Often education and special education focuses solely on content. In turn, the content may focus only on steps and facts to memorize as opposed to ideas and concepts.
A challenge for many students during k-12 education then in post-secondary life is being an independent, self-sufficient learner. The adults supporting them often focus on short term success at the expense of long term success in terms of independence.
I propose shaping the independent learning process early and often. An activity I use is completing jigsaw puzzles.
With guidance, completing a puzzle can activate 3 processes of learning: critical thinking, mindfulness, and perseverance. By having a strategy of identifying the side pieces of the puzzle, the student is analyzing pieces which is critical thinking. Paying attention to the shapes of pieces in mindfulness. Continuing to try different pieces when pieces don’t fit is an act of perseverance. Start with fewer pieces and focus on the process, then use increasingly more pieces of the same puzzle before moving on to another puzzle.
Here is a link to a video of me explaining this.
The Gutenberg printing press was revolutionary because it provided a faster way to share words. In turn, these words and how they were structured were representations of ideas used to make sense of the world around us.
Math is a language with words and other symbols that also makes sense of the world around us. We consume and know more math than we realize or allow ourselves credit for.
When buying the latest iteration of an iPhone, we may call forth algebra. How much will you pay if you buy an iPhone for $1000 and pay $80 a month for service? Well, that depends on how many months you will use this iteration before moving on to the next iPhone. The number of months is unknown so algebra gives us a symbol to represent this unknown number of months, x (or n or whichever letter you want).
Just as there is formal and informal English (or other language), we can engage algebra formally or informally. You don’t need to write an equation such as y = 1000 + 80x to figure out how much you will pay. You can do this informally, compute 80 times 10 months + 1000 on the calculator. Then try 80 times 12 months etc.
Math provides us a means of organizing and communicating ideas that involve quantities like the total cost for buying an iPhone.
The difficulty in learning math is that it is often taught out of context, like a secret code. In contrast, a major emphasis in reading is comprehension through meaning, such as activating prior knowledge (see below).
In fact, math absolutely can and, in my view, should be taught by activating prior knowledge. My approach is to work from where the student is and move towards the “mathy” way of doing a problem.
Without meaning, students are mindlessly following steps, not closer to making sense of the aspects of the world that involve numbers.
Counting out the total value for a set of coins can be very challenging for students who struggle with money.
Here is a video showing how to use a WORD document table a former colleague and I created to support students in a life skills class. The video shows how this handout is used but does so with a virtual version the can be completed on the computer (see image below). Here is a link to the virtual document.
To help students learn how to measure with a ruler, I focus on minimizing the number of tic marks on the ruler at first. The image below shows an excerpt from a WORD document with a halves ruler that I use and an instructional strategy. It also contains a quarters and an eighths ruler that students can slide around the WORD document as shown above and in a video explaining this artifact and how I created it.
This is useful for distance learning as well as in class. Here is a link to the WORD document with the rulers shown in the video.
I will be fielding questions about math and online learning in real time. As a follow up, I will respond to questions through this blog post. If you did not catch the Instagram session and have questions, you can post them here through a comment. I will post replies on this post.
Below is a list of links to resources, e.g. online handouts, activities, which align with the discussion.
A common scenario involves a school official reporting out the grade level in math for a student. For example, a 7th grade student I was helping had tested at a 4th grade level. As a result, the student spent much of her 7th grade year working on 4th grade math.
There are a couple problems in establishing a grade level in math. First, unlike reading, math is not nearly as linear. The image below shows a breakdown of the Common Core of State Standards math categories, called domains. In a video, I use this graphic to unpack why it is more challenging to determine a single level of ability for math. In short, the reason is the student could be doing well in some categories and doing poorly in others. Second, the testing used to establish ability level can be problematic for the student. For example, the student may not have the stamina or attention span to endure a longer assessment.
If you are presented with a single grade level as an indicator of math ability, I recommend that you ask for a breakdown by category and how your student will be provided differentiation to address gaps. This is more appropriate than plowing through all of the math at a lower grade level.
Below is a photo of a hyper-doc that I use to map out a long range plan for math services and academics for students receiving special education services. Here is a link to a video explaining how the document is organized and how it “works.” (Note, the image of the document on the video is not crisp, so I suggest you look at the handout while watching the video.)
The document contains several links to resources such as videos, websites and blog posts that provide additional information. Feel free to reach out to me using the Contact Form on this page if you have questions or would like input. I am happy to help.
I used this site, Explorelearning, with a 7th grader with Aspergers who tested at a 1st grade math and reading level. We used the Photo Synthesis Lab (screen shot below) to gather experimental data on the hypothesis “what helps flowers grow?” He won at the school level and went on to district competition.
(As of April 2020 you can get free 60 day unlimited access.)