MATH EXAMPLE
Step 1- Start With a Guiding Question
Tutor: “What do you notice about this triangle based on what the problem gives us?”
Student: “It’s a right triangle, and we know two sides.”
Step 2- Let the Student Explore
Tutor: “Good. When we know two legs of a right triangle, is there a way to find the third side?”
Student: “Yeah, with that formula... the one with squares.”
Step 3- Ask for Clarification
Tutor: “Can you tell me what the formula is and what it means?”
Student: “It’s a² + b² = c²... it shows how the sides are related.”
Step 4- Apply the Concept Through Questions
Tutor: “Exactly. So if one leg is 6 and the other is 8, how would you set that up?”
Student: “6² + 8² = c²... so 36 + 64 = c².”
Tutor: “And what does that give you?”
Student: “100 = c². So the hypotenuse is 10.”
Step 5- Push for Deeper Understanding
Tutor: “Why do you think this formula works for right triangles but not others?”
Student: “I’m not sure... is it because the right angle creates a specific relationship?”
Tutor: “Yes — the squares of the legs add up only when the triangle has a 90° angle. That’s why the theorem only applies to right triangles.”
Step 6- Reflect and Extend
Tutor: “Could we work backwards? If I told you a triangle had sides of 10, 6, and 8, how could you check if it's a right triangle?”
Student: “I could plug them into the formula and see if it works.”
What the Student Gained:
Mastery of the Pythagorean Theorem
A deeper understanding of why it works
A method for checking triangle types
Stronger reasoning and problem-solving skills
ENGLISH EXAMPLE
Step 1 – Start With a Guiding Question
Tutor: “What do you notice about what the main character experiences by the end of the story?”
Student: “He realizes that his family is more important than money.”
Step 2 – Let the Student Explore
Tutor: “Interesting. What moments in the story helped him realize that?”
Student: “When he missed his daughter’s play and she was really disappointed… and then later when he saw her drawing of the family.”
Step 3 – Ask for Clarification
Tutor: “So what’s the deeper message the author might be trying to communicate through that moment?”
Student: “Maybe… that money doesn’t matter as much as the people around you?”
Step 4 – Apply the Concept Through Questions
Tutor: “That sounds like a theme. How could you express that idea in one clear sentence?”
Student: “Family is more important than material things.”
Tutor: “Great. Can you find one or two other parts of the story that support that theme?”
Student: “Yeah — at the beginning, he’s really focused on work, but he keeps missing things. And then when he finally spends time with them, he’s happier.”
Step 5 – Push for Deeper Understanding
Tutor: “Why do you think the author chose to show this transformation in the character?”
Student: “To show how people can change their values… and maybe to make the reader think about their own priorities.”
Step 6 – Reflect and Extend
Tutor: “If you were to write an essay about this theme, how would you introduce it?”
Student: “I’d say something like: ‘In the story, the author shows that spending time with family is more valuable than material success.’ And then I’d use the parts we just talked about as examples.”
What the Student Gained:
Identified a theme through guided analysis
Supported the theme with textual evidence
Reflected on the author’s purpose
Practiced structuring a literary response
CHEMISTRY EXAMPLE
Step 1 – Start With a Guiding Question
Tutor: “What do you notice when you compare the total mass of the reactants and the total mass of the products in this chemical equation?”
Student: “They’re the same — both sides add up to 44 grams.”
Step 2 – Let the Student Explore
Tutor: “Interesting. Why do you think that is?”
Student: “I think it’s because atoms aren’t lost or created… they just rearrange.”
Step 3 – Ask for Clarification
Tutor: “Can you explain that a bit more? What do you mean by rearranged?”
Student: “Like… the atoms from the reactants just form new compounds, but they’re still there — just in different combinations.”
Step 4 – Apply the Concept Through Questions
Tutor: “Exactly. So let’s look at this equation: CH₄ + 2O₂ → CO₂ + 2H₂O. How many atoms of each element are on both sides?”
Student: “There’s 1 carbon, 4 hydrogens, and 4 oxygens on the left. And on the right — 1 carbon, 4 hydrogens, and 4 oxygens again.”
Tutor: “Perfect. So what does that tell us about the reaction?”
Student: “That no atoms were gained or lost. The mass should stay the same.”
Step 5 – Push for Deeper Understanding
Tutor: “So why, then, do we sometimes see changes in mass in real lab experiments — like when gas is released and the final mass is lower?”
Student: “Maybe because the gas escapes, so it’s not being measured anymore — but it’s still there?”
Tutor: “Exactly. So does that mean mass was truly lost?”
Student: “No — it just wasn’t contained.”
Step 6 – Reflect and Extend
Tutor: “If you were designing your own experiment to prove the law of conservation of mass, how would you make sure your data is accurate?”
Student: “I’d use a sealed container, so none of the gas could escape. That way the total mass would stay the same.”
What the Student Gained:
Understood the principle of conservation of mass
Applied it to a real chemical reaction
Explained discrepancies in lab observations
Designed a valid experiment using the concept
