Tag Archives: problem-solving

Authentic Learning and CCSS



SBAC and PARC problems used to test CCSS are challenging and often draw upon context unfamiliar to students. This means students must navigate the content, problem solving and deciphering context. Below is an SBAC problem dealing with photo albums…PHOTO ALBUMS. Do kids today understand this? In the subsequent pictures you will see the work of one of my students on handouts I created that develop an understanding of the SBAC problem – note the “x-2” at the end. The idea is to shape their ability to do such problems.

photo album sbac problem photo album pizza equation part 1 photo album pizza equation part 2 photo album pizza equation part 3photo album pizza equation part 3

photo album pizza equation part 4


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Scaffolding Multi-step Math Problems

sidewalk problem

This is the figure from Mrs. Olsen’s Sidewalk Problem from the CT CAPT test 2010 (released to public). The problem has four major steps: divide the figure into common shapes, use Pythagorean Theorem to find height of the resulting triangles, find area of these shapes and compute total cost for  pouring the asphalt for the sidewalk. Simply finding an entry point into this problem is a major challenge as is keeping track of the multiple steps.

Below are photos of the handouts I use to break the problem down into parts – scaffolding. Eventually the students have to learn to find an entry point and navigate the steps on their own. They learn to do this incrementally with the teacher shaping the problem-solving skills.

sidewalk problem scaffolded


side walk problem PT

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Supporting Students with Severe Disabilities

Adapting lessons for students with severe disability


I only investigated the page on making predictions and was very impressed. I wrote previously that special education is about problem-solving. Well that’s evident on this site. It appears that this is the work of a Laura Lewis. If so kudos to her.

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Special Ed = Problem-Solving

Received a Tweet from a parent asking about a particular disability. While I do not have experience with the disability in question, I feel I have the tools to address any disability. This is largely due to my professional training.

For my master’s in special ed I took an assistive technology (AT) course at the University of Saint Joseph. The first night the instructor, Carolann Cormier, revealed indirectly that AT (and special education in general) was essentially a problem-solving endeavor.

This was an epiphany. Since that one night I have had the mindset of using problem-solving and thinking outside the box to meet student needs. I give Carolann tremendous credit and identify that course as being one of the best I have ever had. Examples of how this has manifest in my teaching is evident on this blog, e.g. color coding and graphing on the computer.

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Shaping Critical Thinking and Self-help Skills

Below is an example of a puzzle I use to train students to make an effort and to think about problems. I have found that many students not only have a learned helplessness when it comes to math but they have been trained to follow steps mindlessly. Following a task analysis approach the first step is for students to find an entry point to a problem. They also need to feel comfortable taking risks. Slowly moving the students towards solving more complicated problems is called shaping.

Below you can see that the student made a more simplistic attempt. Given that this was done the first day of school I was very pleased with the effort.

How many squares problem

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Sudoku Scaffolded


I wrote in another post about a 7th grader with asperger’s who tested in math at a 1st grade or kindergarten level. I used scaffolding to show him how to do Sudoku puzzles. On the left is a simple version with one digit missing from the box. In the middle is a little more complicated scaffold. On the right is a completed Sudoku puzzle that this student completed on his own (minimal prompting). These worksheets come from http://www.superteachersworksheets.com.

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