Archive for the ‘inquiry’ Category

Open-Ended Tasks and Questions in Mathematics

In education, inquiry, math on September 13, 2014 at 12:28 am

One way to differentiate in math class is creating open-ended tasks and questions (I talked about several differentiation strategies I use here – Mathematically Speaking).

I think it is useful to clarify the scheme of mathematical problems – below I used Foong Pui’s research paper:

Problem types

“Problems in this classification scheme have their different roles in mathematics instruction as in teaching for problem solving, teaching about problem solving, or teaching via problem solving.”

1. CLOSED problems  are well-structured problems in terms of clearly formulated tasks where the one correct answer can always be determined in some fixed ways from the necessary data given in the problem situation.

 A.Routine closed problems – are usually multi-step challenging problems that require the use of a specific procedure to arrive to the correct, unique, answer.

B. Non-routine closed problems – imply the use of heuristics strategies * in order to determine, again, a single correct answer.

*Problem-solving heuristics: work systematically, tabulate the data, try simpler examples, look for a pattern, generalize a rule etc. Read the rest of this entry »

Inquiry: To What End?

In activities, inquiry, thinking on April 27, 2014 at 9:16 pm

This was originally supposed to be a simple reply to Aviva Dunsiger’s blog post. I soon realized it would have been too short and thus I could have been easily misunderstood.
It all started with my question: “How do these projects enable deeper thinking?”, question that I asked after seeing her students’ work. Briefly the sequence of activities was the following:
1. Students brainstormed questions to guide their research on natural phenomena.
2. In groups of 2-3 they would write a poem using onomatopoeia and personification in the context of their natural phenomenon.
3. Last, they would create artwork that showed the natural phenomenon they researched about.
At first glance, this is an interesting and engaging chain of activities. Yet, to me, the over-arching question was missing. To what end? What was the understanding the teacher wanted the students to have? How does each of the three activities help build a central powerful idea about natural phenomena?
I realized then that we adhere to different instruction theories: project-based vs. concept-driven learning. On the surface, many can mistake one for the other, especially since both use inquiry as a vehicle to construct understanding. Read the rest of this entry »

Patterns, Patterns Everywhere

In activities, inquiry, thinking on October 17, 2013 at 11:42 pm

This post was prompted by looking at  Aviva Dunsiger‘s Twitter stream – she is working on patterns with her students.  I would like to engage with her 6th grade class on Skype (my students are in 2nd grade) so we can do some Math together.

I am briefly outlining our inquiry into patterns last year so do not expect a “great” blog post.  It was written in half an hour!


I had 4 groups of students (red, blue etc.) and gave each group a set of 3 photos.


Question: What do these have in common?  Read the rest of this entry »

Mathematically Speaking

In education, inquiry, math, thinking on September 15, 2013 at 2:35 pm

Children love math. That is, when they are curious about it and succeed in their practice. I know, *that* is the difficult part: curiosity and success. How do you make sure both happen?

This post will outline some of the math we do in my classroom and I would truly appreciate teachers to question, add or comment on strategies I use.


Inquiry comes in different forms – from structured inquiry to spontaneous, it should permeate the math class. Creating an inquiry culture is hard work despite the widespread impression that it comes naturally and often with kids. The school setting itself is not conducive to curiosity – 20 or more students in the same room, lessons fractured by the bell, and the list can continue. Plus, children are *supposed to* learn in school – not a very appealing premise for wondering. Moreover, when questions arise they can be quite superficial.  That is why modeling questioning so as to become part of the class language and thinking takes time. Consistency is key.

Questions in a math class:

  • How do you know…? (by far my favorite) I gave an example here using my own students’ responses.
  • Can you give an example of…? 
  • What strategy did you use? Why is it effective? Read the rest of this entry »

Dancing Through Math Class?

In activities, education, inquiry, math, thinking on September 1, 2013 at 4:10 pm

*This post is a reply to a thoughtful educator that I respect and with whom I disagree on certain education-related topics. The stir began with my tweet,


I replied to Shawn,

Dancing in a math lesson will not improve thinking. THINKING advances mathematical thinking.”

A cute “engaging” math song might energize the kids but it won’t make them better at math. Surely, “memory is the residue of thought” and it is actually the main key to thinking (see D.T. Willingham’s posts on cognition and learning), but to use dance in 2nd grade as a way to memorize subtraction facts is not the most effective way. Despite the general belief that testing is damaging, cognitive science demonstrated that testing has a far greater impact than additional study. So if you want kids to memorize their number facts (so as to give space to higher-order thinking in solving problems) instead of making them dance it is better to allow them to self-test or to test each other in pairs.

Read the rest of this entry »