By Guest Contributor Dr. Angelica Gonzalez, Sr. Data Scientist at McGraw Hill
It’s no secret that STEM careers are in high demand, and will likely remain in high demand for some time. The road to a fruitful STEM-centric future is likely to include adversity — and for many learners, particularly underprivileged groups, the path to a rewarding career in STEM will begin with their relationship with K-12 mathematics.
As educators, curriculum providers, policymakers, and other professionals who shape K-12 math education, it’s critical that we work to create a learning environment that mitigates math adversity whenever possible. In my career, as a first-generation Hispanic woman with a Ph.D. in mathematics — both as a student and as a teacher — I have observed that having a community, embracing failure, and working hard are all crucial to overcoming obstacles in math and achieving success. Now as a data scientist at McGraw Hill, I appreciate how data and educational products can help achieve these goals.
In times of celebration, confusion, or despair, one usually gravitates to their community. The same is true for students. Learning is messy and it requires conversation to disentangle; conversations that allow the student to be vulnerable; and collaboration that leads to more questions and provokes curiosity. Knowledge and passion grow from these interactions. From a learning perspective, community is crucial for success. Unfortunately, finding an academic community is not always easy for students, especially for underrepresented and underprivileged students.
What can educators do to build community in math?
A student’s academic community can consist of teachers, parents, or peers. Traditional lecture methods and bias make it difficult for K-12 students to see their peers as part of their academic community. Teachers can play an active role in helping students build connections at an early age. Collaborative and cooperative learning are examples of teaching methods that can encourage community among students.
In practice, such teaching methods require positive interdependence among students. Finding effective groups is challenging and thus time-consuming. Especially when time is scarce, teachers should not be afraid to use data when making decisions. Whether data are obtained simply from a gradebook or from advanced analytics tools, they help teachers efficiently recognize students’ strengths and weaknesses as well as patterns in the classroom.
We are usually taught that success is tied to getting the “right” answer, especially in mathematics where there is almost always a correct final answer to a problem. This leads to a mentality that you either can or can’t do math. But this is not true! Everyone can learn math. Every student eventually struggles to learn and gets the wrong answer. Failure is a natural part of learning. How students react to failure plays a crucial role in their future. It’s important that students embrace failure and grow from it from an early age. Positive reactions to failure can be cultivated by learning to make failure a temporary outcome. Moreover, students should observe and acknowledge that failure is not a unique experience to them but that rather everyone eventually fails.
How can educators normalize and utilize failure in math?
A teacher can empower students to embrace positive reactions to failure in the classroom by simply providing problems where they make it obvious to the students that they do not yet have the relevant skills. As the class progresses and they learn more, they will witness successful outcomes at tasks they once thought were impossible. This will set the expectation in the classroom that it is ok to have knowledge gaps and that everyone can eventually develop the necessary skills.
A teacher can make failure productive by using it to help students reflect on their skills. For example, when a student struggles, teachers can ask students open-ended questions like:
- “How did you decide to use that approach?”
- “Let’s forget about the ‘rule’, how do you want to solve this problem?”
- “How can you use addition to figure out multiplication when you are unsure?”
Open-ended questions are a great way to help students use moments of failure to identify areas of improvement.
It is a teacher’s job to provide students with resources that will help them bridge their knowledge gaps. Students may need more problems, new problem-solving strategies, or new skills altogether. Identifying the appropriate resource for a student takes effort. This is again where data can help teachers optimize their time. Historical data on student performance can help shed light on what resources or problems will help a student meet their current learning objectives.
Mathematics is often learned through extensive time spent practicing and honing skills. Success requires hard work. There is a big misconception that in order to be good at math, you must be gifted in some way; however, long-term success in math requires dedication even for those that appear to grasp concepts quickly. As a result, effort and tenacity should be promoted from an early age.
How can educators encourage students to work hard in math?
Students can be motivated by praise. Positive feedback should be prompted not only by obtaining the “right answer” but when persevering to obtain it. Moreover, hard problems, tests, etc., should not be the only opportunities for recognition. For example, if a student wants to apply order of operations to a multi-step expression, the student may know how to do such problems with guiding parentheses but struggle when they are not present. Highlighting to the student that they have mastered some of the necessary skills because of their previous effort while working towards their bigger objective will motivate the student to continue to apply themselves. Instilling the value of hard work will help students build stamina to overcome their obstacles in the future.
Students are energized when they can visualize their progress and road to success. Easy access to performance metrics and ways to view their progress over time can help provide students with the dedication needed to achieve success.
The path to success in mathematics is complex, but everyone can do mathematics, do it well, and enjoy it. Each of us in the education industry has a responsibility to carve paths to success in math and toward rewarding careers in STEM for every student. Believe in your students, provide them with a safe environment to learn and fail and acknowledge their hard work.
Angelica Gonzalez is a mathematician and data scientist with industry experience doing data analysis, data visualization, mathematical modeling, and algorithm development. She earned her Ph.D. from the University of Arizona where she gained experience teaching and collaborating with K-12 teachers.