How to recognize vertical and horizontal dilations in both graphs and equations.
Recent Posts
Function Translations: How to recognize and analyze them
How to determine both vertical and horizontal translation factors (relative to a “parent function”) when looking the definition of a function.
Inverse Musings: * and /
Inverse operations and functions are wonderful things. Without them, solving equations would be much more challenging. Yet inverse operations can also be odd beasts. My previous “inverses” post pondered addition and subtraction, which led us (as young students) to expand our initial universe of counting numbers into the integers. Addition and subtraction are operations that…… Continue reading Inverse Musings: * and /
Interactive Graphs for Exponential and Logarithmic Functions
A few more interactive GeoGebra applets have been added to my collection. Each of these graphs the function indicated in the name, with parameters that you can adjust using sliders. As you move a slider, you can watch how that parameter affects the graph of the function, and see what the resulting function definition looks…… Continue reading Interactive Graphs for Exponential and Logarithmic Functions
GeoGebra Applets That Help Understand Equation Behavior
A list of GeoGebra applets that help students better understand the relationship between the coefficients in an equation and the corresponding graph.
Multiplication
What does multiplication really represent? An exploration of alternative conceptual models for multiplication, along with a dimensional interpretation of multiplication.
ConcepTests and Peer Instruction
I just came across this 1 hour and 20 minute video of Eric Mazur talking about using the Force Concept Inventory to teach physics, advocating “peer instruction”, and presenting data from his courses before and after he changed his instructional techniques. This is great stuff. My teaching and learning experiences have convinced me wholeheartedly that these…… Continue reading ConcepTests and Peer Instruction
Sigma and Pi Notation (Summation and Product Notation)
Explanation of how Sigma notation describes a sum of terms, with examples. Pi notation, which describes the product of a series of factors, is also introduced. Sum symbol, sum notation, summation notation, product symbol, product notation.
Summary: Algebra
When faced with an algebraic expression or equation, there are only two types of things you can do to it without changing the quantitative relationship that it describes. Re-write one or more terms in an equivalent form This can be done to any expression (no equal sign) or equation (with an equal sign) at any…… Continue reading Summary: Algebra
Inverse Musings: + and –
Inverse operations and functions are wonderful things. Without them, solving equations would be much more challenging. Yet inverse operations can also be odd beasts. This is the first of several postings on operations/functions and their inverses. Addition The first arithmetic operation we all learned was addition. It seems to arise fairly naturally from the counting…… Continue reading Inverse Musings: + and –
Function Notation
Function notation: why it is needed, how to interpret it, and what some common operations would look like if defined using function notation.
Notation & Concept
I use a lot of notation when working a math problem. It is familiar to me, comfortable even. So it is all too easy to forget that this same notation can get in the way for others. Math teachers have many goals for their students, mostly revolving around work and thought habits that help them…… Continue reading Notation & Concept
Multiplication Notation
Exploration of multiplication notations, and ways to help students better understand some of the notation used in algebra.
What Is Algebra?
Algebra is a combination of: A notation system for representing quantitative relationships, andA set of rules for manipulating notation without changing the underlying quantitative relationship that it represents. Why is algebra needed? Because: The notation provides a concise and commonly accepted way of accurately communicating quantitative relationships, andChanging the appearance of the notation describing a relationship,…… Continue reading What Is Algebra?
Why Quadratics?
Exploration of why quadratic equations are worth learning about: how they are related to linear equations and other polynomials, some of the skills students will learn by studying quadratics, and examples of where quadratic equations are useful outside of math class.
MathMaine 