Question 1

For this question, you will design and create a Mathematical Learning Experience incorporating the elements listed below. You will not be implementing the plan at this time. Your plan should demonstrate your understanding of the focus of the experience that you are providing to children, reflecting the constructivist perspective on mathematical teaching and learning.

Begin your response by providing the name of the learning experience (be it an activity/a series of activities, a project, or a provocation), then write up the following segments. Use the questions to guide your write-up.

a) Describe the planned experience and its goal.

• Describe the intended context without revealing the name of the center or people.
• Briefly summarise the learning experience.
• Identify and discuss the intended main learning goal of the experience you have created, and examine the fundamental mathematical concept(s) addressed. You should use the Big Ideas and mathematical concepts discussed in your textbook as far as possible.

b) Implementation plan: Tell us how you would implement your plans based on your analysis of the children and the environment/setting of your class.

• How will you introduce the learning experience to children or prepare the
  environment or provocation?
• How do you intend for the experience to unfold for the children? Include specific questions you might ask and strategies you might use to encourage inquiry, thinking, and problem-solving.c) Discuss how this experience will support and develop children’s mathematical thinking.
• Predict what the children will do during the experience given your knowledge of child development and the characteristics of the children in the setting.
• What questions do you think the children will have as they engage in the experience?
• How will the activity address the main learning goal?
• How will you assess or determine whether and how the learning goal is achieved?

d) How constructivist is your plan?

Describe one or two features of this activity that reflect a constructivist approach to mathematics in contrast to a traditional approach.

Question 2 
Analyze a center’s use of each of the following in relation to supporting children’s mathematical thinking. You may focus on the center where you work or have been placed.

Begin with a brief description of the center to provide a context for your analysis. You do not need to use the center’s real name, so as to keep it anonymous.

For each of the following, describe and critique the center’s practice based on what you have observed. You should identify areas of strength that you have observed in the center as well as areas for improvement. Base your discussion only on what you have observed and described, not what the center should or can do.

a) Time Use: In general, how much time is dedicated to mathematics learning, including everyday routines and transitions as well as intentional teaching. Be specific in terms of how the time is used for mathematics learning, with examples. Include your observations about the time allocated for child-initiated spontaneous mathematics thinking. Analyze the center’s use of time to support children’s mathematical learning.

b) Space and materials: Describe and analyze how the physical environment supports children’s mathematical thinking, including the use of space and materials resources such as manipulatives, toys, games, books and other materials to be accessed for mathematical learning.

c) Teaching strategies: Illustrate some of the strategies you observed and discuss what you think of the kinds of intentional and spontaneous support provided for children’s learning.