Multiple Entry Points and Rich Math Tasks

I was reading this article the other day about how a strength-based approach to learning math (and learning in general) redefines who is “smart” and allows all students to succeed. In her article, Katrina Schwartz has some quotes and reflections from former students who learned math using the complex instruction method, and who were all successful.  They talked about how “math class made them feel safe, heard and able to express their ideas without fear”.  Wow – how often do you hear something like that?!!

Complex instruction is based on the idea that learning is collaborative, where students are learning using rich tasks with multiple entry points and pathways, and each student has a role and accountability. This isimage15 not a post about complex instruction however. What I was thinking about while reading the article was in fact about the Common Core Standards for Mathematical Practice and how they support what the students were expressing in the article – that math class “was a process and it required other people. It wasn’t just you and your work and not talking.”

If you actually read the 8 mathematical practices, you will notice over and over again words like communicate, justify, analyze, plan, make sense, look for entry points, reason, ask questions, make viable arguments, apply.  The practices are all about communicating and talking and finding multiple entry ways to solve problems. And working and talking with others to get there. Like complex instruction, these problems should be rich, where in fact, there are multiple entry points and possible solution pathways. Where each students strengths can support the process and help build the understanding of others. Learning is collaborative, NOT an isolating experience that a worksheet or a lecture so often create.

The Common Core gets a bad rap because so many publishers and testing companies have standardized it – by providing ‘common core problems/strategies’ that are in fact limiting and narrowly focused so they can be graded easily. When I see parents and students and teachers complaining about “common core problems”, I get so angry because what I am actually seeing are ‘forced entry points’ – meaning, rather than allowing all students to approach a problem from their mathematical strength and understanding, they are forced to choose between 1, 2 maybe 3, ways to solve a problem, which may NOT be understandable methods for them.  Therefore, NOT Common Core (or Complex Instruction). As it says in the practices: “Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution”. It does not say mathematically proficient students are given specific entry points to solve a problem.

image16My hope is that with the changes in standardized testing on the horizon under the Every Student Succeeds Act, that math teachers and classrooms can truly begin to focus on students strengths and learning, not preparing for a test. To actually provide learning experiences focused on allowing students to work from their strengths. But it requires a willingness to have a noisy classroom with students talking and collaborating.  It requires  rich mathematical tasks, not standardized worksheets and drill and practice,  that truly provide multiple entry points. This in turn requires teachers who are willing to accept multiple solutions from students rather than the traditional one-way, algorithmic approach we tend to focus on. And it requires support for teachers – in resources, training, time, and expectations.

Read the article by Katrina Schwartz – it also has links to information about Complex Instruction and great feedback from San Francisco Unified School District who has made a concerted effort to teach mathematics this way. Read the Common Core Standards for Mathematical Practice. If you are not already doing so, try to incorporate some of these practices into your math instruction. It’s not what you teach, but HOW you teach, that has an impact on students.  Every student can learn math – it’s up to you to create a culture that helps them believe that.