Reading Aloud in Math Class

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

read_aloud

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.

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

 

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.

First REAL post…

It’s been a long time since I started this blog b/c of the MTBoS.  I appreciate all of these people who are just so SMART and thoughtful about what they do to improve the lives of kids.

I am finding it hard to figure out what I could have to offer in starting a new blog…I understand and respect the reflective process as an educator, so I can see the benefits for myself.  But, I want to contribute as well…

I thought for this post I would ramble on about my observations of kids and their ability (or “inability”) to make meaning from print themselves.  In my role as an Instructional Resource Teacher I have the unique opportunity to see a great variety of students from grades 6 through 8–below grade level to honors.  I have found that a great many of these students have difficulty even making sense of directions independently.

When I was still in the classroom, teaching on grade level 8 students, it would take just a simple verbal prompt from me (basically reciting what the question was asking)…and students would say “ooh that’s all it (the question) wants me to do?”  There could be some learned helplessness in there…but I think that we (math teachers) could do more to help students become better math “comprehend-ers”!!

What does this look like???  When I began to hear the discussion  among ELA teachers at my school re: annotating text (according to Common Core), I thought…WOW!  That could be a useful tool in the math classroom…put the thinking aloud that I usually do with them as I’m teaching–on paper…link it to the print in a concrete way.

I had a Twitter conversation with @JustinAion and @cheesemonkeysf re: just this topic…

The ELA teachers in your building should have a process that the kids are used to.  If you ask them (the kids)…they will tell you that they are annotating in their ELA class (if you are a Common Core state).

There is still a lot to discuss here…but I want to add one more great share by @lsquared76:

https://twitter.com/lsquared76/status/394982935872294912

I retyped it up for a 6th grade class using a task from @IllustrateMath:

I was able to use this in a 6th grade accelerated class (the teacher and I co-teach…he lets me try things).  On this very first go around…I felt like the kids did well with the summarize questions on the left (remember these are the high kids though).  However, articulating a plan (the part on the right) gave them some trouble.  It did allow us to see the divergent thinking about how to solve the problem (which students recognized division of fractions vs repeated subtraction)…and then move into a discussion of efficient strategies.  We will use this model again and collect more data.

So…this is my first “real” post…I have more I want to offer on this topic.  But, I just felt like I needed to get this first one under my belt!

Thanks to the twitter folk that I mentioned here!  *and @algebrainiac for helping with my embed issues!!  😉

Things that make you go hmmmm…..

Well….this is an interesting place to be.  I’m not sure about how I feel about putting my thoughts out there for the world, but I do love the fact that this community exists.

I came here because I am just as intensely obsessed with education as all of these people that have already begun their journey in the reflective world of blogging.  I like to say that education is not only my “job” but my hobby.  Most of my friends and colleagues (even occasionally my husband) do not understand that.

I enjoy ALL things education…

  • Special Education
  • Math Education
  • Professional Development about Education
  • Curriculum Writing
  • Universal Design for Learning
  • The list can go on…

But…first and foremost, I just plain old LOVE MATH.  I’ve loved math my entire life.  I can’t remember having a bad teacher…only teachers that made me love math more.

I even majored in math for my undergraduate degree and didn’t work towards education until my graduate degree.

Interestingly…my very first teaching job was at a place called The Harbour School (this is a non-public special education facility for students K – 21).

This was the best professional development that I have ever experienced…teaching math to ALL of the students that entered the high school portion of the program–students with Autism, Asperger’s Syndrome, Learning Disabilities, Cerebral Palsy, Speech and Language difficulties, etc.  I taught students that were community based…but also students that worked towards your typical advanced math classes.

So, I am certified in both secondary math and special education.  But, now I work in a public middle school in southern Maryland.  This school pulls from Title I elementary schools and serves underprivileged students.  I work as an Instructional Resource Teacher in my building…and work daily with teachers and students.

So, all of these experiences have created the lens through which I view all things math education.  I love to absorb it ALL!