Tuesday, August 23, 2011

Active Participation Strategy: Let Go and Let Students...

Let go and let students...:   This phrase reminds teachers to put students in charge of their learning and in charge of explaining themselves. This practice incorporates multiple effective strategies to support student learning:
  • Give students the chalk or marker and ask them to come to the board or overhead to explain their thinking.   Resist asking students to tell you what they did while you write what they did.   Asking students to write as they explain allows them to organize their thinking and provides insight to teachers about what strategies and organizational methods students use effectively and independently.   This strategy also provides practice for the expected independent test performance.
  • Ask another student to repeat a student's explanation or insight.   Resist the urge to repeat or paraphrase each student's response.   Ask classmates to do this instead, fostering active participation/listening skills in all students.
  • Ask students to read directions or problems aloud rather than reading them yourself.   Once again, this practice encourages students to develop effective reading skills for math activities and tests.   If reading levels are an issue in your classroom, you might begin with buddy reading, pairing students to effectively mitigate this issue.
  • Ask students to define math vocabulary terms in their own words.   Post the best definitions around the room.
  • Post samples of effective problem-solving solutions that meet tough requirements of the problem-solving rubric you use to grade student responses.   Make overheads of student samples and review them regularly so that all students see examples of effective ways to organize solutions and explain thinking.
  • Expect students to be capable of some independent work.   Voice this expectation to students as in "I want to see how each of you does on Math Boxes #3 and #4 today, so please begin with those boxes.   I believe that everyone can do these by themselves and I will be around to check.   After you finish these two math boxes, you may do the others in any order you choose."
  • Quickly spin off students who are capable of independent work.   Provide enrichment activities that go beyond current grade-level expectations and require higher-order thinking skills for solutions.   Encourage these students to play harder versions of math games (i.e. more cards, larger numbers, etc.)
  • Differentiate and scaffold instruction to effectively meet the varied needs of learners in your classroom.   Provide enrichment activities for talented students while you work with small groups who need additional instruction or scaffolded support/encouragement during independent practice.   Use flexible grouping based on informal assessment of student responses during instruction.

More Active Participation Strategies

Download Mathwire's Active Participation Strategies for Math Classes:  a one-page text-only summary of the strategies discussed above.

Download Mathwire's Active Participation Strategies for Math Classes:  the full text of this section with pictures.

Monday, August 22, 2011

Morning Math Routines

Many teachers incorporate morning math routines into their daily math lesson.  The most popular activities include posting the date on the calendar, adding a straw or penny to the days in school count, tallying the day's weather, choosing coins for the date, etc.  These every day routines develop real life math skills and reinforce our base ten number system throughout the 180 day school year.

Mathwire offers a short description of the most common morning math routines for teachers to check out.  Your math series may also prescribe many of the same activities so be sure to read through the introduction of your teacher's manual for more information.  

Teachers use many different charts and organizational practices to streamline these routines, so Mathwire added a Morning Math Routines: Photo Gallery.  This photo gallery reflects how different teachers integrate these routines into real classrooms.  Teachers use many charts and varied organizational methods to provide visual cues for these important mathematical routines.  Hopefully, this photo gallery will provide ideas for teachers looking for different ways to integrate these mathematical routines into daily classroom bulletin boards.

Most importantly, however, is the student role in morning math routines.  Your goal, as a teacher, is to introduce and structure these activities so that students become the active participants.  Some teachers post names next to each station so that student leads the activity for the day or week.  Remember, that these activities are designed to build number sense in students, so it is imperative that students are in control and have the opportunity to demonstrate their understanding and proficiency in number operations.  Kindergarteners are capable of leading their peers and almost all students enjoy the opportunity to be teacher for a day, so let go and let the students take charge.  You'll learn a lot by observing.

Friday, August 19, 2011

What's Your Number Sense?


A person's number gut, or Approximate Number System (ANS), specializes in the "ballpark" figure rather than an outright calculation. It's what lets us see which grocery line in a store is longer, or which part of the movie theater has fewer people. Animals have this ability as well, without any training from humans: a bird picks the branch with the greatest amount of berries or a baboon decides he's better off not fighting a gang of six. The ANS empowers us to decide the most efficient course to take in everyday situations and may impact our performance in school mathematics.

Panamath measures your ANS through a simple task.  You're repeatedly flashed two groups of dots -- one blue and one yellow.  After each flash, you're asked, "Which one had more?"  This enables Panamath to calculate how precise your ANS is.   [from the Panamath website]

Try taking the free online test to measure your own number sense.  You are repeatedly shown a slide with blue and yellow dots for a very short time.  You simply have to say whether there were more yellow or blue dots.  You'll get a correct or incorrect response before moving to the next screen, so you know how well you're doing.  It's a fun experiment and you will get results immediately upon completion of the 2-part trial.

There's a lot of research on the site and suggestions for teachers who might want to use the test with students.  The basic premise is that a person's ANS (Approximate Number System) predicts his success in mathematics.   What do you think?

Try the Panamath Test.