Here at Fishtank Math, we envision a world in which all students are empowered to become critical thinkers, problem solvers, and change agents. We aim to help all students see themselves as confident and competent mathematicians who are able to apply their math knowledge both in and out of the classroom as global citizens. From that mission, we have developed a set of five Guiding Principles that inform everything we do from the resources we create, to the professional learning opportunities we provide.
Our Guiding Principles
Fishtank Math is guided by the following 5 principles:
- Anchoring Standards-Aligned, Content-Rich Tasks
- Valuing the Process of Learning
- Communicating Mathematical Understanding
- Monitoring Progress
- Honoring and building teacher expertise
While all five of these principles are crucial to our Fishtank Math design, today we wanted to dive deeper into one of these principles: Valuing the Process of Learning. Learning is an iterative process where students make meaning over time. By focusing on the process of how students learn, rather than the final result of their work, teachers support a growth mindset and encourage students to be active participants in their own learning.
While it can be easy to focus on the end results, it's imperative that students recognize the value of the learning process, including the mistakes they make along the way. Many students come to our math classrooms with anxiety about the subject, often linked to the seemingly black or white options of right answers or wrong answers. But there is so much more for students to see; By prioritizing the process of learning, and helping students see that there is value in every step, teachers can alleviate some of the anxiety students feel and allow them the space to engage in deeper learning.
Valuing the Process in Practice
As we said before, our Guiding Principles inform everything we do at Fishtank Math, so you can see the emphasis we place on the learning process throughout our lesson plans. Specifically, there are three main ways this Guiding Principle shows up: lesson guiding questions, error analysis, and multiple pathway problems.
Lesson Guiding Questions
For every Anchor Task/Problem across the Fishtank Math curriculum, there are a set of Guiding Questions designed to push students to think critically and make meaning from problems, while also demonstrating the importance of the learning process. Lessons include Guiding Questions that can scaffold student thinking and offer multiple entry points so that all students can access the content. Lessons also include Guiding Questions that specifically ask students to notice the key moments in a solving process and use neutral language to discuss misconceptions with new content.
For example, in Lesson 13 of the 6th Grade unit Understanding and Representing Ratios, students and teachers focus their attention on the learning process through the following Anchor Problem and aligned Guiding Questions. The Guiding Questions start by activating students’ prior knowledge, helping them understand how their learning builds over time. Students are asked whether it makes sense to do something in their models to solve. This neutral language allows students to think about why it could be helpful, necessary, or neither to add a step to their solving process. Finally, students are asked to find additional ways to defend their answers.
The combination of these Guiding Questions allows students to deeply engage with the problem and build meaning throughout the process as opposed to simply answering the question with one word.
Error Analysis
One way to show students the value of the learning process, and specifically the value of making mistakes, is to engage in error analysis. Across Fishtank Math units, students deep dive into guided error analysis that builds their problem solving skills, and their ability to identify and diagnose errors in their own work and that of their peers.
When engaging students in error analysis, it's important that teachers model how to talk about mistakes—students shouldn’t be saying things like “Oh that person has no idea what they're doing!” or, even worse “They must be stupid.” Instead, teachers should model and hold students accountable for using language that focuses on the solving process, not the person solving, and applies an asset based approach. For example, teachers might model saying things like “It looks like we went wrong somewhere. I know the first step was correct, but what do you think happened from there?” or “Why do you think someone could make that particular mistake and what would you tell them to help them avoid it in the future.”
Students engage in an error analysis in Lesson 1 of the 5th Grade unit Multiplication and Division of Whole Numbers. Here, students are presented with two different solutions to a problem and tasked with determining who is correct. With the help of the Guiding Questions, teachers can help students understand the process each person used to find their solution, compare those processes, and determine which is correct. Additionally, teachers can push students to think critically about how they would avoid making the same mistake in their own solving process.
Multiple Pathway Problems
When talking about valuing the learning process, it’s also important to consider problems that have multiple correct solutions or multiple ways of arriving at a single correct solution. In the Fishtank Math curriculum, there are opportunities for students to engage with these types of problems and discuss how different answers or processes might be more reasonable in a given context. By engaging students in a discussion about the multiple pathways that exist to solve a problem, teachers demonstrate the value of the solving process and validate that students can approach things in unique ways.
For example, in Lesson 7 of the 3rd Grade unit Rounding, Addition, and Subtraction, students engage with an Anchor Task that could be answered in multiple ways. Teachers can guide students to think about different contexts in which one answer might make more sense than another, helping students recognize the value in how they interpreted the problem and decided to solve it.
Through the Fishtank Math curriculum, we hope that all students will feel empowered to approach problems with confidence and recognize the value their unique ideas bring to the classroom.
Want to learn more about Fishtank Math? Dive into our other Guiding Principles and explore our courses today. Create your account today to unlock access to hundreds of free, standards-aligned lesson plans for your classroom.