Wednesday, April 13, 2011

Ten Paperless Math Assessment Strategies

by John T. Spencer

I recently wrote a post about the ridiculous nature of standardized testing. Somebody e-mailed me about why an authentic approach might work in some subjects, but not in a subject like math.  So, here are a few ideas of paperless math assessments. 
  1. Math Blog: This serves two purposes.  First, it's a personal journal where students write reflections on mathematical processes, ask critical thinking questions or describe methods used to solve problems.  However, it also becomes the student portfolio, where they choose items that represent their best work, most challenging works, goals for improvement and areas of growth.  Finally, blogs become a place where students share their processes and have a chance to compare and contrast with one another.  It becomes a peer-led method of formative assessment. 
  2. Concept Maps: I want to see how students connect concepts from various math standards, a concept map becomes a valuable tool.  I've watched students create their own color-coded and shape-based strategies to add layers of meaning to their mental process.  
  3. Debate / Discussion: I think it's sad that teachers tend to restrict debates and discussions to social studies or language arts.  I want to see students engaged in critical thinking discourse regarding the best ways to solve problems or present data.  Sometimes this looks like a half-circle discussion of graphing methods.  Other times I have  students move to places in the room that represent various strategies (where they then discuss the strategy).  The goal here is to assess student thinking process in a way that is verbal and interactive.
  4. Projects: Here students have a chance to go in-depth into the math using multimedia methods.  In the case of the budget process, it involved using spreadsheets, shared documents and adding a video or podcast component.  In the case of the eco-friendly houses, it involved hands-on construction models after using Google Sketch-up and doing online research.  A project can be formative, in terms of helping students find applications to what they are learning; but they are also summative, in terms of developing a final product that proves mastery of math skills.  
  5. Mental Math: When people hear "paperless," they often assume it means technology.  However, we do mental math each day as a chance to assess each students' mathematical process. Students share their processes with one another on simple scenarios like finding the tip at a restaurant or judging how long a road trip will take. 
  6. Multimedia Instructions / Tutorials: Here I start with a sample problem that contains multiple mistakes, though sometimes I start with a class brainstorm of potential mistakes.  From there, students create videos, podcasts or functional text descriptions on how to avoid the mistake and solve a problem correctly.  
  7. Scenario Response: Similar to Dan Meyer's "What can you do with it?" questions, the students have a multimedia clip and then develop their own problem based upon it.  The idea here is to assess inquiry and process.  So much of math revolves around, "Can I figure out what you don't know?" Here, I get to ask, "Can I figure out how much you actually know?" Students can use any tools they use to solve the problem, including manipulatives.
  8. Forms: Sometimes I want a quick assessment of student answers.  I want to know how many solved a specific problem correctly and how each student explained the process.  For that reason, I will use a Google Form and then share the overall class data with students, so we can identify potential mistakes or misunderstandings. 
  9. Self-Assessment of Skills: I start with a shared document with each skill, written as a student-friendly objective.  A Student will then modify his or her shared document as they learn new skills or concepts.  I have a space for teacher and student feedback, so it becomes a chance to combine objective scoring with customized feedback. 
  10. Create a Problem: Here the students find a scenario and develop an authentic problem based upon it.  For example, one group used linear inequalities to demonstrate which local taxi services are ideal for specific tasks (going to the airport, going across town, going to the supermarket).  It was relevant to our urban environment and it began with a concept that intrigued them.  Other times, I will ask students to salvage a really bad example of pseudocontext and create an alternative that uses the same skills. Either way, this becomes a chance to assess if they understand the application of a math concept in an authentic context. 
John T. Spencer is a teacher in Phoenix, AZ who blogs at Education Rethink.  He recently finished two books, Pencil Me In, an allegory for educational technology and Drawn Into Danger, a fictional memoir of a superhero. You can connect with him on Twitter @johntspencer

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