Tag Archives: perseverance

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 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.

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Perseverance in Math

perseverance checklist

A major challenge for students is not content but how to “do math” which includes perseverance. The photo above shows a table that can be used to monitor progress on perseverance. It addresses two situations involving perseverance (see below).

The focus of perseverance in math is making an informed attempt when a path or next step is unclear (and does not necessarily result in a solution). Paths can be categorized as using a strategy, e.g. drawing a picture, or following an algorithm, e.g. steps to solve an equation. (See excerpt of CCSS Standards of Mathematical Practices below).

Perseverance in math involves two situations:

  • The initial entry point (strategy or algorithm) is not apparent but one is selected and implemented
  • An ongoing strategy or algorithm is determined to be insufficient and an alternative strategy or algorithm is selected and implemented

From the CCSS Standards of Mathematical Practice (bold font is my emphasis on the perseverance component)
1. Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

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