Monthly Archives: July 2016

Recap: Math as a Second Language, Day 2 (July 12, 2016)

Today we discussed the burning questions from yesterday and found that some of the material we are covering is important to help teachers of younger grades to prepare their students for material they will be learning at a later time.

We discussed solutions to the math homework problems and then moved on to discuss addition, subtraction and many different ways to interpret the action.  We also tackled signed numbers and how to deal with addition and subtraction of these with the tally method and the number line methods.  We made the connection that addition and subtraction are connected and often times the problems is better thought of as one or the other.

We discussed the issue of subtracting a negative number from a positive number with chips and how we can represent the concept of one-half on a geoboard.

The pedagogy homework led us to a discussion of how our different curricula fit with the levels of cognitive demand explained in our book “Principals to Action” and what levels are required of our students in our classroom lessons and homework.

We finished with some more problems and are looking forward to learning about multiplication tomorrow.

From your feedback we realized that some students are struggling with the handshake problem and how to create a formula that represents the situation when the number of people is very large.  This will have an impact on the homework for tonight but we will be addressing it again tomorrow.  I am going to make another post of a way to think about the sums that you can look at if you are still struggling with this idea.

Homework:  Read Beneath the Tip of the Iceberg and P to A 42-48.  In your notebook identify a procedure or a skill that you consider essential for your students at your grade level to learn.  Describe the conceptual understanding that support students’ learning of the procedure or skill.

Also – the library problem and the writing the word problem from page 3.16.

 

 

Recap: Math as a Second Language, Day 1 (July 11, 2016)

Today we…

We begin with a welcome from the chancellor of Penn State Brandywine: Kristin Woolever.  We were also greeted by Andrew Baxter, Charles Helou, Marina Skyers and Kim Schultz.

We then began the Kayaking on the Susquehanna River problem, and discussed the different approaches taken by members of our group including tables, equations, and graphical representation.  It was noted that graphing the example of a line was not quite accurate because of the way parts of hours were handled by the kayak company but because the answer to the third part of the problem was an integer the linear approach as a graph or as solving system of equations successfully produced the solution.  However a table worked just as well.  After the break, we spent the rest of the morning on the pre-assessment.

After lunch we discussed the “Smarter Than We Think” article. Then we read the beliefs chart on page 11 of Principles to Action and had small group discussions about our own beliefs about teaching and learning mathematics.  We will continue to discuss the ideas of a “growth mindset” and “fixed mindset” as the weeks go on.

We finished Unit 1, discussing what equality should mean, and how students might misunderstand it.  We also began Unit 2 by discussing the adjective-noun theme and how it applies to addition.   We then applied the adjective-noun theme to see how it makes sense of the place-value system in addition and adding fractions with a common denominator.  We also discussed the idea of even and odd numbers and divisibility.  We discovered how to handle two division problems by the same divisor and how to combine their remainders to find a shortcut to determining the division of their sum by that same divisor.  We began to discuss the geometry of square numbers but will continue that tomorrow.

 

Handouts

  • Paperwork to be completed.
  • Front matter for Math as a Second Language (e.g., title page, table of contents, expectations)
  • Unit 1: Fundamentals
  • Unit 2: Perspectives on Addition

Homework

For Tuesday:

  • Page 2.6 Guess my Noun
  • Page 2.12 #7
  • Read in Principles to Actions:
    • Sections titled “Progress and Change” and “Effective Teaching & Learning” (pages 1-12 – stop reading at the middle of page 12)
    • Section titled “Implement Tasks that Promote Reasoning and Problem Solving” (pages 17-24).
  • Respond (in your notebook) to the following prompts:
    • Reflect on a typical in-class math lesson (use your textbook to refresh your memory) that you have taught. Using the descriptions of Levels of Cognitive Demand in Figure 3 (p. 18), describe the types of mathematical thinking your students are required to engage in during a typical lesson.
    • Reflect on a typical homework assignment that your students complete (use your textbook to refresh your memory). What level of cognitive demand do most of the tasks on a typical homework require of your students?
  • Bring your math textbooks to PMI on Tuesday.