3.4: Counting Collections- Uncovering Number Sense and Mathematical Thinking Project

Purpose

This assignment helps you develop essential mathematical teaching skills by engaging in hands-on exploration of counting strategies with individuals of different ages. By documenting, analyzing, and reflecting on how different people count, you will:

• Enhance your understanding of how counting skills develop from early childhood to adulthood.
• Practice analyzing mathematical thinking in real-world scenarios.
• Learn to identify and address misconceptions related to counting and early operations (addition, subtraction, multiplication, and division).
• Develop skills in video analysis and peer feedback, critical for professional reflection and growth.

Connections Beyond This Course:

• This project simulates real-world classroom experiences, helping you prepare for student observations as a future teacher.
• Understanding how people count differently enhances your ability to differentiate instruction for diverse learners.
• Peer review skills will be valuable when collaborating with colleagues in professional learning communities.

Tasks (What You Need to Do)

Step 1: Prepare Your Counting Collection

• Gather a set of 50–100 small objects (e.g., buttons, beads, Legos, paper clips).
• Choose objects that allow for different grouping strategies (by 1s, 2s, 5s, 10s).
• Prepare a recording sheet or notebook to document observations.

Step 2: Engage Three Participants

• Select three individuals of different ages:
  • A child (ages 4–8)
  • A peer (teenager or young adult)
  • An adult (30+)
• Present the same collection to each participant separately.
• Ask them to count the objects in any way they prefer while you observe and video record the interaction. (Make sure to get their approval to be recorded)

Step 3: Record & Observe the Counting Strategies

• Video record each session (1-3 minutes per participant). The participant’s face does not need to be visible—hands and objects are sufficient.
• Take notes on:
  • How do they count? (One by one? In groups? Estimating?)
  • What tools or gestures do they use? (Fingers, trays, verbal counting)
  • How efficient is their method? (Do they backtrack? Use grouping?)
  • Do they self-correct or adjust strategies?
  • Are there any errors or misconceptions?

Step 4: Mathematical Analysis & Discussion

After the counting session, ask as least two follow-up questions appropriate for their age:

• "What happens if we add/subtract 10 objects?"
• "How could we divide these equally among 4 people?"
• "If we doubled this collection, how many would we have?"
• "Could you count in a different way to check your answer?"

A Full List of Potential Questions

Counting Strategies & Nunmber Sense

• Can you think of another way to count the collection?
• If I rearrange the objects into a different shape or pattern, does that change how you count?
• Why did you decide to count the way you did?
• Would you count differently if you had more objects? Fewer objects?

Grouping, Addition & Subtraction

• Can you group these objects in a different way? What do you notice?
• If I add 5 more objects, how many do we have now? How did you figure that out?
• If I take away 10 objects, what is left? How do you know?
• Is there a way to count this that makes adding easier?

Multiplication & Division Connections

• If we made equal groups of 5, how many groups would we have?
• If I double the collection, how many objects would there be?
• Can we split these into 4 equal groups? How many would be in each group?
• What happens if we divide the objects among 3 people? Would any be left over?

Patterns & Mathematical Properties

• Did you notice any patterns while counting?
• What would happen if we skip-counted instead of counting one by one?
• If we arrange the objects in rows and columns, how does that help us count?
• If we count backward from the total, what does that look like?

Reflection & Problem-Solving

• What was the easiest part about counting this collection? What was the hardest?
• How would you teach someone younger than you how to count this collection?
• What mistakes do you think someone might make when counting this collection?
• If you were counting a really large number of objects (like 500), how would you do it efficiently?

Step 5: Video Reflection & Analysis Submission

• Select one of your three recorded sessions for deeper analysis.
• Submit either:
  • A 5–7 minute video reflection where you analyze the counting strategies used, discuss misconceptions, and connect findings to teaching, OR
  • A 2–3 page written analysis covering the same points.

Your analysis should include:

✅ Description of the interaction (who they counted with, setting, what happened).

✅ Mathematical analysis (counting strategies, efficiency, operations explored).

✅ Key takeaways (misconceptions, learning styles, connections to teaching).

✅ Implications for teaching (How would you help a student who counted this way?

Step 6: Peer Review & Discussion Board Participation

• Upload your video reflection OR written analysis to the class discussion board.
• Review two peers' submissions, using the structured Peer Review Protocol below.

Peer Review Protocol

Each student must review two classmates’ submissions by following this structured feedback framework:

✅ Describe (What do you notice?)

• Summarize the counting strategies used in the video.
• Identify one strength in how the participant engaged the counter.

🤔 Analyze (What patterns or teaching implications emerge?)

• What insights did the student make about counting strategies?
• Did they analyze efficiency, errors, or operations deeply?
• Were there any gaps in the explanation?

📌 Suggest (What feedback would strengthen the analysis?)

• What additional questions could they explore?
• Could they connect this to broader teaching strategies?

💡 Reflect (What did you learn from this?)

• How does this change your understanding of how children count?
• How might this influence your teaching approach?