Improving mathematics education through problem-based learning

You don't become an expert mountaineer simply by reading or watching others climb. You become proficient at climbing mountains, climbing, facing challenges, and getting back up when you stumble. And that's how people learn mathematics.

The traditional approach

Problem-based learning has a rich history in American education, with John Dewey laying the theoretical foundations in 1916 and McMaster University pioneered the PBL program for medical education in 1969. More recently, the National Council of Teachers of Mathematics published Principles and standards for school mathematics in 2000, establishing a vision that emphasized problem solving, reasoning and communication, closely aligning with the principles of PBL. He encouraged teachers to design learning experiences that engaged students in meaningful mathematical thinking and problem solving.

However, PBL as a pedagogy has seen varying levels of adoption in mathematics classrooms across the United States, and many mathematics teachers have turned to Traditional teachings of formulas and procedures.. In 1998, a critical investigation examining data from the Third International Mathematics and Science Study (TIMSS) revealed Teaching methods varied significantly across cultures.which results in a “teaching gap.†According to video documentation of the study, mathematics teaching in the United States focused predominantly on procedural skills, where students spent most of their time acquiring isolated skills through repetition. In contrast, Japanese teaching focused considerably more on deeper understanding, where students became more involved in collaboratively solving challenging problems.

Not “Math People”

The procedural approach can be effective for students who thrive in structured environments and excel at memorizing formulas and algorithms. However, for many students, this approach leads to a feeling of disconnection and a belief that they are not “mathematical people,” a negative self-perception related to math anxiety. Math anxiety can increase cognitive load, which is the mental effort required to process information. When students are anxious about mathematics, their Working memory resources may be diverted to managing anxiety instead of focusing on solving math problems.Resulting in Decreased performance on procedural tasks..

So what makes ABP different? The key to making it work is to introduce the right level of problem. Remember Vygotsky's zone of proximal development? It is essentially the space where learning and development occur most effectively – where the task is not so easy that it is boring, but not so difficult that it is discouraging. As with a mountaineer in training, that area where the level of challenge is appropriate is where commitment really occurs.

I have seen PBL build the confidence of students who thought they were not math experts. It makes them feel capable and that their knowledge is valuable. They develop the most creative strategies; The children have said things that leave me speechless. Suddenly, they're math people.

Support teachers with implementation

Why aren't more math teachers adopting problem-based learning in their classes? One of the main obstacles is the lack of training of teachers in PBL methods. Effective implementation of PBL requires a shift in the teacher's role from knowledge provider to learning facilitator.

In my experience presenting the problem-based curriculum Imagine instant messaging For teachers, professional learning is key to helping them achieve that change. Experiencing PBL first-hand allows teachers to develop a deeper conceptual understanding of mathematics while building confidence in their own teaching practices. Teachers are not only mastering content knowledge, but also shifting their mindset toward a more exploratory and inquiry-based approach. I see the same reactions from teachers as I do from students, the same joy at being creative with math: “Hey, I did it! I discovered! And then after that, and this is what we do in Imagine learning — Ongoing support and training is helpful.

Skills and understanding

Despite the challenges, the trend towards PBL in mathematics education has been growing, driven by evidence of its benefits in developing critical thinking, problem-solving skills, and a deeper understanding of mathematical concepts, as well as building more positive mathematical identities. The incorporation of PBL aligns well with the broader contemporary shift toward more student-centered, interactive and meaningful learning experiences. It has become an increasingly important component of effective mathematics education, equipping students with the skills and understanding necessary to succeed in the 21st century.

In the heart of Imagine instant messaging lies the commitment to providing students with opportunities for active and deep mathematical practice through problem-based learning. Imagine IM builds on the problem-based pedagogy and instructional design of the renowned Illustrative Mathematics curriculum, adding a series of exclusive videos, digital interactives, design-enhanced print, and hands-on tools.

The value of Imagine IM's improvements is evident in Inspire Math's beautifully produced videos, from which the mountain climber scenario emerges. Inspire Math videos show the mathematics of each Imagine IM unit in a relevant and often unexpected real-world context to help spark curiosity. The videos use contexts from around the world to make interdisciplinary connections and increase engagement.