One recurring theme we hear from math teachers around the country: they already use technology—the graphing calculator. While the statement is certainly true, there are a whole host of reasons to put down those old calculators and pick up SAS Curriculum Pathways. Here are just a few:
1. We provide better support for the Common Core State Standards for Mathematical Practice.
The Common Core State Standards for Mathematical Practice identify important proficiencies for students, including the use of appropriate tools to “visualize the results of varying assumptions, explore consequences, and compare predictions with data.”
While calculators are efficient tools that allow a student to visualize and explore, they can be a bit cumbersome without pre-programmed applications and instruction. Let’s take interpreting key features of a line. Using a graphing calculator, students can input multiple linear equations and then compare the graphs. But unless the student has a pre-programmed application, the linear equations must be written in slope-intercept form. So what about standard form? Unlike slope-intercept form, all linear equations can be written in standard form.
Using QL #1311, Exploring Graphs of Linear Equations, students can explore linear equations and their graphs using both forms. The available sliders for the slope and y-intercept of the slope-intercept form and the coefficients A and B as well as the constant C for the standard form allow students to recognize relationships between the parameters of the equation and the graph. Additionally, students can select the alternate equation and compare the two forms.
2. Our Graphers enable students to visualize equations much better than a calculator can.
Many students quickly grasp the concept of how a and c affect quadratic functions written in standard form, but recognizing how b affects the graph is more challenging. Using QL #1445, Exploring Graphs of Quadratic Functions, students can actually see that b affects the location of the vertex of a parabola with respect to the y-axis. Students will also notice that as a and c remain constant, changing the value of b moves the vertex of the parabola along the path of the reflection of the quadratic function over the x-axis.
And what about transformations? Using QL #1309, Exploring Transformations, students—working individually, in pairs, or as a whole class—can seamlessly graph segments and polygons in the coordinate plane and investigate the relationship between translation units, lines of reflection, angles of rotation, or scale factors and the transformed graph. Students can also discuss similarity and congruency using the table of measures. In addition, the copy options allow teachers to create their own worksheets or assessments and students to use graphs to complement their investigative responses.
3. Curriculum Pathways Graphers allow students to assess their knowledge.
After exploring graphs, students can then assess their knowledge using graphing tools such as QL #1429, Graphing Linear Inequalities. In practice mode, students can graph a linear inequality by determining two points on the line, selecting a solid or dashed boundary line, and then indicating the solutions by selecting the appropriate shaded region. Students can check their answers, receive feedback, and then (if necessary) view the correct answer. In quiz mode, students can complete similar problems, and then save, print, or send their results to their teacher.
From a technology perspective, calculators are powerful computers, and our tools are software. We provide pedagogical guidance and feedback that you just can't get from a calculator. Years of research and work have enabled our team to craft tools that help students grasp concepts. Once these concepts are mastered, the calculator then becomes a tool for a more advanced learner rather than a crutch for a beginner.
While graphing calculators certainly have their uses, Curriculum Pathways' Graphers provide better support for Common Core proficiencies, help students visualize concepts, and allow students to self-assess their understanding.
Check out all 19 graphers we offer: