Philosophies & Values

Why does this math class look different?

Many people have compared the work of math and music. You probably can’t imagine time in music class only being used to write notes on a page and make sure they looked correct. You would be missing out on the whole point of writing those notes down, the music that happens when you look at the whole picture. The same is true for mathematics, even though many of us have never experienced the “music” of math. Traditional math classrooms across the US have focused too much time on specific rules and methods, and we have lost the bigger picture of math. When we view mathematics by concepts, like English and Science classes do, we are able to use a mathematical lens which deepens our understanding of the world around us.

Below, I have compared the benefits of conceptual teaching to traditional teaching.

Conceptual

  • Can be compressed and stored in the brain
  • Lends itself to communication, creativity, critical thinking, and collaboration
  • More closely resembles the work of mathematicians
  • Shows that there really is room for growth and learning in math
  • Supports connectedness of ideas

Traditional (Procedures / Rules)

  • Most are dumped out of the brain after completed high school
  • Lends itself to drill and practice, techniques which have been proven ineffective in mathematics learning
  • Is only one part of a mathematician’s work and is often replaced by computers
  • Shows math as a right/wrong subject
  • Disconnects ideas that are actually interconnected

To read more about the benefits of teaching conceptually, check out this short paper.

What happens in math class?

A typical day in my classroom will prove to be energetic, engaging, collaborative, and reflective. This will be achieved through a series of activities that supports Growth Mindset, the Four C’s (Communication, Collaboration, Critical Thinking, and Creativity), and the Common Core Standards for Mathematical Practice. The typical day’s main lesson will include a Warm Up, group work with the Mathematical Method (Wolfram, 2010), and a Debrief. Interspersed among the main lesson will be two separate activities targeting either Number Sense or Logic & Reasoning, both fundamental skills for mathematical thinking.

Below, I describe each daily activity in more detail.

Warm Up: To prepare the student for the targeted content for the day. This is always something the student can accomplish, a reminder of the fundamental skills which lead into the day’s content. Activities include: Journal, “Do Now” Slip, Discussion Prompt, Chalktalk, Google Form, among others.

Mathematical Method: The Mathematical Method is a name I came up for Wolfram’s (2010) four stages of mathematics. Typically, each of the four stages will be included sequentially, as this will reflect truest practice as a mathematician, but this is not fixed and the class could explore one or more specific stage deeply instead of the whole sequence. The four stages are:

  1. Initial thoughts - Explain the meaning of the problem, ask a specific question, identify important information, consider available tools, plan a solution pathway
  2. Using mathematical models - Represent the problem or pattern as a picture, graph, description, symbols, and/or table, and explain the connections between them
  3. Determining a solution - Use technology to solve, look for shortcuts or general methods, check answer with a different method
  4. Justifying a solution - Explain what the solution means, include units, explain why the solution does or does not make sense using estimation, revisit the models if necessary

Debrief: Always an assessment of the effect of the lesson and daily learning. This information is used by the teacher to adjust lessons to match the needs of students. Activities include: Journal, Thumbs Up / Middle / Down, Exit Ticket, Red / Green Cards, Chalktalk, Google Form, among others.

Number Sense Activity: You can think of number sense as a way of flexibly interacting with numbers. It enhances mathematical thinking and it is necessary for high level mathematics (Feikes & Schwingendorf, 2008). Number sense includes estimating, using patterns, understanding the meaning and validity of work.

Logic & Reasoning Activity: A small portion of each class day will include time spent practicing logic and reasoning, whether it be individual, as a group, or as a class. This includes thinking ahead, collaborating with different approaches, and checking in with the plan.



** A few notes about Number Sense and Logic & Reasoning...

These two skills reach to a deeper, richer level of understanding, necessary for learning in a conceptual manner. Two daily activities will be targeted specifically at the fundamental skills of algebra and mathematical thinking, number sense and logic & reasoning. These can be related to the content material, although this is not the intention of the practice, as the content will practice these skills in their own right. My intention is to have these activities help develop the fundamental skills explicitly and in a more generalized manner, rounding out mathematical thinking over the course of the year.