The Common Core State Standards Math (CCSSM) provides the following definition: “Rigor: Pursue conceptual understanding, procedural skills and fluency, and application with equal intensity. Rigor refers to deep, authentic command of mathematical concepts, not making math harder or introducing topics at earlier grades.”
Thinking about this definition, we as educators need to consider who is doing most of the work in the classroom. If rigor is present, students are doing the cognitive work. They are the ones thinking deeply and problem solving. Teachers need to act as facilitators, and help students move towards the learning target. Keeping this in mind, here are three suggestions for adding rigor to your classroom.
Numberless Word Problems: Brian Bushart has created a blog with a bank of word problems with various situations. The numbers are missing so students can focus on the context of the problem. This increases the rigor of the problems because students are required to develop a “deep, authentic command of mathematical concepts”. Once you see the structure of Brian’s examples you and your students will be off and running, creating numberless problems.
Open Middle Problems: This resource provides teachers with “challenging problems worth solving,” which are based on the CCSSM standards and listed by grade level K-12. Some characteristics listed on the website:
- “Closed beginning” – All start with the same initial problem
- “Closed End” – All end with the same answer
- “Open Middle” – Multiple ways to approach and ultimately solve the problem
- Easy to get an answer but more challenging to get the best or optimal answer
- Appear to be simple and procedural but turn out to be more challenging
- Less complex than a performance task
One example of an open middle problem was developed by Graham Fletcher. Think about the what the student is having to process as they solve this task:
Directions: Using the digits 1-9, at most one time each, fill in the blanks to complete the number sentence.
_ _ + _ _ = _ _ + _ _
Taking away the numbers increased the rigor of this problem. Students can solve this and begin to design other problems. Remember, the students are doing the work! Reflecting to the definition of rigor, Open Middle Problems “pursue conceptual understanding, procedural skills and fluency, and application with equal intensity.”
Which One Doesn’t Belong (WODB): This resource provides thought-provoking puzzles with shapes, numbers, graphs, and equations. Students choose which part of the puzzle does not belong and state their reasoning. As the discussion continues, a claim can be made for each number. Teachers are able to facilitate the student-led discussion and also gain insight into the students’ understanding of mathematics. WODB is not limited to numbers! You will see geometry and fraction examples that can often shine a light on misconceptions.
If this is a resource you would like to use next year, check out the discussion on Twitter (#WODB) to see how teachers are using WODB and additional ideas. Several examples posted are developed by the students! Rigor!
Make a plan this summer to work smarter, not harder next year. Increase the rigor in your classroom by allowing the students to do the work!
Cindy Cliche is a classroom teacher with over 30 years experience. She currently is the Math Coordinator for Murfreesboro City Schools. Cindy has worked in the past as a Teacher Trainer with the Tennessee State Department of Education. She was the Presidential Awardee in Math and Science Teaching in 2004. She has a passion for math education in the elementary grades. Cindy received her Bachelor’s Degree from Ball State University and her Masters from Berry College. She also serves as a Hope Street Group Tennessee Teacher Fellow, engaging her colleagues in providing classroom feedback to the Tennessee Department of Education on public education policy issues.