Tag Archives: representations

Example of Using Support Class to Support Current Math Content

I have posted on how to effectively provide support for current math topics. Here is an example (below) of how support can focus on both the current topic and prerequisite skills.

For example, on the 22nd in this calendar the current topic is solving equations. The steps for solving will include simplifying expressions and may involve integers. The support class can address the concept of equations, simplifying and integers which are all prerequisite skills from prior work in math.

examples of support class prerequisites

This approach allows for alignment between support and the current curriculum and avoids a situation in which the support class presents as an entirely different math class. For example, I recently encountered a situation in which the support class covered fractions but the work in the general ed classroom involved equations. Yes, equations can have fractions but often they do not and the concepts and skills associated with the steps for solving do not inherently involve fractions.

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Function Notation for Algebra

Below is a video of a lesson I recorded on function notation using the Explain Everything app. The lesson starts by addressing the concept of function notation by connecting it to the use of the notation “Dr.” as in Dr. Nick of Simpson’s fame. The lesson builds on prior knowledge throughout with a focus on color coding and multiple representations.

This videos shows an instructional approach to teaching function notation and concepts in general and video lessons can be used for students who miss class or who need differentiation.

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AWESOME Online Graphing Calculator

Desmos graph pizza function

This can be a game changer for students with special needs who struggle with math. The Desmos graphic calculator allows students to interact with math equations through multiple representations. It is far superior to graphing calculators in terms of quality and ease of use and is free. The app for Smartphones is outstanding.

Here are features that make this calculator user-friendly and an outstanding instructional strategy.

  • Students can click on dots and the ordered pair will appear (see top photo below).
  • Students can change features of the equation and immediately see how the graph changes.
  • Students can collect data and create a graph and convert the data into “mathy” representations like equations (see top photo below).

Desmos regression price vs mileage of used cars

 

Desmos parabola

image

 

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Scaffolding Higher Level Math Topics

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The graph shown involves derivatives – a calculus level topic. Before getting into this heavier mathy stuff, consider the title of this post and the other content presented on this blog. Making math accessible to all students is not a special ed or a low level math thing. It is a learning thing. This artifact is what I drew to explain the math concept to a student in calculus to help her grasp the concept as well as the steps. The following are strategies used.

  • color coding – each of the 4 sections written in different color
  • connecting to prior knowledge – the concept of velocity was presented in terms of a car’s speed and direction (forward or backing up)
  • chunking – the problem was broken into parts and presented as parts before exploring the whole
  • multiple representations – the function was represented with a graph, data (1, 2, 3, 4, 5) and a picture (at the bottom)

As for the mathy stuff, the concept of velocity was address by its two parts: speed (increasing or decreasing) and direction (positive or negative). The graph was broken into the following parts: decreasing positive, decreasing negative, increasing negative and increasing positive. Each part was presented with possible y-values (data) and the sign. The most intuitive part is increasing positive which is a car going forward and speeding up.

I find that when I provide intervention, this approach especially by addressing conceptual understanding is effective as the students respond well.

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Color Coding and Representation for Integers

adding integers chips and colored pencils

This example involves adding integers which is a major challenge for many students. There are two strategies present in the photo.

Color coding is an effective way to break down a concept into parts. Here red is used for negative numbers and yellow for positive. The numbers are written in red and yellow with colored pencils.

The chips are a concrete representation. Typically integers are only presented in number form and often with a rule similar to the one below. The strategy is to count out the appropriate number of red chips for the negative number and yellow chips for positive number. Each yellow chip cancels a red chip and what remains is the final answer. If there are two negative numbers then there is no canceling and the total number of red chips is computed (same with positive and yellow).

  • + + = +
  • – – = –
  • + – use the bigger number…

Rules are easy to forget or mix up especially when students learn the rules for multiplying integers. Concrete allows students to internalize the concept as opposed to memorize some abstract rule in isolation.

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Daily Checklist for ASD

Daily Checklist for ASD

This is a daily checklist (list of expectations) for a student with an autism spectrum disorder. This student completes it as we proceed through class. He gets a daily grade for this. This particular student loves The Avengers so I added a Captain America sticker as reinforcement (which he likes).

Other students have a more detailed checklist with a reliance on words alone. Kids with ASD often need visual representations.

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Representations of Concepts

Representations of Concepts

Three ways to represent perimeter: I taught a lesson on perimeter to a 5th grade class. First I had them create a rectangular pen for their animals and they counted the number of fence pieces. Then we drew a rectangle to represent the pen. Finally we looked at the formula. This allows a deeper conceptual understanding of the concept. This is known as Concrete-Representation-Abstract – representing the concept at all three levels.

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