Problem-solving beats vocabulary

Sorry we’ve been incommunicado for a while! In the last month, we’ve had one week of outdoor education (camping), one week of spring break(yay!), one week of standardized testing(no comment) and a week of school-wide theme-based learning(fun).

The trick is not to stress about curriculum 🙂 All those other things matter! If we are measuring LEARNING as our main goal, then each of those (except the standardized testing – yuck!) involves lots of learning.

So this week, we had to start by spending a couple days reviewing the unit we started last month – Angles. Here’s what we believe:

  • Geometry should be fun. Let kids prove that vertical angles are equal by drawing a few and investigating. Let them slide patty paper between parallel lines to show their congruence, tear off vertices of a triangle to prove they add to 180, etc. Use spaghetti pieces, tangrams, pattern blocks, geometry software.
  • Vocabulary is not the goal of any geometry unit. Most people forget these terms in a few months anyway. What stays is a visual understanding of what an angle is, how angles relate to each other, and how we use that information to solve problems.

As soon as possible, give students challenging angle problems to solve. Sweeten the deal with class-reward points or similar. Here are 2 excellent sources of such puzzles, both by Michael Serra:

Here’s a puzzle example:

Serra-1.jpgThe lure of puzzles, and challenging work altogether, is that it credits students with the intelligence needed to solve these problems, and increases their self-respect as they work on them. Who doesn’t want to feel smart?

2 FAQ’s :

1. What if my students don’t have the perseverance to keep working on puzzles like this?    … Our answer:  At the beginning, we have to sweeten the deal a LOT. Offer extra recess minutes, for example, if everyone is working on the puzzle (whether they’re getting all the answers right or not is not a primary consideration at first). Let them work in twos. Let them use tracing paper or patty paper to help isolate the individual parts of the puzzle – that’s fun. If you have to at first, let them use calculators. Have students praise each other for hard work. Bring candy if you have to (Corrinne approves!)   Choose your priorities! At first, perseverance is more valuable than other goals. The perseverance “muscle” is built on success. Students have to feel success in their problem solving activities. That means we have to praise every effort at first. Once the students build their perseverance muscle, we can attack other goals.

2. What if some students are fearful of problem-solving, and just copy from others? … Our answer:  We feel you here. We’ve worked on this so much, and it still happens. Here’s a list of interventions that often work – please add to them!

  • Is the problem computational? Give the student blocks. We usually find that students who struggle with memorizing algorithms are fully competent when they can use blocks or drawings. Intersperse ‘Calculator Days’.
  • Is there a problem with taking risks? Does the student feel insecure and have a fear of mistakes? Have them develop a “toolkit” that they can use in classwork and quizzes/tests. This is a self-created set of rules, vocabulary and examples that they can refer to.
  • Is there a problem with speed? Does a child give up because others are faster? First, reward students for working hard, not finishing fast. Don’t send unfinished work home. Give fast workers a challenge problem to finish with that is really challenging, so the others see them struggling.  Let students answer a question in nontraditional ways – with a drawing, a story, a project. If one of your slower workers sees something unique and interesting in a problem, point that out to the whole class, so they feel seen for their strengths.

Happy MAY!

 

 

 

 

 

 

 

 

 

 

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