We introduce variations on the Fibonacci sequence such as the sequences where each term is the sum of the previous three terms, the difference of the previous two, or the product of the previous two. We consider the issue of the ratio of the successive terms in ways that reinforce key behavioral concepts of polynomials.

# Browse

##
Variations on a Theme of Fibonacci^{
1
}

### Sheldon P. Gordon and Michael B. Burns

## Making Connections Between Representations

### F. Paul Wonsavage

Three approaches to the Doughnut task highlight how representing functions in multiple ways can support student understanding in interpreting key features of functions within a context.

## Music Makes Mathematics Memorable

### Caleb Goff

This article describes how using music and the TikTok platform can help students recall mathematical definitions in a whimsical and relatable way.

##
Routines for Learning Modeling Practices *and* Content

### Rebekah Elliott, Elyssa Stoddard, Megan Brunner, and Jenny White

The authors share a teacher-designed mathematical modeling routine geared to support teachers and to leverage opportunities for their students in learning important modeling practices and mathematical content.

## From Notes to Strings

### Rob Wieman, Lindsay Freedman, Paul Albright, Deb Nolen, and Jessica Onda

Four teachers and a teacher educator move from guided notes to strings in a series of problems that support students in increased engagement, reasoning, sense making, and problem solving.

## “Filling Bottles with Water"

### Emiliano Gómez, Risa A. Wolfson, and Introduction by: Trena L. Wilkerson

## Positioning Students to Explore Math with Technology

### Allison W. McCulloch, Jennifer N. Lovett, Lara K. Dick, and Charity Cayton

The authors discuss digital equity from the perspective of using math action technologies to position all students as mathematics explorers.

##
Making Word Problems *Meaningful*

### Melissa A. Gallagher, Laura Ellis, and Travis Weiland

Teachers can employ four strategies that students in K–12 already know and use in literacy to better comprehend mathematical word problems.

## Parameters, Sliders, Marble Slides, Oh My!

### Nina G. Bailey, Demet Yalman Ozen, Jennifer N. Lovett, Allison W. McCulloch, and Charity Cayton

Three different technological activities to explore parameters of quadratic functions each has its own pros and cons.

## Guiding Questions for Selecting Mathematical Examples

### Rachel B. Snider

Examples are an essential part of mathematics teaching and learning, used on a daily basis to teach and practice content. Yet, selecting good examples for teaching is complex and challenging. This article presents ideas to consider when selecting examples, drawn from a research study with algebra 2 teachers.