Over the past two decades, an educational narrative has gathered momentum that more youngsters should study science, technology, engineering, and mathematics. This rationale is based on the unchallenged belief that STEM subjects will lead to more financially rewarding and resilient careers than other academic disciplines.

Several research studies investigating integrated STEM curriculum models have examined how well the constituent disciplines are connected. These investigations typically focus on identifying the distinctive forms of epistemic knowledge characterizing each discipline.

## What is Mathematics?

Ever wonder how those colossal pyramids defied gravity, how bridges dance defiantly over roaring rivers, or how we took a giant leap onto the moon? The answer, my friend, lies not in magic or brute force but in the elegant language of mathematics. It’s the hidden architect, the silent engineer. This invisible force unlocks the secrets of the universe, and at the University of Illinois math department, unlocking these secrets is an art form. Hence, it’s unsurprising that many people pursue careers as engineers, statisticians, actuaries, math teachers, and computer programmers – jobs with a clear connection to STEM.

But there is more to studying mathematics than what can be easily defined by the concepts and skills involved. For example, some studies that ask participants to work on interdisciplinary STEM tasks highlight the need to find a rich contextual intersection between science and mathematics. This suggests that a crosscutting approach to teaching better serves the conceptual and procedural knowledge of mathematics.

## Why Study Math?

Many students study math because of the great career opportunities available for people with degrees in math. According to Bankrate, mathematics is one of the best-paying majors, with jobs including engineering, technology, business, finance, medicine, and teaching.

Recent research into integrated STEM curriculum models is investigating ways to connect the constituent disciplines while preserving their disciplinary integrity. For example, Leung (2020) developed a framework representing the dominant epistemic problem-solving processes of science, engineering, and mathematics within a scientific inquiry cycle.

Other studies have investigated how to identify meaningful interdisciplinary STEM tasks, such as engaging learners in learning about real-world phenomena. For example, a task about modeling ecosystem dynamics might be high on the S slider for science content, medium on the T slider for engineering design and technology, and moderate on the M slider for mathematics.

## What is Mathematical Thinking?

Rather than teaching students math as a set of procedures or rules, teachers must challenge and engage them in mathematical thinking. This involves building and enhancing their ability to think analytically, logically, and abstractly.

For example, instead of simply asking students to solve a routine algorithmic problem or story problem such as “how many bouquets must be sold each month to achieve a sales goal,” we should encourage them to discuss the problem with others, analyze how they achieved their responses and results, defend and justify those answers and results in written technical and creative writing and use concrete representations of their understanding (like drawing diagrams or using paper models).

Developing their mathematical thinking skills, students will become more flexible, resourceful, and collaborative – necessary traits in any profession.

## What is Mathematical Problem-Solving?

Math problem-solving is the process of using mathematical tools to find solutions to real-world problems. Problem-solving is an active and flexible process that allows students to try out different strategies, learn from their failures, and develop a deeper understanding of the mathematical concepts they’re studying.

When tackling a problem, students should take time to analyze the givens (problem information) and constraints. They may also explore different entry points into the problem and try exceptional cases or more straightforward versions of the original problem. They should be able to explain and justify their reasoning.

Problem-solving skills are essential for students because they help them apply their knowledge and skills to new situations. However, students’ problem-solving skills have been shown to differ based on age, gender stereotypes, and school location [1,2]. Developing solid problem-solving skills can help all students succeed in math.

## What is Mathematical Design?

Achieving artistic balance and visual tension in a design requires mathematical calculations. For example, in a painting, arranging focal points to draw the viewer’s attention to certain parts of the image requires the application of perspective and proportional reasoning.

Similarly, digital graphics and generative art use mathematical algorithms to create complex patterns, fractals, and visually stunning compositions. Mathematical design also enables interactive and responsive designs that adapt to user input.

Culturally responsive teaching and learning can help students from diverse backgrounds feel more confident in their ability to succeed in math. This includes making math more relevant to students’ lives. For example, connecting math instruction to traditions of oral communication, using mnemonic strategies tied to music and dance, and pairing student partners from different cultural backgrounds can all help students build connections to the work of math.

## What is Mathematical Communication?

Mathematical communication refers to communicating one’s mathematical thinking, ideas, and reasoning. This is a critical component of successful learning in mathematics.

Students who can express their thinking orally and in writing help others understand their concepts. This enables them to build links between their informal, intuitive ideas and the abstract language and symbols used in mathematics.

Creating opportunities for students to communicate their ideas in math class helps them develop conceptual understanding, improves their achievement, and reduces anxiety. This is especially true for English learners and students from low SES backgrounds.

Developing mathematical communication skills requires teachers to provide challenges, multiple representations, and repeated structured practice. It also requires ensuring that students can access the content through vocabulary and sentence stems, short writing exercises, and modeling of their work by the teacher.

## What is Mathematical Collaboration?

Research shows collaboration promotes a positive learning environment, communication skills, social development, a more profound understanding of concepts, and preparation for real-life situations. Moreover, collaborating with others is essential for success in all disciplines.

This can be facilitated in mathematics by incorporating group work into classroom activities. However, for students to collaborate effectively, they must be able to discuss their ideas, strategies, and conjectures openly and respectfully with one another.

For this reason, conferring—a practice that involves a teacher listening closely to student thinking and providing a supportive response—is an essential classroom strategy for supporting collaboration in math. This discussion-centered approach has also improved students’ ability to explain and illustrate their thinking. It helps them develop a shared language for explaining abstract math concepts.