Like every good though experiment or conversation, this article was sparked by a colleague who recently shared about a technique, a framework I had long forgotten about. This all happened as we looked over some directional decisions to be made about next Academic year, because as any educator will tell you, even when the school closes for the summer, we cary on cooking! And that’s what we’ll do. Have a Great Framework Bake Off!
We all know the simple, heartwarming joy of a freshly baked sponge cake. It’s reliable, it’s comforting, it’s a success. In the grand bake off of learning, getting that sponge cake out of the tin is the first, crucial victory. It’s the right answer, the correct sum, the solution to the problem.
We can look at it and say, “Yes, that’s it. Well done.” For years, in many of our classrooms, we’ve been celebrating the production of plain sponge cakes. But what happens next in the kitchen? Does a master baker stop at the sponge?
Imagine a different kind of bake off. In this competition, the sponge is just the ticket to the main event. One baker presents their plain sponge and is told, “Correct.”
Another baker takes the same sponge, carefully slices it, and adds a rich layer of jam and cream, presenting a Victoria sandwich. A third baker goes further still, icing the entire creation, piping intricate designs, and topping it with fresh fruit. This baker doesn’t just present a cake; they present a story, a creation that explains its own deliciousness.
Now, let’s look at this through our classroom lens. The first baker gave the Answer. The second Proved its structure and substance. The third Explained its artistry and logic, creating a true showstopper.
If our goal is to nurture deep mathematical and computational thinkers, why are we so often content with just the plain sponge? Why are we settling for the answer when the real learning, the real mastery, lies in the proving and the explaining?
Deconstructing the Recipe: What is APE?
APE is a simple, powerful framework that moves learning beyond the surface-level answer, moving toward true mastery. It stands for Answer, Prove It, Explain It. It’s not a checklist, but a recipe for deeper thinking that dovetails perfectly with the principles of mastery and “Low Floor, High Ceiling” tasks. It provides the structure for every child to become a master baker of their own ideas.
- Answer (The Sponge Cake): This is the solution, the result. It’s getting to ‘7’ or making the robot arrive at its destination. It’s the essential foundation, but it tells us very little about the thinking that went into it. It’s the what, not the how or the why.
- Prove It (The Layers & Filling): This is the evidence. It’s where a child shows how they know their answer is correct. They make their thinking visible. This isn’t about a single, prescribed method; it’s about providing proof. They might draw a picture, use a number line, build it with cubes, or create a diagram. They are adding substance and structure to their initial answer.
- Explain It (The Icing & Decoration): This is the highest level of thinking: the justification. The student articulates their reasoning in their own words. They explain the choices they made, the patterns they noticed, and the logic they followed. This is where they reveal the depth of their understanding and secure the knowledge in their long-term memory.
APE in the Key Stage 1 Kitchen
Let’s be clear: this isn’t about asking a six-year-old to write a formal mathematical proof. It’s about creating a classroom culture where thinking is valued, shared, and celebrated in all its forms, and mistakes are welcomed along the way.
Mathematical Example 1: Money (Year 1)
The Core Task: “I have a 10p coin and a 5p coin. How much money do I have?”
- Answer: “15p!”
- Prove It: The student draws the two coins or grabs plastic coins to show the physical proof. Another might draw a number line and show a jump of 10 and a jump of 5.
- Explain It: “I knew I had to add because you have a 10p and a 5p, so you need to put them together.”
Mathematical Example 2: Shape & Geometry (Year 2)
The Core Task: “I’m thinking of a 2D shape with 4 equal sides and 4 right angles. What is my shape?”
- Answer: “A square!”
- Prove It: The student draws a square on a whiteboard. Another might make a square on a geoboard. A third might find a square-shaped object in the classroom and point to its properties.
- Explain It: “It can’t be a rectangle because you said the sides are equal. It has to be a square because it has four equal sides and the corners are all perfect ‘L’ shapes, which are right angles.”
Computer Science Example: Screen-Free Coding (Year 2)
The Core Task: Using a robot like a Dash Robot or a Matatalab Tale-Bot, program it to move from the house to the tree.
- Answer: The student inputs the correct sequence and the robot successfully moves.
- Prove It: The student lays out physical arrow cards (➡️, ➡️, ⬆️) on a floor mat, tracing the algorithm they created.
- Explain It: “I used two ‘move right’ commands first because the tree was two squares away. Then it only had to go up one square to get there.”
Scaling Up the Recipe: APE in Action with Python (Year 7)
The beauty of the APE framework is that it scales perfectly as students tackle more complex, abstract challenges. The “baking” just gets more advanced. Consider a Year 7 Python lesson.
The Core Task: “Write a Python program that calculates the sum of all whole numbers from 1 to 10.”
Answer (The Sponge Cake): A student might simply write print(55). This is correct, but it’s a very plain sponge. A more sophisticated student will produce the working code. This code is their “answer.”
total = 0
for number in range(1, 11):
total = total + number
print(total)
Prove It (The Layers & Filling): This is where debugging and code tracing become the tools for proof. The teacher asks, “How can you prove that your code is adding up the numbers correctly?”
Proof 1: The print() statement. The student modifies their code to print the value of total during each step of the loop, making the process visible.
total = 0
for number in range(1, 11):
total = total + number
print(f"Added {number}, the new total is {total}") # This line proves the logic
print(f"The final total is {total}")Proof 2: The Trace Table. The student draws a table on paper with columns for number and total and manually steps through the loop, writing down the changing values. This is a powerful, unplugged proof of their algorithm’s logic.
Explain It (The Icing & Decoration): The teacher probes for the deep understanding. “Walk me through your code. Why did you start total at 0? And why range(1, 11)?”
The student explains:
“I had to create a variable called total and set it to 0 to act as my starting point. The for loop repeats the adding action for each number. I had to use range(1, 11) because the range function in Python stops one number short, so to include 10, the range has to go to 11. The line total = total + number is the key part that updates the running total with the new number in each loop.”
A Powerful Pairing: Connecting APE with PRIMM
For those of us teaching programming, the PRIMM (Predict, Run, Investigate, Modify, Make) framework is a fantastic pedagogical tool. APE doesn’t replace PRIMM; it supercharges it by embedding a culture of proof and explanation at every stage.
- Predict: A student looks at code and predicts the outcome. This is their initial Answer. The teacher immediately asks them to Explain why they think that.
- Run: They run the code, confirming or challenging their prediction.
- Investigate: This is the perfect stage for Prove It. The student examines the code line by line to prove how it led to that outcome.
- Modify: As students tweak the code, they are in a rapid APE cycle. They get a new Answer (the outcome), Prove it by pointing to the change, and Explain why it worked.
- Make: When a student creates their own program, the code is their Answer, their plan or trace table is the Proof, and their description of how it works is the final Explanation.
Why APE is the Ultimate Low Floor, High Ceiling Tool
If you read my previous article on “Rethinking The Three Little Pigs,” you’ll know the danger of pre-judging potential with tiered challenges. APE is the ultimate “everyone gets bricks” strategy. The Answer is the low floor. The Prove It and Explain It phases provide the high ceiling. The key is that every single child is expected to engage in the entire process. We are communicating the same high expectation to all: “I don’t just want your answer; I want to see your brilliant thinking.”
The Way Forward: Cultivating a Culture of Explanation
- Model It Relentlessly: When you solve a problem, talk through your proof and explain your reasoning out loud. If this is something you like, you’ll LOVE Rubber Duck Debugging!
- Make Thinking Visible: Turn your classroom into a gallery of proofs and explanations. Use whiteboards, post-it notes, and posters.
- Use Powerful Prompting: Your questions are the tools. Move from “What did you get?” to “How do you know?” and “Can you show me in a different way?” Open-ended is your friend here!
- Value Process Over Speed: Celebrate the thoughtful proof just as much as the quick answer.
The APE framework reminds us that a right answer is not the end of a learning journey; it is the starting point. Our role as educators is to be the master bakers who don’t just praise the sponge cake but hand over the icing bags. Our job is to teach every child how to add the layers of proof and the beautiful decorations of explanation.
Let’s stop serving plain sponges and start equipping every young mathematician and programmer to create their own showstopping, multi-layered, beautifully explained masterpieces.