Algebra for Secondary Mathematics Teaching at Western Governors University (WGU) treats algebra as the language of structure and change, not a set of procedures. This is the undergraduate course in the secondary maths teaching degree.
WGU's guide lists Calculus I as a prerequisite and describes a focus on rational numbers, ratios and proportions, variables and functions. Students find the course hard because they must explain why algebra works and where students stumble, not only solve equations.
Course at a Glance
| Item | Details |
|---|---|
| University | Western Governors University (WGU) |
| Course code | D898 |
| Level | Undergraduate (BS Mathematics Education, Secondary) |
| Size | 3 competency units in the 202402 program guide |
| Prerequisite | Calculus I (202402 guide; confirm on your degree plan) |
| Typical work | Explaining algebraic ideas, analyzing student thinking, designing tasks |
What D898 Covers
| Idea (WGU description, summarized) | What it means in practice |
|---|---|
| Algebra as an extension of number, operation and quantity | Seeing variables as generalized numbers and relationships |
| Equivalence in algebraic structures | When two expressions or equations mean the same thing |
| Patterns of change as covariation | How two quantities change together |
| Connections between representations | Tables, graphs, equations, geometric models and contexts |
| Functions and inverses | Exponential, logarithmic, polynomial, rational and quadratic functions |
The course also asks you to draw on algebra's history and cultural perspectives.
Key Concepts Explained
Covariation and Representations
Instead of only plugging in values, ask how outputs change as inputs change. A constant difference signals a linear relationship, a constant ratio signals an exponential one.
Example: For f(x) = 2^x the table gives 1, 2, 4, 8 for x = 0, 1, 2, 3. Each output is double the last, so the constant ratio is 2. For g(x) = 2x + 1 the outputs 1, 3, 5, 7 grow by a constant difference of 2. Showing both tables, both graphs and both equations side by side lets students see how each representation reveals the same structure.
Equivalence
Equivalent expressions give the same value for every input. For example, x^2 - 9 and (x - 3)(x + 3) are equivalent. Students often think the equals sign means "write the answer", so spend time on its meaning as a statement of balance.
Inverses
An inverse function undoes the original. Exponential and logarithmic functions are inverses, which explains why logarithms solve for an exponent. Link inverse to reflection across y = x.
Typical Assignments and How to Approach Them
| Task type | What it tests | How to approach it |
|---|---|---|
| Content explanation | Depth of algebraic understanding | Explain the idea, give a worked example and link two representations |
| Student thinking analysis | Misconceptions and ways of thinking | Describe a student's likely response, why it is reasonable and a next question |
| Technology integration | Using tools to support learning | Specify what students manipulate and what they should notice |
| Historical or cultural connection | Broader perspective | Choose one idea and relate it to a classroom task |
A Representation Grid
A grid forces you to connect representations, which the course emphasizes. Complete one for each function family.
| Function family | Key feature in a table | Key feature in a graph | Context example |
|---|---|---|---|
| Linear | Constant difference | Straight line | Fixed fee plus hourly rate |
| Quadratic | Constant second difference | Parabola | Height of a thrown object |
| Exponential | Constant ratio | Rapid growth or decay | Compound growth |
| Rational | Undefined values | Asymptotes | Average cost per item |
Common Algebra Misconceptions and Responses
Because tasks ask about student thinking, prepare a short bank of well-known ideas and what they reveal.
| Student idea | What it shows | Useful response |
|---|---|---|
| (x + 3)^2 equals x^2 + 9 | Treating squaring as distributing over addition | Test with x = 1, then expand with an area model |
| The equals sign means "the answer is next" | An operational view of equality | Use a balance and true or false number sentences |
| A variable is a fixed unknown | Limited meaning of variable | Use situations where the variable changes |
Using History and Culture Well
The course asks you to bring in algebra's historical development and perspectives from diverse cultures. The aim is to deepen understanding, not to add decoration.
For example, early methods of solving quadratics by geometric completion of a square show why the algebraic procedure works. In a task, name the idea, say what students learn from seeing the older method and describe the classroom activity, such as cutting paper squares to complete a square for x^2 + 6x.
Where Students Get Stuck
- Procedure without meaning. Explain why a step is valid, not only what it is.
- One representation only. Tasks reward connections across tables, graphs and equations.
- Vague misconceptions. Quote a plausible student answer and diagnose it.
- Ignoring prerequisites. Weak Calculus I skills make function analysis slower.
Study Tips for D898
- Rebuild each function family from a context, then move to the equation.
- Write down three common student errors and what each reveals.
- Always state the domain and what the variables mean.
- Confirm the prerequisite on your degree plan.
How We Help with D898
Send the prompt, rubric and grade band. A mathematics writer prepares a model explanation, reviews your draft or tutors you through the content and the teaching analysis.
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Frequently Asked Questions
WGU's 202402 BS guide lists Calculus I. Confirm on your degree plan.
D898 is the undergraduate course. D904 is the graduate version and stresses task-based instruction and vertical alignment.
Exponential, logarithmic, polynomial, rational and quadratic functions and their inverses.
No. It focuses on conceptual understanding, student thinking and teaching.
How two quantities change together, used to understand function behavior.
Yes. Send the task and rubric and we prepare a model or review your draft.