Jan 21 2019
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Connections to Prior Knowledge, instructional strategies, special education in general

Retaining Information

Below is a model for information processing (retention and retrieval). Here are a couple key points I want to highlight:

  • A lot of information is filtered out so what gets through? Information that is interesting or relevant.
  • Information that is connected to prior knowledge, is relevant or that is organized has a better change of being stored effectively for retrieval.
  • Working memory has a limited capacity. Consider what happens to your computer when you have a lot of apps open. Your computer may start to buffer which is basically what happens to our kiddos if instruction involves opening too many apps in their brains.
  • Long term memory is basically retrieval of information. Think a student’s book bag with a ton of papers crammed in it. How well can he or she find homework? Compare this to a well maintained file cabinet that has a folder labeled homework with the homework assignment in question stored in this folder. That paper is much easier to retrieve. This is analogous to long-term memory. If the information is relevant or meaningful it will be stored in the file cabinet folder and more easily retrieved. In contrast, rote memorization like the rules teachers present students are papers crammed into an overflowing bookbag.

Information Processing.jpg

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Jan 21 2019
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Math Support Time, Notebook and self-help skills, special education in general

Overlooked Skills for Success

Ask employers what skills are desired in graduates and you will not see academic competence at the top of the list. In schools we talk about creating life long learners and similar qualities but the major focus in the 7+ K-12 schools in which I have served is academics, or more appropriately grades as a proxy for academic mastery.  Add to this the focus on exit exams for graduation and you see major disconnect between the desired outcomes and the focus.

I have taught math at 5 colleges or universities and have seen first hand students struggle with content but also with independent study skills. Manchester Community College in Connecticut conducted a survey of students and asked students to cite reasons why students struggle in their classes. The second most commonly cited responses by students themselves is that students don’t know how to study (see below). In high school we talk about study skills. Teachers will share they expect students to be independent but often the focus is on academic mastery and not the study skills.

MCC survey

At Manchester Community College I serve as an instructor at a highly successful (based on objective outcomes) bridge program for first generation students. A major emphasis is a focus on student academic discipline with a mantra that discipline is the bridge between goals and accomplishment (see below). Learning how to BE a good math student, especially academic discipline, is as important as developing the prerequisite skills to be successful. This could be a major focus in the IEP for students who have a goal of college or post-secondary training..

discipline bridge

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Jan 20 2019
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Consumer Math, Number Sense

Opportunities for Parents to Engage Students with Math

Math is often considered an esoteric set of information that is disjointed from the reality people face, aside perhaps from money. Sadly, in school, especially in older grade levels, math is indeed presented this way.

sally math problem

A situation as simple as riding an elevator provides opportunities to show and engage a student with math applied in authentic and common situations. For example, the elevator buttons address counting and cardinality (4 indicates a total of 4 floors – ignoring the R), comparison (if we are on floor 2 and need to go down, which floor do we go to?) and measurement (height above ground floor measured in floors). Such situations also provides opportunities for generalization into other settings – the important settings of every day life!

2019-01-18 18.33.56

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Jan 20 2019
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Concrete-Representation-Abstract, Consumer Math, Number Sense

Authentic Activities – Money and Prices

Below is a photo of a typical worksheet for money. I worked with a parent of a high school student severely impacted by autism and she explained that her son worked on nothing but worksheets when he worked on math. For students with more severe disabilities the worksheet is not real or meaningful. The photos and the setting is abstract.

adding-money-worksheet-1

Below is a photo of shelves in a mock grocery store we set up at our school for students who were in a life skills program. They would have a shopping list, collect the items in a basket then compute the total cost. We had a mock register set up (eventually we procured an actual working register) and the students made the same types of calculations they would on a worksheet but in an authentic setting, which was more concrete. We would start with simple money amounts, e.g. $1.00 then make the prices increasingly more challenging, e.g. $1.73.

mock grocery store

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Jan 19 2019
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ADHD, assessment, Behavior Management

Performance vs Ability

In the effort to assess student ability performance factors are likely present. It is incumbent upon the educators to mitigate the performance issues to assess true ability.

For example, I conducted an evaluation on a student in middle school who has ADHD. All of her testing records indicated that she would lose focus during the assessment and that the focus was problematic for testing. Before we met I surveyed her on her favorite snack (didn’t know Sour Skittles is a thing), brought this reinforcer along with a bottle of water. She sat through an entire 1 1/2 hour KeyMath Assessment without incident.

performance vs ability

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Jan 18 2019
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Algebra 1, Concrete-Representation-Abstract, Connections to Prior Knowledge, CTALGEBRADUDE Video Series, Scaffolding

Introduction to Solving Equations

I introduce solving equations by building off of the visual presentation used to introduce equations. The two photos below show an example of handouts I use. Below these two photos I offer an explanation of how I use these handouts.

intro to solving equations

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First I develop an understanding of a balanced equation vis-a-vis an unbalance equation using the seesaw representation.intro to equations balanced vs unbalanced

I then explain that the same number of guys must be removed from both sides to keep the seesaw balanced.

intro to solving equations balance and unbalanced

I then apply the subtraction shown above to show how the box (containing an unknown number of guys) is isolated. I explain that the isolated box represents a solution and that getting the box by itself is called solving.

intro to solving equations adding

I use a scaffolded handout to flesh out the “mathy” steps. This would be followed by a regular worksheet.

solving 1 step equations add scaffolded

I extend the solving method using division when there are multiple boxes. I introduce the division by explaining how dividing a Snickers bar results in 2 equal parts. When the boxes are divided I explain both boxes have the same number of guys.intro to solving equations multiplying

The students are then provided a scaffolded handout followed by a regular worksheet.solving 1 step equations multiply scaffolded

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Jan 18 2019
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Uncategorized

Rate of Change in Real Life

61 cents per ounce is a rate of change. Graph the line modeled by this (y intercept is 0) and it becomes slope of the line. In referring to algebra we often hear, “when will I ever need this?” My response is “all the time!” Our job as teachers is to make this connection for students.

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Jan 18 2019
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special education in general

Graduation, Now What?!

I believe that the high school diploma is widely viewed as the end game of K-12 education. The purpose of special education focuses on life AFTER the diploma. The focus of our collective efforts should be on NOW WHAT?

nowwhat-589

I have posted on this topic and want to circle back to it. If the purpose of special ed is to prepare students for life after K-12 education then I believe we should use backwards planning to guide services. I stumbled across a website on LinkedIn that can be very useful. This site (see below) provides detailed information about requirements for various occupations – useful for backwards planning. For example, I worked with a student in 7th grade with a more severe disability who was interested in working with cars. The math needed for this occupation was largely measurement and that was the focus for his math – a modification.

career one stop

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Jan 18 2019
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Differentiation, instructional strategies, special education in general, Uncategorized

Strategy to Individualize Instruction

It is difficult to individualize instruction in a whole class or small group setting. I created and taught the curriculum for a Consumer Math course at the high school where I teach. For a class of 10-12 students, all with an IEP, I developed an approach that allowed me to individualize the instruction for each students.

In the photo below is an example of a folder set up I used with the students in Consumer Math. Each student would have a dedicated folder, kept in the room and updated daily. The smaller paper shows the individualized agenda. The other paper shows an example of how the folder can be used as a resource. Student computer login information, accommodations like a multiplication table or notes can be secured inside the folder. The agenda would be changed out each day. (In case you are wondering about the label in the agenda, “Math Group 4.” This particular folder was used in a special education training session for teacher candidates.)

individualized folder

 

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Jan 17 2019
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Algebra 1, instructional strategies

Introduction to Equations – (Meaning Making)

This is a meaning making approach to introducing equations. I will walk through the parts shown in the photo in the space below this photo. (A revised edition of this handout will be used in a video on this topic.)

intro to equations

First I explain the difference between an expression (no =) and an equation (has =). An equation is two expressions set equal to each other (21 is an expression).

intro to equations definition equation

I then develop the idea of a balanced equation and will refer to both sides of the see saw as a prelude to both sides of the equation. I also focus on the same number of people on both sides as necessary for balance.intro to equations balanced vs unbalanced

At this point I am ready to talk about an unknown. Here is the explanation I use with the photo shown below.

  • I start with the seesaw at the top. The box has some guys in it but we don’t know how many.
  • We do notice the seesaw is balanced so both sides are equal.
  • This means there must be 2 guys in the box.
  • I follow by prompting the students to figure out how many guys are in the box(es) in the bottom two seesaws.
  • Finally, I explain that the number of guys in the box is the solution because it makes the seesaw balanced.

intro to equations definition solution

There are multiple instructional strategies in play.

  • Connection to student prior knowledge – they intuitively understand a seesaw. This lays the foundation for the parts of an equation and the concept of equality.
  • Visual representation that can be recalled while discussing the symbolic representation, e.g. x + 1 = 3
  • Meaning making which allows for more effective storage and recall of information.
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