The Common Core State Standards (CCSS) for Math are a blend of content standards, the content of our courses, and practice standards, the manner with which students tackle that content. In an ideal world, our students would bring the mindset of these practice standards, their math disposition if you will, to class each day. But these, too, have to be developed, facilitated, and practiced, which admittedly adds to a teacher’s load. Many teachers, and I would be bold enough to say rightly so, feel that a problem-based learning experience (mini-projects essentially) is a great way to allow students to participate in experiences that will ask for a blend of these two types of standards. NCTM research, New Tech Network work with math facilitators, and my own experience in the classroom back this up. But that doesn’t make it any less daunting to take this on – to go against the way you yourself was taught (and were likely successful at) math and probably the way you were taught to teach math as well. So where do you start? I have an idea!
The CCSS math practice standards come with some guidance stating, “Expectations that begin with the word “understand” are often especially good opportunities to connect the practice to the content” (CCSS for Math, page 8). If you are looking for spots to help develop your students’ ability to engage with the content, I suggest starting here. As an example, below is the Geometry Overview taken from CCSS for Math with the appropriate “understand” expectations highlighted. If you view the full list of standards, there are a few smaller strands that also begin with the word “understand”, but I think the big picture perspective of the Overview is just the ticket if you as you think about curriculum planning for next year.
- Experiment with transformations in the plane
- Understand congruence in terms of rigid motions
- Prove geometric theorems
- Make geometric constructions
Similarity, Right Triangles, and Trigonometry
- Understand similarity in terms of similarity transformations
- Prove theorems involving similarity
- Define trigonometric ratios and solve problems involving right triangles
- Apply trigonometry to general triangles
- Understand and apply theorems about circles
- Find arc lengths and areas of sectors of circles
Expressing Geometric Properties with Equations
- Translate between the geometric description and the equation for a conic section
- Use coordinates to prove simple geometric theorems algebraically
Geometric Measurement and Dimension
- Explain volume formulas and use them to solve problems
- Visualize relationships between two-dimensional and three-dimensional objects
Modeling with Geometry
- Apply geometric concepts in modeling situations
There are three critical places where you have key opportunities to dive into PrBL, places that the authors of the standards highlight as excellent crosswalks between the math content and the math practices. I do not mean to understate the importance of the others expectations that ask students to use, apply, describe, or explain; these are important to gain a well-rounded and thorough view of Geometry. But if you are looking for a spot to start your PrBL journey, here it is! The standards themselves narrow down the scope of expectations and hopefully guide you to standards/units where you can throw some energy into really creating PrBL experiences for your students. So grab a copy of your standards, bust out a highlighter, and dig in!
P.S. Once you’re done highlighting and know where to kick off your PrBL planning, I recommend stopping by emergentmath.com and checking out all of problem ideas Geoff Krall has gathered together under the “Curriculum Maps” tab.