectrum.

…in addition to helping teachers see the importance of this “horizontal content knowledge” as a way to create instruction that engages, inspires, and makes math a meaningful, connected body of work.

 

Mosvold, R., & Fauskanger, J. (n.d.). Teachers’ Beliefs about Mathematical Horizon Content Knowledge. Retrieved May 27, 2016, from http://www.cimt.plymouth.ac.uk/journal/mosvold2.pdf

 

We Need More Drawing in Math Class

I worked with a 6th grade student in our In School Intervention classroom today.  I do this every day.  A boy had been assigned a set of pages from a workbook and had begun the work on his own. From what he had already completed, I could tell that this student had a strength in math. He was unsure of what he had done, so he was looking for validation from me.  We looked at this next problem together:

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He said, “so you gotta subtract right?” I said, “yes you do, but that’s if you’re looking for the answer. This is asking you to write an equation.”

He began to write y = x – 14.

I talked to him about variables, and how many unknowns were in this problem and he could tell that there was only one.

I asked him to draw a picture of the situation.  Here is what he drew.

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HMMMM….(maybe they’ve recently worked on area and perimeter???)

I then asked him to reread the problem and prompted him to draw the house and the airport.Screen Shot 2016-05-17 at 5.56.08 PM

He drew the line between the house and the airport, and I had to do some questioning to get him to realize it represented the distance of 29 miles.  We reread the problem and I asked him about the 14 and how he would represent that on the drawing.

He thought to himself for a moment and then began drawing the tick marks.  I could tell that he was counting them.  He labeled the 14th tick mark and the 29th, and then circled the 14.

I drew the bracket and asked him what that would represent.  He said with a questioning tone, “the remaining distance?” Thinking for a minute, he then said, “oh I know…would it be 14 + x = 29?”

We did one more problem together that we represented with a drawing, and then I left him to be independent in the rest of his work.

He came over to show me one of his drawings and the equation he had written:

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(In a previous part of the problem they were told there are 150 seats in coach seating.)

We high-fived!


Teaching students how to create math drawings is a valuable sense-making tool that can be over looked in math class.  I know numerous reading language arts teachers that ask students to draw pictures to portray what’s going on in a story.  We need more of that in math class.

Teach Math as a Story

 

I had the opportunity recently to complete peer observations outside of my content area. I scheduled a half day of observations with a sixth grade social studies teacher new to our building.  We observed in two eighth grade social studies classrooms and one sixth grade classroom.

If you’ve never observed outside of your content area I highly recommend it.  I think it forced me to pay closer attention to the general instructional practices, rather than focusing in on the content.

In the sixth grade classroom the teacher began by reviewing what the students discussed in the previous class.  They were in the middle of learning about Julius Caesar and the fall of the Roman Republic. The students eagerly answered her questions and were incredibly engaged with the “story” she was telling.

I was engaged with the story, intrigued by the cast of characters and happenings that she described.  The students were making predictions about what would happen next and the teacher responded, “just wait…maybe we’ll see today…”

The students knew the characters in this story, they understood how they related, they recalled the parts of the story that were told to them in the previous class, they made predictions about what would happen next. The teacher also knew this story, oh so well, that she could add on interesting and important details and maintain the curiosity that she had sparked.

I wondered…can we teach math as a story?

I decided to Google “Teach Math as a Story” and the first result was this.

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It is an excerpt from a book and it’s mostly about using stories in the math classroom, but it has useful think-a-bouts like this…

“In our description of how to teach mathematics, we are not concerned with fictional stories about the topic, but rather we are concerned with how we can shape the topic to enhance its attraction to students. In doing this, we will not be falsifying anything, or giving precedence to entertaining students over educating them. Instead, we will be engaging them. We see engaging students with mathematical activity as a crucial aspect of successful education as, and it is the real vividness and importance of this subject in which we want to engage students.

In summary, the great power of stories, according to Kieran Egan (1986, 2004, 2008), is in their dual mission: they communicate information in a memorable form and they shape the hearer’s feelings about the information being communicated.”

I did some additional searching through Peter Liljedahl’s work and found this interesting article that seems related to what teacher planning might look like in order to teach math as a story.

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In this article, Zazkis and Liljedahl contrast a typical lesson plan to what they’ve termed a lesson play.

“In terms of the pedagogical features of the lesson play, we wish to draw attention to some aspects of its format. The structure of the lesson play – as a dialogue occurring overtime with possibilities for different points of view – allows for the portrayal of the messy, sometimes repetitive interactions of a classroom. This structure stands in stark contrast to a necessarily ordered and simplified list of actions such as: take up homework, state definition, provide examples,give problems, and evaluate solutions.”

Crafting a lesson play provides for the improvised interactions that may occur with teaching math as a story-being able to respond and shift according to responses from students.


I don’t think any of this is dissimilar from the ideas in books such as 5 Practices,  but I now have a different analogy that I’m considering. As I continue the thinking that I’ve started here, I want to keep in mind these things in terms of how I work with the math teachers in my building:

  1. On the macro level-How can I help teachers to tell the math story as a set of interconnected ideas and concepts?
  2. On the micro level-How can I help teachers to consider a lesson play, so that the day to day story is just as interesting as the year long story they are telling? How do we get students to want more?

 

A Round Up of Posts on Professional Development

As an Instructional Coach one of the favorite things that I do is plan professional development.  However, it also produces such great anxiety because we all know how most of our colleagues feel about sitting through another round of professional development.   Professional development shouldn’t feel like something that is done to you…it should be done with you.  I realized that there are some great posts by those that deliver professional development and I wanted to round them up here.

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Wrapping Up A Year Of Math Intervention PD  by @bstockus

This means having a skill set that allows you to adapt and customize as needed to help the children grow mathematically, not to follow some prescription as though we’re trying to cure a cold.

Professional Development:  Doing Mathematics by @NicoraPlaca

My goal is that through experiencing math this way, teachers will see a benefit to this way of learning–that when we have the experience of seeing why a formula works or how it works, we have a different experience, which leads to a different type of understanding.

Changing Our Practice, Slowly by @jwilson828

When are we going to realize that over the past few years teachers have been making efforts to change their classroom instruction from students “sitting and getting” to students actively engaging in the mathematics?

I Did Professional Development All Wrong by @davidwees

So instead of spending the entire time I present talking, I give participants much more opportunity to talk. Instead of participants sitting around listening, I give them opportunities to do.

Establishing a Culture of Learning…The First Hour by@MathMinds

A culture where teachers talk about instruction, math problems, and student ideas, feel ownership in their lessons and the lessons of others, and can comfortably visit one another’s classrooms.

 


 

And because I value this bigger view on the current state of professional development…

Professional Development is Broken, But Be Careful How We Fix It by @tchmathculture

As long as we don’t have strong frameworks for understanding how teachers learn, PD –– even localized, teacher-led PD –– risks being just another set of activities with little influence on practice.

Thinking about Feedback

There have been some really great posts lately about how teachers are giving feedback on assessments.  You could read this post here by Nathan Kraft or this post here by Fawn Nguyen.  Also, there is a great Teaching Channel video on highlighting mistakes as a grading practice for you to watch here.

All of these posts show the power of the highlighter.

A strategy that I started using last year involves the highlighter…but in a different way.

Problem-Attic  is a resource I’ve been using to create weekly assessments.  I wanted to figure out a way to help students to be more independent in identifying and revising mistakes.

I decided to turn each problem from the assessment into its own one page station where I highlighted important features and made notes of important think-abouts.  For the most part…these related to common misconceptions or careless errors.

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Students then had the opportunity to work around the room and read the “hints” that were provided in order to revise their work.  Some of my hints were probably too “hinty,” but it was a starting point for a process that I was working out.

I did this with 8th grade-on grade level students.

Students reported liking the process–and were able to figure out their errors independently of me.

I’m hoping to refine this process this year.

Everything I learned about teaching I learned from teaching students with special needs…

I came about a teaching career in a round about way.  As a math major at a small liberal arts college in Southern Maryland, I earned money by tutoring local middle and high school students.  I realized that I really enjoyed this experience and decided to pursue a teaching degree at the graduate level.

While taking classes towards a graduate degree for secondary math instruction, I fell into a job at a non-public special education facility.  I worked under a conditional certificate with some very wonderful special educators.  I ended up becoming THE math teacher for the entire high school program (the Harbour School is a k – 12 facility).  This meant that I taught all of the students ALL of their high school math.

I believe that I wouldn’t be the educator that I am today without this experience.

At the Harbour School I worked with students with all sorts of ABILITIES.  This school was their SAFE HARBOUR.  The students came to the school because it was found that their home school couldn’t meet their educational needs.

Teaching math at this school was an exercise in flexibility.  I had to really listen to the students to understand their understanding.  I do believe that math was a mystery for most.  I’ve always used this analogy for teaching math…

If I couldn’t get through the front door, I found a way in through the window, the garage, or around the back of the house.

By having to ask the right questions and make the right connections, this experience helped me to understand the math I was teaching at a deeper level.

At the Harbour School I also learned:

  • acceptance
  • tolerance
  • patience
  • community
  • awareness
  • perseverance
  • resilience

If you are wondering about how to meet the needs of the students in your classroom with learning challenges–my advice is to listen to them.  ...Then figure out how to get into the house…

My favorite talk about listening from @maxmathforum