Open-Ended Tasks and Questions in Mathematics

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 More

Tracking Student Progress

This is a response to Damian Watson who asked me on Twitter to share some materials I created to keep track of student progress in math. I will, however, insert some photos, too, because some charts seem confusing without the aid of a visual.

I think it is also helpful to explain the process. (NOTE: These are my grade 2 samples.)

  • First, I check the standards (given in the school Math curriculum). They are the big picture of what is expected and it is good to know them. However, they only help so much.

Math 1

 

I correlate them with the report card objectives – as shown here Math – standards Read More

Inquiry: To What End?

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 More

Patterns, Patterns Everywhere

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!

1. PROVOCATIONS

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

Photo3591

Question: What do these have in common?  Read More

Dynamic Duos

Joy …children need to enjoy learning. As simple as that. It makes sense to *want* to learn. Effort…difficulty or complexity of tasks makes us think better. That can sometimes impact the level of engagement.
WONDER….encouraging and giving time for children to question; knowledge was historically built BY asking questions and wondering KNOW …building knowledge to be able to ask better questions and think better. You DO need to know things in order to think better. Read More