## Wednesday, June 08, 2011

### Fifteen Paperless Math Strategies

#1 - Critical Thinking
Description: Students answer critical thinking questions such as, "Are numbers neutral?" or "When are decimals less accurate than fractions?" The goal here is for students to go deeper into thinking conceptually about the math they use.  For additional ELD support, I've found that definitions work well here as well as digital sentence strips to help scaffold the vocabulary.
Grouping: This can work individually or in groups.  One allows for more introspection while the other creates a greater sense of dialogue.
Tech Tools:  blog, form, shared document

#2 - Vocabulary
Description: When introducing new words, I like to have students keep a vocabulary blog, where they can list the vocabulary word, find a picture (either draw one and take a picture of it or find one online), use it in a sentence and then use the labels for synonyms. Later, I have students answer critical thinking questions that require them to use this math language.  Or they can create a short podcast using their vocabulary blog as an additional support.
Grouping:  This can work in pairs or small groups, but the blog should be individual.
Optional Tech Tools: blog

#3 - Find the Pseudo-Context
Description: This one works best for older grades.  However, it's a great chance to teach students how to construct quality, realistic word problems.  I show them a sample word problem and have students analyze it with questions such as, "Is this realistic?  Would someone do this in real-life?  Is there a better example you could find?"
Grouping:  This works well in the math blog, but also as a discussion question on a class blog or a small group analysis with a shared document
Optional Tech Tools: blog, shared document, Evernote

#4 - Create a Metaphor
Description:  Students develop a metaphor for a particular math concept.  For example, they want to think about division, decimal, percent and fractions being a similar process with a different way of displaying it and thus they use the metaphor of someone who is multilingual or someone who uses the same actions in different sports (different rules, different names, same action).  Students then have to explain their metaphor.
Grouping:  This works well individually or in pairs (if you want the students to compare the metaphors) where you might compile it into one presentation
Optional Tech Tools: blog, shared document, drawing, photo editing, podcast, presentation, comic-style photo editing

#5 - Prove It
Description: I start with a statement and students have to prove whether it is wrong or right.  It might be something like, "There are no vertical lines on a graph."  It then forces them to think through vocabulary like linear equation and function and prove whether my statement is true or false.  I ask them to prove it visually, orally or in written form.
Grouping:  This can work well individually or in a small group
Optional Tech Tools:  A shared document or wiki, blog, e-mail (to get quick responses), form, photo with annotation (do it by paper and then use an annotation program to add to it), audio/podcast or video

DURING
#6 - Mental Math
Description: Students answer a simple math question and then follow this up by sharing their process.  The goal here is to get them to think through the process and engage in discourse.  I might show them a bill and ask them to find the tip.  As I walk around, I'll hear, "Why would you divide it by five instead of moving it one decimal over and doubling it?"
Grouping:  This should start individually and then move to partners or small groups
Optional Tech Tools: podcast / audio recording, photo and description in a blog or on smaller blogs like Posterous or on Evernote

#7 - Word Problems
Description: Students struggle with word problems.  Sometimes this is a vocabulary issue.  Other times, they can't visualize it.  So I have students use a few strategies.  First, they copy the text to a Google Document and highlight it according to the elements of literature (the conflict, the characters, etc.) or using a word problem analysis process (find critical details, take out extraneous details, etc.)
Grouping:  individual, pairs or small group
Optional Tech Tools: shared document

#8 - Multimedia Inquiry
Description: I might have students look at Google Maps, a photograph I've taken, a video or a few websites and then ask a math-related question based upon what they see.  It might be a snapshot of a batter with the stats below, a jar full of jelly beans or a list of services and prices for Dish Network and Cox Cable.  The goal here is for students to look at a situation and develop a math problem that interests them and fits their level.
Grouping:  individual and whole class
Optional Tech Tools: blog with response, Posterous, social media (Twitter works well for this one), Evernote

#9 - Concept Connections
Description: Sometimes students struggle to see how various concepts connect.  One non-techie strategy that works is to get them to physically connect the concepts with yarn and a verbal description.  However, a concept map works really well for this, too, because they can change the colors, use multiple arrows and figure out their own style of organizing the information.
Grouping:  individual or partners
Optional Tech Tools: concept map

#10 - Name It, Claim It
Description: The idea here to get students out into their world and finding examples of their current math concepts.  They can shoot video or take pictures and then annotate it, present it or download it. This works well as a challenge, such as, "See how many acute angles you can find at our school," or "Interview five adults who have used fractions in the last month."
Grouping:  Small group works well for this.
Optional Tech Tools: Students can use a photo editing program (such as instagram) label it comic-book style or they could annotate it verbally using presentation or podcast software.  They could also shoot a video and edit it with labels.

ENDING / ASSESSMENT
#11 - Life Connections
Description: Similar to number ten above, I might ask students to write or audio-record a reflection about how they see a particular math concept connect to life.  I don't buy into the theory of math for math  sake.  Nor do I want them reaching to far and getting into pseudo-context.  Students need to see that math is around them.  So, I challenge them with something like, "give me an example of a linear relationship in your world."
Grouping:  This can work individually or in groups (to get a higher level of discourse) both orally or on a blog
Optional Tech Tools: blog, podcast, shared document, social media (creating a hashtag for it and then seeing the examples)

#12 - Reflection
Description: Sometimes I ask students to describe a process they used.  Other times, it's simply a description of what they know, don't know and want to know more about. This helps me figure out potential intervention and it helps the students articulate their own strengths and weaknesses.
Grouping:  I prefer to go individual with this one.
Optional Tech Tools: blog, podcast, video (to actually show the difficult part visually)

#13 - Student-generated Tutorials
Description: This works best as an enrichment activity.  Students might solve an algorithm and show the steps with a t-chart (hyperlinking the vocabulary).  Or they might show an example and give a verbal tutorial, taking pictures of each step along the way.  Finally, they might show it on the board and video-tape it.
Grouping:  Small group works well here, because it gets the entire group talking about the process and how to communicate it
Optional Tech Tools: You can use video, audio, presentation or photo editing software here.

#14 - Self-Assessment
Description: Students take a self-assessment of skills once a week in my class.  This doesn't tell me where students are at (that's what authentic assessments are for) but it lets me know how they feel about their learning.  I then meet three students a day and go over the data and their shared document as we plan future math goals.
Grouping:  This works well individually.
Optional Tech Tools: I use Google Forms for this one.

#15 - Conference Document
Description: The conference document is a shared document that has a chart (with the standard written as a student-friendly objective, the progress, my input, student input and any notes), a list of goals and a written record of our one-one-one conferences.
Grouping:  Individual with teacher
Optional Tech Tools: shared document

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

1. Great stuff John,

Fascinating how your teaching skills from social studies influence these ideas. I know you have shared this (or similar) before, but can you post a link to one of your Conference templates? I think seeing that is very helpful for understanding how your assessment works.

My team will be discussing grading next week and I am trying to balance PBL with SBAR.

2. Let me know if the link above works.

3. Lots of great ideas here, but can I suggest for #2 (Vocabulary) instead of drawing a picture and taking a photo (which would use paper) why not have students draw the picture using their computer, in a word doc for example, and avoid using paper?

4. You can also try Math Tricks for inspiration :
http://www.pedagonet.com/maths/mathtricks.htm