Geometry for Secondary Mathematics Teaching at Western Governors University (WGU) is the undergraduate version of a course for future secondary maths teachers. It asks for deep geometry knowledge and for the ability to teach it.
WGU's program guide for the Bachelor of Science in Mathematics Education (Secondary) lists Calculus I and College Geometry as prerequisites, so the course assumes solid proof-based geometry already. The challenge is moving from solving problems yourself to explaining why a geometric idea works and how students typically misunderstand it.
Course at a Glance
| Item | Details |
|---|---|
| University | Western Governors University (WGU) |
| Course code | D895 |
| Level | Undergraduate (BS Mathematics Education, Secondary) |
| Size | 3 competency units in the 202402 program guide |
| Prerequisites | Calculus I and College Geometry (202402 guide; check your current degree plan) |
| Typical work | Geometry explanations, interactive lessons, responses to student misconceptions |
What D895 Covers
WGU's program guide describes constructions and transformations, congruence and similarity, analytic geometry, solid geometry, conics, trigonometry and the historical development of the content. The newer course description adds geometric reasoning and the use of GeoGebra and Desmos to build interactive lessons.
| Competency theme (WGU guide, summarized) | What it means in practice |
|---|---|
| Historical development and diverse cultural perspectives | How geometric ideas arose and how to use that story in teaching |
| Instructional practices to support and assess geometry learning | Tasks, questioning and assessment that reveal student thinking |
| Technology to support and assess geometry learning | Dynamic geometry tools used with a clear purpose |
| Conceptual underpinnings and misconceptions | Why students struggle and how to create opportunities to learn |
The competency wording above is from the 202402 BS guide; your current course page may word it differently.
Key Concepts Explained
Transformations as Functions
A rigid motion (translation, reflection, rotation) preserves lengths and angles. A dilation preserves shape but scales lengths. Describing a transformation as a rule on coordinates makes it concrete.
Example: Reflecting A(2, 3) across the y-axis gives (-2, 3). Reflecting across the line y = x swaps the coordinates and gives (3, 2). A dilation with scale factor 2 centered at the origin sends A to (4, 6). Lengths double and areas multiply by 4.
Congruence and Similarity
Triangles are congruent by SSS, SAS, ASA or AAS. SSA does not guarantee congruence, which is a classic misconception to address. Similar figures have equal angles and proportional sides, and the ratio of areas is the square of the scale factor.
Teaching with Dynamic Geometry
A dynamic tool lets students drag a figure and see what stays the same. The purpose is to form conjectures that students then justify, not to replace proof.
Typical Assignments and How to Approach Them
| Task type | What it tests | How to approach it |
|---|---|---|
| Content explanation | Depth of geometry knowledge | State the idea, justify it and give a diagram or coordinate example |
| Misconception analysis | Understanding student thinking | Describe the error, why it makes sense to a student and a task that helps |
| Interactive lesson using GeoGebra or Desmos | Technology with purpose | Give the learning goal, student actions, prompts and how you check understanding |
| Historical or cultural connection | Broader mathematical perspective | Pick one contribution and link it to a classroom activity |
Planning Around the Prerequisites
Because the course builds on College Geometry and Calculus I, diagnose gaps first. A short self-check saves time later.
| Area | Quick self-check | If shaky |
|---|---|---|
| Proof and congruence | Prove two triangles congruent in two ways | Revisit triangle criteria |
| Coordinate geometry | Find a midpoint, slope and distance | Practice with the distance formula |
| Trigonometry | Solve a right triangle and state the unit circle values | Review ratios and special angles |
| Solid geometry | Compute surface area and volume of common solids | Make a formula sheet with reasons |
Proof and Justification in Teaching
Teaching geometry means teaching students why, not just what. Tasks often ask how you would help students move from observation to proof.
Example: Students notice that the base angles of an isosceles triangle seem equal. Moving towards proof, you could ask them to draw the line from the apex to the midpoint of the base, name the two smaller triangles, say what is equal and why they are congruent. Each question shifts them from "it looks true" to "here is why".
Describe the sequence you would use, including what a student giving an incomplete argument might say and how you would respond.
Where Students Get Stuck
- Answering as a student, not a teacher. The tasks ask how learners think and how you respond.
- Technology for its own sake. State what the tool lets students notice that paper does not.
- Generic misconceptions. Choose a specific, well-known one such as confusing area and perimeter scaling.
- Skipping justification. A conjecture from a dragged figure still needs reasoning.
Study Tips for D895
- Practice one dynamic construction and write what you would ask students to notice.
- Keep a list of five misconceptions with a task for each.
- Explain every formula with a picture, not only an equation.
- Check your current degree plan for prerequisites before starting.
How We Help with D895
Send the prompt, rubric and any standards or grade level. A writer with a mathematics education background prepares a custom solution or lesson, reviews your draft or tutors you through the geometry.
GradeEssays is independent of WGU. Our work is a study and reference aid. Use it to learn the approach, then write and submit your own work under WGU's academic integrity policy. Orders are written from scratch, with free revisions within the scope of your original request and a full refund if late.
Make Sense of Your D895 Task
Share the prompt and rubric. A maths writer prepares a custom worked solution or lesson you can study.
Start My D895 HelpFree revisions · Full refund if late · Written from scratch for your order
Frequently Asked Questions
WGU's 202402 BS guide lists Calculus I and College Geometry. Confirm against your own degree plan.
D895 is the undergraduate course. D903 is the graduate version, with task design and technology activities at the center.
Constructions and transformations, congruence and similarity, analytic and solid geometry, conics, trigonometry and historical development, plus teaching approaches.
The course description refers to both for interactive lessons. Check which your task requires.
Believing that SSA proves triangles congruent, or that doubling lengths doubles area.
Yes. Send the task and rubric and we prepare a model or review your draft.