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  • Developing Perseverance

    Developing Perseverance

    Perseverance is defined as continued effort despite encountering difficulties. It is identified as the first mathematical practice in the Common Core of State Standards. We encourage and celebrate perseverance. What is missing is developing perseverance, and even defining it. Often, we conflate completion of work with perseverance. Sometimes students complete work but did not have…

  • Critical Thinking

    Often we adults engage students with closed-ended questions and then consider this as having a conversation with the student. I witnessed this first hand in a high school consumer math course I co-taught. The adults sat with the students the first day after December break for a conversation about their break. The questions were consisted…

  • Critical Thinking through Questioning

    Critical Thinking through Questioning

    Often we adults engage students with closed-ended questions and then consider this as having a conversation with the student. I witnessed this first hand in a high school consumer math course I co-taught. The adults sat with the students the first day after December break for a conversation about their break. The questions were consisted…

  • The Process of Learning

    The Process of Learning

    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…

  • Graphs Representing Variable Relationships

    Students often struggle with the jump from 1 variable situations to 2 variable situations, i.e. functions. Visuals are an effective way to present concepts which may be abstract, e.g. functions. Graphs and visuals in general are designed to allow a big picture view of a concept. The photo above shows mileage and price for Honda Odyssess…

  • Matching Cards for Discount and Tax

      This is a photo of matching cards for the topic of percent discount and percent tax. Students are given a card with an item to buy, a percent discount and our state tax rate of 6% (not listed). We’ve identified 4 steps for to find the total amount to pay the cashier: compute discount,…

  • Questioning and Critical Thinking

      This is a page from an Elmo book in which a cutout figure of Elmo can be inserted into various settings such as a bakery. In lieu of reading the book I asked my 4 1/2 year old son questions about each setting, e.g. “what is Elmo now?” The questioning approach I used was…

  • Conceptual Understanding

    I gave a student a pop quiz on percent change – find discount and tax – after she completed  independent practice on this objective. The student followed the steps very well, as you can see in the photo (I added the ink later) up to the very end. At that point she added the tax…

  • Art = Critical Thinking

    In my MATH class I use Picasso’s Guernica to get students to think – shaping critical thinking. This is a tribute to my art and architecture class which was the coolest class I had as an undergrad – the act of art speaking to life blew me away. I show them a photo with the following…

  • Shaping Behavior

    Shaping is a term in special ed which basically means to train a student to incrementally follow through on a sequence of substeps to accomplish a task. B.F. Skinner coined a different name for this which he called operant conditioning. The top photo below shows “Skinner’s box.” The pigeon was placed in the box and…