# Thinking in the Concrete~Manipulatives in Math Class

Amie Albrecht retweeted this the other day over a year ago (I just came back to finish this post):

It reminded of me when I used my son to try out the first part of this NRich problem:

I’ve used this problem with middle school students before…but I wanted to use it in a math for elementary teachers undergraduate class, so I needed to see how an elementary student would think it through (he’s in 5th grade).

He attempted some mental thinking about the problem at first. But, I could tell he was going to get frustrated. I found something that could work as counters for him and asked him to represent the problem. He argued with me about it and finally said “only babies use these.”

I pushed him to use the counters…and he figured the problem out quite simply.

Using manipulatives makes problems so interesting to think about. But, I just asked him about that day and he agreed that the tool made the problem easier, but he didn’t like using them.

We need to use more manipulatives in math class!

# Reading Aloud in Math Class

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

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

# 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

# #WODB and Polygraphs: Lines in the Classroom

I’ve been using these sorts of problems in my classroom intermittently for many years.  My first exposure was at an NCTM conference in Baltimore in 2004.  This type of problem was titled “Puttering with Patterns”  similar to this one here:

I worked as the math teacher in a k-21 special education facility at the time and immediately understood the benefit of posing problems like this to students with special needs…EVERYONE can notice something meaningful to contribute.

Here are several reasons why each one is different:

I was reminded of this type of problem by Christopher Danielson when he released “Which one doesn’t belong?  A shapes book.”

I’ve been out of the classroom for many years, but this year have returned to lesson plan for an 8th grade classroom that is being taught by a long term sub (the teacher moved out of state in October).  I’ve been in this classroom more often than not–co-teaching with the sub.  This has been my opportunity to really try out many of the activities that I have come across on Twitter–YAY!!!

When @MaryBourassa created the new site “Which One Doesn’t Belong?”, I was excited that she brought this type of problem to the forefront AND gave it a more secondary sort of spin.

A good portion of the students in these 8th grade classes that I am working with are reluctant learners.  But, #WODB pulled them all in.

We’ve been working on linear equations, including graphing lines using slope and y-intercept.  So for the last day before spring break I decided to use this:

as a lead in for this:

The sequence of instruction worked perfectly for these 8th graders…because, really, Polygraph is just a giant “Which One Doesn’t Belong?”

Fo the #WODB task, my students noticed that the 2nd graph was proportional, that the 3rd graph had a negative y-intercept, and that the 4th graph had a negative slope.  We needed to have a classroom discussion to determine an attribute for the first graph that didn’t fit in with the rest.  We ended up talking about x-intercept for that one (a term that they didn’t have yet).

All of these observations became questions they asked when playing Polygraphs.

I’m looking forward to making the #WODB problems a larger part of our typical daily routine.

# 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
• 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!