The First NCTM Innov8 Conference: A Reflection

Posted on December 2, 2016 by Andrew

People at NCTM’s #NCTMInnov8: I’m having trouble figuring out what is innov8tive — what I see seems like standard conference stuff. Help?

— Michael Pershan (@mpershan) November 17, 2016

It has been a busy end to the first trimester, so this is the first time I’ve had to sit down and reflect on NCTM’s first Innov8 conference, held in St. Louis a couple of weeks ago. The focus of the conference was “engaging the struggling learner.” I’ll leave it up to you to define that term on your own, because it seems to encompass quite a vast swath of educational labels (e.g., “at risk,” “difficulty,” “intervention,” “tier 3,” “disability,” etc.).

As a special educator and advocate for students with disabilities, this conference was a breath of fresh air. It was refreshing for numerous sessions to relate in some way to the students who are in my classes. One of the major themes from this conference was what was truly meant by the term “struggling learner.” Fawn Nguyen broached this topic during her keynote:

Continue reading →

Ask More Questions!

Posted on May 28, 2015 by Andrew

Encouraging students with disabilities to think deeply about mathematics has always been one of the goals of this blog. But since the audience of this blog is mainly teachers, the goal is really to encourage teachers to encourage students with disabilities to think deeply about mathematics.

So here goes…Ask More Questions!

Duh! You’re thinking, “I asked 35 questions today! Numbers 1-35 on the multiplication fact fluency worksheet were math questions. This guy!”

But, the questions I’m referring to come after you ask those initial questions. Sure, you proposed a math problem to your students or even better they proposed one to you based on some mathematical situation you presented, but then what happened?

Andrew Stadel recently wrote about and collected questioning strategies from the MathTwitterBlogosphere. His focus was on strategies for asking questions before and after the launch of the day’s mathematical problem, task, lesson, activity, etc. My focus has been on post-launch questioning strategies. The stuck/unstuck questions and questions to explore student misconceptions. In an NCTM article, which discusses warning signs of instructional moves that generally lead to taking over student thinking, the alternative teacher moves are also focused on asking questions when a student is stuck or has a misconception.

Continue reading →

Why Count Your Money, When You Can Estimate?

Posted on April 14, 2015 by Andrew

The end of spring break means we are in the midst of our school’s spring financial literacy unit. This is always a favorite of both students and teachers. We ground our work in very concrete community related activities, such as going to the bank and going to the store. Students love spending money and teachers love going on community walks in the spring and early summer. Everyone wins!

Before we start going on trips, I wanted to do some number sense work with my classes relating to the counting of money. As we left for spring break I tweeted about an estimation idea inspired by counting money.

Money counting practice today led to this #estimation180 idea! How much money in the stack? @Estimation180 @gfletchy pic.twitter.com/0C8P1W49UR

— Andrew Gael (@bkdidact) April 2, 2015

Right on cue, Graham Fletcher, who writes his own amazing blog here, gave me some sage advice.

@bkdidact @Estimation180 maybe don’t share the chart piece up front and hold on until after initial guess. See who wants to change 1st guess

— Graham Fletcher (@gfletchy) April 2, 2015

I took Graham’s advice and ran with it. As much as we like our money math standards to relate to identification of coins and bills and getting accurate counts on prices and change, estimation is a key skill in any “real world” financial transaction. When was the last time you stood at the supermarket register counting out the entire pile of change you got from the cashier? Generally, we look at the coins in our hand and make a quick estimate as to whether we think it is the correct change or not. So I used the idea from my tweet, took some inspiration from fellow math teachers Andrew Stadel and Joe Schwartz, and turned it all into a financial literacy lesson.

Here’s how it went…

Continue reading →

The Importance of Implementation

Posted on March 5, 2015 by Andrew

A recent NPR article entitled, 5 Lessons Education Research Taught Us in 2014, seems to have a lot of definitive answers about our currently polarized educational climate. The article mentions a research paper which encourages the use of teacher-directed, explicit instruction of mathematical computation skills for procedural fluency with students with mathematical difficulties. To me this read as favoring explicit instruction and direct modeling of mathematics for students with disabilities over the project or problem-based, hands-on (manipulatives), collaborative (student-led), investigative style instruction that makes up some “reform” mathematics curriculum.

As a counterpoint to the NPR article, the National Council of Teachers of Mathematics lists procedural fluency as just one part of what is referred to as Mathematical Proficiency. In chapter 2 of the book, Achieving Fluency: Special Education and Mathematics, mathematical proficiency is discussed as including the following four components: procedural fluency, conceptual understanding, strategic and adaptive mathematical thinking, and productive disposition. Together these four components lead to mathematically proficient students which lead to mathematically proficient adults, disabilities or not.

1. Procedural fluency involves using basic skills such as facts, procedures, and formulas efficiently (i.e., quickly and accurately). It also entails knowing when to use them and, if necessary, how to adapt them. In other words, procedural fluency is skill in carrying out routines appropriately and flexibly as well as efficiently.

2. Conceptual understanding is knowledge of facts, generalizations, or principles underlying the comprehension of concepts (categories), relations (between categories), or operations (actions or events involving categories).

3. Strategic competence involves the ability to formulate, represent, and solve mathematical problems, and adaptive reasoning entails the capacity for logical thought, reflection, explanation, and justification.

4. Productive disposition entails believing that mathematics makes sense and is useful, that learning it requires diligence, and that everyone is capable of significant mathematical learning.

Since the NPR article about educational research only references one paper specifically about mathematics instruction, you only get one point of view. This NCTM book provides another viewpoint of what are important goals for mathematics lessons with struggling students.

Continue reading →

To Calculator, or Not To Calculator, That is a Question

Posted on February 6, 2015 by Andrew

When it comes to planning lessons in special education, or general education for that matter, the goal is for all students to be able to access, understand, and be able to successfully apply the content to show evidence of full understanding. The application can take many forms: performance assessments, formative assessments, summative assessments, teacher observations, etc…

But how do you get to that final assessment piece? This post is about the planning process that goes into successful lessons for all students. Let’s begin with Universal Design for Learning (UDL). UDL is a model for planning lessons and units that creates access to the content for all students. Here is a cartoon that embodies the philosophy of UDL.

One major component of planning in special education math classes is prioritizing the mathematical goals and the needs of the students to access the mathematics in a lesson. A Teaching Children Mathematics article from 2004 suggests the following steps for beginning to plan a successful math lesson for students with disabilities:

Continue reading →