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:

“Problems in this classification scheme have their different roles in mathematics instruction as in teaching ** for **problem solving, teaching

**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

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.

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

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

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.

Question: **What do these have in common? Read More**

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 |