Mathematician's Plan: Promoting Thinking In Math

From KNILT
Revision as of 07:50, 13 June 2020 by Gjj (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Follow this link back to the personal page for this mini-course: Andria Manolopoulos

Follow this link to my mini-course: Mini-course: The Mathematician's Plan: Promoting Thinking In Math

Showing ALL of her thinking while solving math problems

My Topic/Purpose

This course will focus on the implementation of the Mathematician's Plan. This plan will encourage exceptional work habits in young mathematicians in order to improve their ability to solve complex, contextual word problems. Learning math through context has given students the ability to ground their learning in the real world. Through the Mathematician's Plan students learn to be more precise, flexible, and confident mathematicians by showing their thinking clearly. Some questions that will direct the design of this course:

  • What is the Mathematician's Plan?
  • How can it be taught to students?
  • Why is it helpful for students?
  • In what ways can it be used in the classroom?

Learning Outcomes

The purpose of this course is to assist educators in improving student work habits in mathematics. Learners will be able to:

  • Describe the Mathematician's Plan and its place in the classroom
  • List the purpose and benefits of the Mathematician's Plan
  • Use the Mathematician's Plan to diagnose faults in student work
  • Choose to promote the Mathematician's Plan in the classroom

Needs Assessment

The Problem

As the standards for mathematics across the U.S. shifted to a contextual, complex approach we have seen drops in test scores. This drop can be attributed to the lack of deep understanding when it comes to math. Students have traditionally been taught an algorithm or rule without any real understanding of why the numbers work in that way. In addition, students have previously been given straight forward questions with little context. As the shift to Common Core and now Next Generation Standards occurs, teachers scramble to shift their teaching to best support their students. Teachers are looking at a "students' ability to transfer learning [as] an important indicator of the quality of their learning" (American, p.10).

Students often know how to use an algorithm but it is the disconnect from the content to the context that causes students to understand content but not have knowledge. As stated by Collins, “memorization leads to inflexible use of the memorized knowledge and reliance on drill and practice, which is unmotivating for students” (Collins, p.349). This issue is pervasive in education not just in math, but in all subjects. The inability of students to apply math in their everyday life proves the disconnect between content and context.

What is to be Learned

Educators will learn how to use the Mathematician's Plan to encourage students to think deeply about the context of the math when reading and solving word problems.

The Learners

Learners will include any pre-service or current Grade 3-12 educators, specifically those teaching math as a content area. Learners will have a concrete understanding of the math content for their teaching grade. Learners will have varying background knowledge on strategies to solve word problems. The learners are any educator working with students ranging from third to twelfth grade on math word problems.

Instructional Context

Instruction will take place fully online. In order to successfully participate learners will need access to a computer and internet connection. Learners may participate at any time.

Exploring the Problem and Solution

Participants will explore the benefits of the Mathematician's Plan by working through this course. Learners will understand the current problems with students' understanding of word problems, and learn how the Mathematician's plan can be implemented to enhance student understanding. Participants will learn through activities, readings, and assignments.

Goals

The main goal of this online mini-course is for participants to learn how to implement a new strategy in order to improve student work habits and understanding of math word problems. Another goal is for teachers to see a need for improvement in math instruction in order to better equip students with the flexibility to apply content to multiple contexts.

Performance Objectives

  • Participants will describe the Mathematician's Plan by identifying all steps.
  • Participants will be able to create an example of how the Mathematician's Plan looks on paper for one word problem.
  • Participants will use the Mathematician's Plan to diagnose faults in student work by identifying a step in the Mathematician's plan that was not used.
  • Participants will create a lesson plan in which they create an exemplar, teach one step of the Mathematician's Plan, and anticipate student misconceptions in a problem set.

Mini-Course Units

This mini-course includes the following units. Click the title of a unit to go to its page.

Unit 1: What is the Mathematician's Plan?

  • Participants will identify the steps involved in the Mathematician's Plan.
  • Participants will understand the purpose and benefits of the Mathematician's Plan by understanding the theory behind it.
  • Participants will create an exemplar using the Mathematician's Plan.

Unit 2: How Can I Use the Mathematician's Plan in My Classroom?

  • Participants will analyze the student thinking behind each step of the Mathematician's Plan.
  • Participants will analyze student work in order to identify the area of the Mathematician's Plan in which the student struggled in.

Unit 3: Creating a Lesson Plan to Teach The Mathematician's Plan

  • Participants will use the lesson plan structure provided to create a lesson plan around one step of the Mathematician's plan.
  • Participants will analyze the student work after implementing the lesson plan to determine its success in teaching the chosen step of the Mathematician's Plan.
  • Participants will use student work to make plans for the continuation of the Mathematician's Plan in the classroom.

References and Resources