For a deeper understanding, read this blog alongside Step 0 is a cognitive placeholder for thinking.
In circle trig problems, students often leap into formulas without pausing. But real thinking begins not with equations—it starts with a felt direction: a misty sense of the goal, or a silent endpoint you haven’t yet defined. That’s the visible–invisible end in mind—you know you want to find the chord length or angle, even if the steps aren’t clear yet. That gentle pull is the true ignition of Step 0.
What is Step 0, Really?
According to the LearningDesigns blog, Step 0 is “the pause to visualise the problem, recall key theorems or trig laws, and choose the best approach before writing a single equation.” learningdesigns.co.za
What this doesn’t fully capture is the spark: that felt, half-formed endpoint—the sense that “I will find length AB” or “I want to connect center, chord, and angle before calculating.” That subtle intention is what activates Step 0.
How the Invisible Endpoint Activates Thinking
| Phase | Description |
|---|---|
| Trigger | A felt sense: “I want to know the chord length (AB).” |
| Exploration | Visual: sketch circle, draw radii, half-angle triangle; note possible theorems (sine, cosine, isosceles). |
| Emergence | Strategy forms: decide to use chord-length formula or half-angle method. |
For deeper insight into the role of Thinking Tools in Maths, click HERE
https://learningdesigns.co.za/pre-planning-or-step-0-is-a-cognitive-placeholder-for-thinking/Here is more information on Step 0
In circle trigonometry, students often leap straight to plugging numbers into formulas — and that’s when mistakes creep in.
Step 0 is the pause to visualise the problem, recall key theorems or trig laws, and choose the best approach before writing a single equation.
Click here for the PDF on Step 0 in Circle Trigonometry: Thinking Before Calculating
The above describes WHAT must be done during Step 0. For training how to engage learners in Step 0, click HERE to enrol for a live Zoom Thinking Tools course.
To enrol for an online Thinking Tools course in English, click HERE
To enrol for an online Thinking Tools course in Afrikaans, click HERE
