Juggling Gaps and New Content

In math, many students with special needs fall behind. What results is a Catch-22 in programming and services. If the student is provided extra time to work on the gaps, he or she likely falls behind with current content. If the student is provided extra time to receive support for current topics, the gaps are not addressed

In both cases the extra support time can actually be counterproductive.

  • The focus on gaps likely results in the student working on different math topics which in effect means the student has TWO math classes – just what a student with math anxiety doesn’t need.
  • The focus on current topics means the student is trying to learn math topics for which he or she doesn’t have the prerequisite skills needed.

I recommend identifying the prerequisite skills for a current math topic and address ing these skills concurrently in math support or during the summer. For example, I used a Common Core coherence map (top photo below) to identify Common Core prerequisite standards for the standards a student faces in her upcoming school year. Then I listed these with each grade level standard (bottom photo below). The prerequisite skills can be identified using a task analysis approach as well. Screenshot 2018-06-12 at 6.03.52 AMScreenshot 2018-06-12 at 5.45.22 AM

This approach allows for a systematic approach to fill in gaps and to prioritize when they are to be addressed. When implemented effectively, the student can see the immediate benefit of the support time – it helps them in math class. Even better, the support teacher can match instruction and work with what is covered in math class.

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Post-Secondary Education Goal – Points to Consider!

In special education and in K-12 education in general graduation is viewed as a culmination or the end game. In fact it is just the opposite. Graduation is a STEP towards the future. If the plans for your student is post-secondary education, including vocational training, it is important to understand a couple false assumptions.
  1. A diploma indicates the student has the academic mastery for post-secondary education. Below is a link to some documents. One is a study of how well prepared high school graduates in Connecticut are for college. In 2009 more than 2 out of 3 students entering a community college or a Connecticut State University needed to take a remedial (developmental) course in English or Math despite earning a high school diploma (and passing a state graduation exam).Screenshot 2018-05-25 at 3.22.50 PMScreenshot 2018-05-25 at 3.24.12 PM
  2. A diploma indicates the student has the ability to perform as an independent student. In a survey from Manchester Community College (Connecticut) students were asked why students struggle academically. 60% of MCC students reported that students don’t know how to study. MCC survey
Here is some information about the placement tests, with Manchester Community College used as an example. The placement test results are what determine if a student will have to take a remedial course.
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Here are related documents including those referenced above. The placement test is the Accuplacer and the documents linked include a handout with example problems for math and English from the Accuplacer.
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Summer Math Intervention Sessions


A graduate level math intervention course at USJ has a practicum component in which graduate students work 1 on 1 with students with special needs over a 5 week period. An experienced math interventionist oversees the work. The focus of the sessions is on an identified math objective selected by the family or teacher of the student with special needs in math (students with IEP or 504, who are receiving extra services like SRBI, who are below grade level or who have a history of struggling with math)

Each graduate student, in collaboration with the supervising instructor, conduct initial assessment, implement a variety of instructional strategies and conduct ongoing progress monitoring and provide lots of objective data!


The sessions run 5-6PM every Thursday from July 12 to August 9 at the USJ campus.


  • Parents are provided objective data from curriculum based assessments that can be provided to the home school educators.
  • Parents are provided a portfolio of an array of instructional strategies. This could provide insight for the home school educators on what works for the student with special needs.
  • Parents observe the sessions to gain first hand knowledge of how their student with special needs engages in math and knowledge of what effective math services look like.
  • At the end, the graduate student will meet 1 on 1 with the parents to explain the assessment data and instructional strategies and will provide a comprehensive report.
  • At the end, the instructor will meet with parents to explain how to leverage the information provided by the graduate students with the home school educators, especially PPT or 504 teams.

Next Step

If you are interested, please contact Randy Ewart (email address below). Note: these sessions are designed to benefit both the student with special needs and the graduate students. Hence, families who participate are expected to attend all 5 sessions.


The instructor is Randy Ewart, a veteran math teacher and math interventionist who received his master’s in special education at USJ. He has provided consultation and services to multiple districts and over 100 students with special needs to make math accessible. You can visit his blog for examples of his work: www.ctspedmathdude.com. Email him at ctspedmathdude@gmail.com

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Autism Explained

Excellent production and effective explanation.


Graphing Linear Functions

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Graphing linear functions and the underlying concept are challenging for many students. The video below shows a scaffolded approach to teaching how to graph. This approach also addresses the concept of the graph as a visual representation of all possible solutions (see photo above). Students often do not realize that the line is actually comprised of an infinite set of points which represent all the solutions. Here is a link to the document used in the video.

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1 to 1 Correspondence Scaffolded

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I have encountered several students who struggle with 1 to 1 correspondence with the educators struggling to figure out how to teach this to these students who continue to struggle. This post reveals an approach I used with a student.

I broke down the task using a formal task analysis approach. This approach involves identifying the different individual steps and to address these steps in isolation. Here is the sequence I use and suggest.

  1. Conduct a pretest using a task analysis pretest data sheet I created for this topic. I do not use any scaffolding and prompt the student to count out the objects (in this case decks of cards) and to do so independently. I prompt the student after they show they cannot complete a step which allows the student to attempt the next step. (Think of teaching a student to get dressed and he cannot put his socks on. You help him with the socks then ask him to put on his shoes.)
  2. I then focus on the movement of the objects. I provide scaffolding for start and stop piles (see mats with track photos above). The student is asked to move the cards one at a time without counting.
  3. The student must learn the “rules of the game” which includes how to place the items in the stop pile. Students may be confused about placement, e.g. one student ran out of room while placing the decks in a straight line and I had to demonstrate that it was OK to place them on different spots on the mat. Once the student demonstrates mastery of moving the items we move on to the next step. IMG_20171221_080726834 - Edited
  4. We then focus on counting in isolation. The card decks are labeled with numbers (photo below) and the student does not move anything but simply reads the numbers. (More on these numbers in a later step.) More numbers can be added as necessary.IMG_20171221_080604425 - Edited
  5. The next step (photo below) is to have the student read the number on each card. I have a stack of decks of cars on the start pile with the numbers facing down. I show the student the number of the deck that I am moving to the stop pile and the student reads off the number. I place the used deck face down to hide the number. This activity forces the students to focus on each item as he reads the number. One student kept counting ahead to the next number and I prompted him to return his focus to the current number. This is the crucial step as it focuses on the 1 item 1 number aspect of counting. IMG_20171221_080526960 - Edited
  6. The next step is to have the student move the decks from the start pile to the stop pile and to read each number while doing so. I turn each deck face up as a prompt for the student to move and read.
  7. The student then is prompted to select the cards on his own and read (the cards can be in a pile in order by number).
  8. Eventually 1 then 2 then 3 decks have the number missing which adds an extra task demand for the student – identify the next number as he is moving the item.
  9. Finally the items do not have any numbers and the student counts, with the mats eventually be faded.

Note: this is especially effective for students with ADHD because it helps to focus and organize their task demand for the activity of counting.

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Kahoot Game

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A Kahoot is an online and app quiz game that allows students to answer questions using a personal device (e.g. simulated phone in photo above). The teacher can create the questions (e.g. example question I created in photo above).

My approach is to use a Kahoot to scaffold learning. In this post I use plotting points as an example.

  • I start with simple questions, e.g. identify the letter and number coordinates for the dog and chick below. Notice in the top photo below that I provide the actual coordinates in question 1 (“for the dog C4”) as a scaffold to show the students what to do.
  • Then I show numeric coordinates for a point, but only with positive numbers.
  • Eventually I present problems that address all 4 quadrants and ask questions about the parts of the coordinate plane (photo bottom one, below).
  • Notice that the questions have times (in seconds). This indicates the time allotted to answer each question (teacher sets this). For students with special needs I print a hard copy to allow them more time to read the question. If necessary, they can respond by circling the answer on the handout.

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Congruent Triangles

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As Piaget highlighted, our brains make connections between new information and previous information (prior knowledge). I introduce the concept of congruent triangles by connecting it to prior knowledge of identical twins (photo above).

This connection is carried throughout the chapter. For example, to show triangles are congruent we look at parts of the triangle, just as we can look at shoe size, pants size and height of 2 people to determine if they are twins (see photo below).

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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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Hands on Triangles for Boring Worksheet


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A student came to me with a geometry worksheet, excerpt in photo above. Extemporaneously I created cut out sides of a triangle to help make the concept of lengths of sides of a triangle more concrete.

The concept is that the shorter 2 sides must be longer than the 3rd side or you cannot get a triangle. The worksheet is very abstract and very inaccessible. (Actually there is more to this topic but I am keeping it simple to allow lay people to focus on the instructional strategy and not the “mathy” stuff.)

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