Picture yourself as a mountain climber. What really thrills you is challenging your abilities, strength, and toughness in some of the toughest places on Earth. And now, you've chosen to face the biggest challenge of all: Mount Everest, the tallest mountain on the planet. You'll be getting ready for at least a year, gradually building up your stamina. Climbing Everest means walking for many hours each day, every day, for several weeks. How do you prepare for that.

The secret, like in many cases, involves math. Climbers make their training better by keeping track of their heart rate. When they exercise, they target a heart rate between 60 and 80 percent of their highest possible rate. If it goes beyond that, they might get too tired. If it's below 60 percent, it means the training is not challenging enough — they need to work harder. By using this method along with other types of training, their overall fitness will improve over time, and, hopefully, they'll be prepared for Everest.

## Real-World, Meaningful Problems.

Imagine combining the excitement of mountaineering with middle school math! This kind of situation can be a fun way to learn through **problem-based learning (PBL)** in the classroom. PBL is a way of teaching where students learn by actively working on real-world problems. Instead of just listening to a teacher, PBL in math lets students explore, discuss, and understand math by solving problems together. It helps with critical thinking, problem-solving skills, and really understanding math by making students active learners, not just listeners.

### Knowledge Through Experience.

Constructivist ideas have played a big role in shaping **problem-based learning (PBL).** One important idea comes from **Jean Piaget**. He believed that we build our knowledge through experiences and interactions. Another person, **Leslie P. Steffe**, emphasized how students should create their own understanding of math instead of just hearing information without doing anything.

Becoming a great mountain climber doesn't happen by only reading or watching others climb. You get good by going to the mountains, climbing, facing challenges, and getting back up when you make mistakes. And that's how people learn math too.

### The Traditional Approach.

Learning by solving problems has been a part of **American education** for a long time. John Dewey started talking about it in 1916, and **McMaster University** began a special program for medical education using **problem-based learning (PBL)** in 1969. In 2000, the **National Council of Teachers of Mathematics** shared a vision in their book Principles and Standards for School Mathematics. This vision focused on **problem-solving**, reasoning, and communication – all things that PBL is about. It suggested that teachers create lessons that let students think about math in a meaningful way by solving problems.

But, using** problem-based learning (PBL)** in math classes is not something all teachers do the same way in the **United States**. Many math teachers still prefer teaching the traditional way, with formulas and steps. Back in 1998, researchers looked at data from the **Third International Mathematics and Science Study (TIMSS)**. They found out that teaching methods were different in various countries, creating a "teaching gap." The study showed that in the U.S., math teaching mostly concentrated on step-by-step skills, where students spent a lot of time practicing the same things over and over. On the other hand, in Japan, teaching focused more on really understanding math, and students worked together to solve tough problems.

### Not “Math People”

**problem-based learning (PBL)?**The key is to choose the right level of challenge. Remember

**Vygotsky’s Zone of Proximal Development?**It's like finding the sweet spot where learning happens best – not too easy to be boring and not too hard to be discouraging. Just like a mountaineer in training, that perfect level of challenge is where the fun and engagement really kick in.

**problem-based learning (PBL)**can boost the confidence of students who didn't think they were good at math. It helps them believe in themselves and see that their ideas are important. They come up with really creative ways to solve problems; some kids say things that amaze me. Suddenly, they realize they are good at math.

**Supporting Teachers With Implementation.**

**problem-based learning**work means teachers need to change their role from just giving information to helping students learn on their own.

**problem-based learning**themselves, they understand math better and become more confident in their teaching. They not only learn the subject but also start to think more creatively and ask more questions. Teachers feel the same excitement as students when they say, "Hey, I did it! I figured it out!" And that's not all – continuous support and coaching, such as what we provide at Imagine Learning, are incredibly important too.

### Skills and Understanding.

Even though there are some difficulties, more and more teachers are starting to use **problem-based learning (PBL)** in math. This is happening because there's proof that **PBL** helps students think better, solve problems, understand math more deeply, and feel better about themselves when it comes to math. PBL fits well with the modern idea of making learning more about students, where they're involved and it actually means something to them. It's becoming a big part of good math education, helping students learn the skills they need for success in the 21st century.