Foundations of Fishtank Math

Explore the Fishtank Math guiding principles

Written by former classroom teachers and leaders, the Fishtank Math curriculum is designed with students and teachers in mind first and foremost. We believe that all students deserve access to high-quality curriculum and that students should not need to prove they can do rigorous, grade-level math in order to gain access to it. We see these beliefs as key components of supporting anti-racist school practice, and we share our curriculum as a trusted resource for educators in this work. As a curriculum team, we are continually listening, learning, and iterating on our curriculum and resources to get this work right. We strive 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. 

With this in mind, we designed the curriculum to include a balance of student-directed and teacher-led learning. Students have ample opportunities to investigate, explore, and be the drivers of their own learning. At the same time, teachers have what they need to ensure students are adequately guided through the process of learning and towards strong conclusions. The curriculum is also designed to be comprehensive yet flexible. Every Common Core State Standard for mathematics is covered in the Fishtank curriculum, with a focus on the major work of each grade and a thoughtful vertical progression embedded from course to course. Teachers are provided with a flexible lesson structure that gives them the content and tools they need to make the decisions that are right for their students. Lastly, we designed the curriculum to be standards-based and content-rich. This means you can be sure students have access to and practice with standards-aligned problems that are engaging, accessible, and supportive of productive struggle. 

Our Math Guiding Principles

Read more about the guiding principles that are core to the design of the Fishtank Math curriculum.

Anchoring standards-aligned, content-rich tasks

We believe that the content of a curriculum plays a critical role in student learning, and this content must not only be standards-aligned but also rich in a way that engages all students in multiple layers of understanding.

A student working on a handheld whiteboard.

In the Fishtank math curriculum, the content is placed front and center. Each lesson is organized around a handful of Anchor Problems or Tasks, both originally created by the Fishtank curriculum team and selectively curated from trusted resources. To support the best learning opportunities for students, we designed and curated these problems to meet a variety of criteria:

  • Accessible to all students with low-floor/high-ceiling opportunities for students to engage in grade-level content
  • Offer more than one solution pathway and encourage the use of a variety of strategies
  • Support worthwhile mathematical discussions 
  • Are intentional in building strong conceptual foundations before introducing procedural algorithms or processes
  • Support productive struggle
  • Make connections to mathematical concepts explored within and across grade levels

We believe that tasks put in front of students should be tasks that are worth doing. While not every task will encompass all of these characteristics above, we aim for tasks that engage students as active, thoughtful participants. At times, this means students dive into deep, complex tasks that challenge them to grapple with a new concept; other times, this means students are solidifying generalizations and working towards fluency. As a standards-aligned curriculum, we stay true to the standard language and the aspect of rigor that is called for in each standard.

Further reading:

  • Smith, M. S. & Stein, M. K. (1998). Selecting and creating mathematical tasks: From research to practice. Mathematics Teaching in the Middle School, 14(9), 548--556. 
  • The National Council of Teachers of Mathematics (2014). Principles to Actions. (pp. 17-24). NCTM. www.nctm.org/PtA/
  • National Council of Teachers of Mathematics (2021). Problem Solving. The National Council of Teachers of Mathematics. www.nctm.org/Research-and-Advocacy/Research-Brief-and-Clips/Problem-Solving/ 

Communicating mathematical understanding

We believe that providing students with opportunities to communicate and discuss their thinking improves student understanding, provides teachers with useful information to inform instruction, and shifts power away from teachers being the possessors of knowledge to students being the constructors of it. 

Students talking and smiling.

Discussion offers unique benefits to teachers and students that are hard to come by any other way. It can reveal understanding and misunderstandings - to the speaker themself, their classmates, and their teacher. Discussing ideas helps students retain understanding and information, both by articulating their ideas and hearing them repeated by others in their own words. It supports language development and the construction of logical arguments. It also increases social skills, helping students develop effective ways to communicate with others like patiently listening, understanding other people's points of view, respectfully disagreeing, and being empathetic and kind to their classmates. Perhaps most importantly, discussion helps empower students to see themselves as sense-makers, building their own confidence in their abilities and increasing their motivation, and decentralizes the power dynamic in the classroom. Thus, by providing a curriculum full of rich discussion-worthy tasks that provide students opportunities to describe and evaluate their ideas, share strategies, and make conjectures, we aim for students and teachers to develop a deeper understanding of the content and themselves. 

Further reading: 

Valuing the process of learning

We believe that learning is a process and must be valued in classrooms.

A student working on a whiteboard.

Students do not learn content overnight and as such we believe learning is a process. We believe the focus should not be on just getting the right answer, but rather on students developing their mathematical toolkit and conceptual understanding. When students have strategies and reasoning skills, they can work towards applying them fluidly and flexibly to content-rich tasks and communicating their mathematical understanding with others. Throughout the curriculum, students encounter opportunities to challenge themselves and extend their learning, and at the same time, teachers are provided the guidance to support students in productive struggle. We believe that mistakes should be treated as opportunities for student learning. Students learn not only by refining their own work, but by being able to explain and understand the thinking of others as well. We also understand the importance of meeting students where they are in their learning process in order to provide them with the right support to access and succeed with grade-level content. With the reality of unfinished learning, we strive to support teachers with what they need to ensure that, no matter what, all students are spending as much time as possible on grade-level tasks because we know, and research shows, that this is what drives student learning and achievement.

Further reading: 

  • National Research Council (2001). Adding It Up: Helping Children Learn Mathematics, (pp. 333-335, 422-423). Washington, DC: National Academy Press.
  • Hiebert, J., Grouws, D. A. (2007). The Effects of Classroom Mathematics Teaching on Students' Learning.  In F. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning. (pp. 379-393). Charlotte, NC: Information Age.
  • Cintron, S. M, Wadlington, D., ChenFeng, A. (2021). Stride 1: Dismantling Racism in Mathematics Instruction. (pp. 66-69).  A Pathway to Equitable Math Instruction.  equitablemath.org/wp-content/uploads/sites/2/2020/11/1_STRIDE1.pdf 

Monitoring student progress

We believe that monitoring student progress through various kinds of assessment is an integral part of a curriculum that informs teachers' instructional decisions and students' metacognition. 

Teacher and student talking and looking at a piece of paper.

While “assessment” can often imply tests and quizzes for many, we define the term much more broadly. We believe that summative assessments like our post-unit assessments have value in evaluating student understanding, but formative information, like that gleaned from our pre-unit assessments, Target Tasks, and even our Problem Sets, is an even more powerful tool to help teachers make in-the-moment instructional decisions that are best for their students. We also believe that students play an important role in monitoring their understanding, which is why we provide pre- and post-unit student self-assessments. With these assessments, students can diagnose their own understanding and reflect on what actions they took to be successful to build metacognition and foster a growth mindset. With each of these resources, we believe that students can demonstrate their understanding in various ways, such as through computing, drawing, or explaining, none of which is inherently more valuable than another. By providing teachers and students with frequent feedback, they are able to learn from their mistakes and improve their understanding. 

Further reading: 

Honoring teacher expertise

We believe teachers bring their expertise to their classrooms, and that providing them with a strong curriculum with the resources they need to make decisions for their students will help drive student learning. 

Teacher in front of a projector screen.

The Fishtank math curriculum was designed by former classroom teachers who believe and acknowledge that teachers have both knowledge of their subject and knowledge of their students. The curriculum provides teachers with autonomy and flexibility so they have the support and freedom to make informed instructional decisions. Because the curriculum is also focused on students, teachers are encouraged to make adjustments based on the students in front of them, as a way to speak directly to student choice and engagement. We designed the curriculum so that teachers feel empowered to use a variety of classroom structures, from pair and group work to student-led opportunities. Whether teachers are veterans or in their first years of teaching, we aim for the curriculum to provide the content support needed to make both teachers and students feel successful without a completely scripted lesson. Lastly, we believe that teachers have the desire to continually build their own content knowledge and become greater experts in their fields. To support them in this work, we are continuously working on resources to support intellectual preparation so teachers can plan smarter and more efficiently and effectively. 

Further reading: