Much has changed in the teaching of mathematics. In fact, some of the most successful mathematicians from years past might not recognize modern mathematics education. Today’s students learn through hands-on activities and collaboration more than ever before. Technology is also changing mathematics education. Here we will look at four of the best digital tools for teaching modern mathematics.

**1. Core Math Tools**

Core Math Tools was developed by the National Council of Teachers of Mathematics (NCTM) for grades 9-12. Since 1920, NCTM has advocated for exceptional mathematics education, developing standards for teaching mathematics based on 11 core beliefs, including the idea that students must learn to use technology to enrich their understanding of mathematical concepts. With this in mind, NCTM developed Core Math Tools.

Core Math Tools is a suite of downloadable software for teaching algebra, geometry, trigonometry, statistics, and probability. It features general-purpose tools for learning about spreadsheets, data analysis, and simulation, as well as advanced apps for graphing, voting, and diagramming. Users also have access to help documentation and downloadable lesson plans.

Highlights from the lesson plans include simulation lessons in which students imagine scenarios related to blood donation. One lesson involves determining the number of donors needed to collect a certain amount of type B blood when the percentage of donors with that blood type is known. Another lesson involves determining the probability that a particular number of donors have type B blood.

**2. Illuminations**

Illuminations is another mathematics teaching tool provided by NCTM. It contains resources for grades PreK-12 such as lesson plans, mobile games, interactives, and brain teasers. These materials are compatible with NCTM Principles and Standards and with Common Core State Standards. Users can also sign up to receive Bright Ideas, the monthly e-newsletter containing updates and news about the initiative.

A searchable interface allows users to find lesson plans and learning materials by grade level. They can also search by NCTM Principles and Standards or by Common Core State Standards.

Illuminations covers key math skills such as numbers and operations, algebra, geometry, measurement, data analysis, and probability. Counting, base ten, fragments, equations, ratio, and proportion are also addressed.

One featured interactive focuses on multiplication. The interactive game can be customized for grades PreK-2 or 3-5. Starring rabbits eating carrots, the game grows in complexity, with early stages requiring simple multiplication and later stages growing in difficulty as fog obscures the carrots. The interactive features 11 different skill levels.

**3. Illustrative Mathematics**

Illustrative Mathematics (IM), a nonprofit organization devoted to improving mathematics education, offers K-12 teaching tools. Co-founded by two mathematics professors, one from the University of Arizona and one from the University of New Mexico, IM has created materials based on the latest research in mathematics education. IM offers materials via free download through approved distributors, including Kendall Hunt, LearnZillion, and McGraw-Hill.

IM currently offers curricula for grades 6-12 (K-5 will be available in 2021). Integrating communication skills, the curriculum is problem-based and collaborative. IM also provides professional development materials for teachers that help support their shift to problem-based teaching practices. Educators can even become certified IM facilitators to assist fellow educators. Finally, IM offers free resources, including a blog written by the developers of the IM curricula.

One example lesson from the 6th-grade curriculum focuses on voting for a school mascot. Students are introduced to a table of data regarding classroom votes and must determine which mascot won and by what percentage. They must also devise a written plan about how to achieve proportional representation in voting. A later lesson involves expanding the vote to the entire town and determining how to arrange voting districts to achieve fair results.

**4. Khan Academy**

Khan Academy is a nonprofit organization aiming to make high-quality education available online for free. Khan Academy provides learning materials in a variety of subjects, including physical science, humanities, health and medicine, art, mathematics, and more. The mathematics content is designed by specialists ranging from elementary school teachers to college professors.

Math resources are listed by grade, from PreK-8. Early math skills include counting, addition, subtraction, and measurement, while later elementary skills include multiplication, division, fractions, and decimals. At the middle school level, skills include ratios, percentages, negative numbers, equations, and modeling.

Higher-level mathematical topics include geometry, algebra, trigonometry, statistics, probability, and calculus.

Khan Academy offers video-based lessons with interactive follow-up problem sets. For example, an early math lesson involves recognizing shapes and counting sides to classify shapes. Students watch videos that explain these concepts then answer questions to practice the skills. Lessons are combined into units, so after identifying basic shapes, students learn about properties of shapes, composing shapes, and fractions of shapes to complete the unit.