Computer Science · Grade 11

Active learning ideas

Tree Traversal Algorithms

Tree traversal algorithms are abstract until students see them in action. Active learning works here because students must physically trace paths, predict outcomes, and correct errors in real time. Coding the algorithms themselves turns invisible steps into visible patterns, building deep understanding through doing rather than observing.

• Ontario Curriculum Expectations
• CS.HS.A.3
• CS.HS.A.4

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Collaborative Problem-Solving
• 35 min · Pairs

Pair Programming: Traversal Coders

Pairs sketch a binary tree, then implement recursive in-order, pre-order, and post-order functions in Python. They input the tree and print outputs side-by-side for comparison. Pairs swap code with another duo to test and discuss differences.

Differentiate the output of in-order, pre-order, and post-order traversals on the same binary tree.

Facilitation Tip

During Pair Programming: Traversal Coders, run through one traversal together as a class first to model collaboration and debugging strategies before pairing begins.

What to look for

Present students with a small, pre-drawn binary tree. Ask them to write down the sequence of nodes visited for each traversal type: in-order, pre-order, and post-order. This checks their ability to apply the traversal rules.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 02

• Collaborative Problem-Solving
• 30 min · Small Groups

Small Groups: Prediction Relay

Provide tree diagrams to small groups. Each member predicts output for one traversal type, passes to next for verification via quick code run. Groups present matches or mismatches to class.

Analyze the applications of each traversal method in different computing contexts.

Facilitation Tip

During Small Groups: Prediction Relay, give each group a different tree to start so they can compare multiple structures side by side.

What to look for

Provide students with a simple binary tree structure and a specific computing task (e.g., 'copy this tree' or 'evaluate this expression'). Ask them to identify which traversal method (in-order, pre-order, or post-order) would be most suitable and briefly explain why.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 03

• Collaborative Problem-Solving
• 25 min · Whole Class

Whole Class: Application Sort

Display traversal types and scenarios like directory printing or postfix evaluation. Class votes and sorts matches on board, then justifies with coded examples projected live.

Construct a recursive algorithm for a specific tree traversal.

Facilitation Tip

During Whole Class: Application Sort, use a large tree drawn on the board so every student can see the progression of node visits.

What to look for

Pose the question: 'If you were designing a system to automatically delete all nodes in a binary tree, which traversal order would you use and why?' Facilitate a class discussion where students justify their choice based on the order of node visitation and deletion requirements.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Activity 04

• Collaborative Problem-Solving
• 20 min · Individual

Individual: Custom Tree Builder

Students draw their binary tree, code all three traversals, and analyze unique outputs. They note one real-world use per traversal and share digitally.

Differentiate the output of in-order, pre-order, and post-order traversals on the same binary tree.

Facilitation Tip

During Individual: Custom Tree Builder, require students to include at least one node with two children to ensure balanced tree practice.

What to look for

Present students with a small, pre-drawn binary tree. Ask them to write down the sequence of nodes visited for each traversal type: in-order, pre-order, and post-order. This checks their ability to apply the traversal rules.

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

A few notes on teaching this unit

Start with concrete visuals: draw trees on the board and have students physically point to nodes as you name each traversal order. Avoid diving straight into code. Use recursion analogies students already know, like nested folders or family trees, to make the concept familiar. Research shows students grasp recursion better when they see the call stack visually, so trace the steps on the board with arrows or sticky notes. Warn against teaching the orders as isolated facts; always connect them to real problems like sorting, copying, or deleting nodes to give purpose to the patterns.

Successful learning looks like students confidently predicting traversal sequences from static trees, explaining why each order matters for specific tasks, and choosing the right traversal for a given problem. By the end, they should articulate how recursion drives the process and recognize which traversal fits which scenario without hesitation.

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Watch Out for These Misconceptions

• During Pair Programming: Traversal Coders, watch for students assuming all traversals produce the same node sequence regardless of order.

  During Pair Programming: Traversal Coders, have pairs run their code on the same tree and compare outputs side by side. Ask them to annotate the code with which node is visited at each step, forcing them to see the distinct paths.

• During Pair Programming: Traversal Coders, watch for students arguing that recursion is unnecessary and loops always work better.

  During Pair Programming: Traversal Coders, require pairs to code both recursive and iterative versions. Have them trace the call stack with arrows on their code printouts to compare depth and clarity, then discuss which version feels more natural for tree structures.

• During Small Groups: Prediction Relay, watch for students starting in-order traversal at the root instead of the leftmost leaf.

  During Small Groups: Prediction Relay, provide each group with colored pencils to draw the traversal path on their tree. Require them to mark the starting point with a star and arrow to the next node, making the left-to-root flow visible before coding.

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Methods used in this brief

• Collaborative Problem-Solving