Curriculum design must take into consideration some of the many demands on educators, incorporating another “thing” into classrooms seems impossible.
Sufficient time must be provided in classrooms to:
- Engage students in tasks that promote problem solving and reasoning to make sense of new mathematical ideas;
- Engage students in meaningful mathematical discussions; and
- Build fluency with procedures on a foundation of conceptual understanding.
(Principals to Action, 2014)
Mathematical Tasks allows for all of these
Using a rich task engages students in problem-solving to address a question and consults with others to reason through ideas. Teachers engage by facilitating discussions in small groups or in the classroom and supports students to make the connections between math ideas. Telling isn’t teaching, so why keep doing the same thing hoping for a different response from our students. Rich tasks need students to work in groups, privately and publically reason, justify their thinking and make connections between different mathematical models. If you thought it was difficult to incorporate multiple Common Core Mathematical Practices (MPs), look no further than a task to help you out. It is not uncommon to see 4 or 5 MPs in a single task, mainly because they happen automatically with math tasks.
Homogeneous classrooms of students are a thing of the past. Each of our students come to us with radically different backgrounds and experiences. If your classroom is anything like mine, there are major gaps in content understanding when my students move up. Heterogeneous groups of students provide wide ranges of backgrounds for students to draw upon when starting and engaging in a task. We want this diversity so that students can make more connections when discussing their tasks within their group or to the whole class. Jo Boaler (of Stanford and YouCubed), facilitates a Dot Talk with a young group of female mathematicians (see video below). While this task is simple for introducing Mathematical Tasks in the classroom, the model of facilitation carries weight about who can/can’t do mathematics in a classroom. When students contribute to the discussion in a math classroom, they increase their academic status. Tasks allow for this discussion and reasoning to happen.
Conceptual Understanding First
Notice the NCTM language “build fluency with procedures on a foundation of conceptual understanding” suggests that conceptual understanding must lead before procedures are taught. Students memorize math facts without any understanding of where they came from or why they work. I call this “Magical Mathematics” because it just works. I’m always surprised by some of the “methods” my students walk in with…one that always catches me off guard is “Slide & Divide” for Factoring which is not conceptual understanding before procedural fluency and it just magically works. Rather, we want our students to build understanding from experiences in problem-solving and reasoning to generate new ideas. The “Tabular Method” is a rich concept that allows students to build ideas about multiplication and division…consider this alternative using reasoning and problem-solving. Neither of these videos represents math tasks, but one is clearly based on reasoning and problem solving and the other is not. Tasks can be easily built from concepts that use reasoning and problem solving to build procedural fluency, those which use “Magical Mathematics” are increasingly difficult for teachers and students to justify reasoning.
This site has two major goals from its inception. The first is to provide a central location for teachers to access FREE mathematical tasks and second is to provide a space for teacher knowledge to be shared within the mathematical tasks community. Using rich tasks in classrooms is very different from direct instruction and requires some new perspectives in teaching. All of us have failed when implementing a task…learn and try again. We hope the teacher articles provide getting started material for you and will lead you to inquire about your practice implementing mathematical tasks. If you have a suggestion for an article, please feel free to email firstname.lastname@example.org. We always want to grow in our support of high-quality math instruction. Please also consider sharing your experience with using math tasks in your classroom.
We hope you will try some mathematical tasks in your classroom. They are challenging at first, but with practice and perseverance, you will see much more growth in your students. Consider taking a look through our teacher knowledge section to learn more how-to information or advice from fellow teachers.