CristinaM.

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 and THINKING

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?
  • Is… always true?
  • How is… similar to/different from…?
  • What if we changed….?
  • How is this connected to…?
  • How does…work?
  • What is a real life example where we could apply…?
  • Can you prove…?
  • Can you explain the solution to…?
  • Can you show a different way to solve this problem?

BIG IDEAS

Try to make students aware of the big picture in math. Whether it is place value (as I showed in the previous post), fractions or other concepts, always link to real life applications and other disciplines so that the children can see their importance, to value mathematics and connect with the world around them.

My favorite strategy is Jigsaw Groups because it engages the entire class. Write the questions on different papers, assign a color to each group and let them think. Clap hands (or use another signal) and the papers are switched with another group. This can only be a starter – keep the papers onto the class wall so students can add more throughout their exploration (use post-its).

*This year we are going to design posters, too – the idea occurred to me when seeing these math posters. Problem is, I don’t want them to be completely teacher-made so I will engage the students to help me (I will do the formatting but the content/ideas should be pulled from them).

*Here is another sample of how we explored the importance of numbers – student-generated answers (2n grade, first week of school) – What If Numbers Vanished?…

Numbers vanished

DIFFERENTIATION

Differentiation can be done in many ways. Some that I use are below:

1.      Differentiation through questions/math problems

a). OPEN-ENDED tasks

They allow for a full participation – both from students with relatively low math skills as well as from those who are more confident. The choice of numbers can range from 2-digit to 4- or 5-digit numbers so all students can actively contribute to the Math Talk afterwards.

A single word or very few can turn a closed task into an open one. Examples below:

  • (closed) There are 316 animal books in the library. 118 books are about dogs. The rest are about other animals.

(open)  There are ____ animal books in the library. Most books are about dogs. The rest are about other animals.

Questions: How many books are about other animals? How can you add to show that your answer is correct?

  • (closed) What is half of 20?

(open)  10 is the fraction of a number. What could the fraction and the number be?

  • (closed) How much is 3+4?

(open) Show at least three  ways to get 7.  (Answers can vary tremendously, from easy ones such as 5+2= 7 to 2X3+1= 7 or 100-93=7)

  • (closed) Ten ducks were on a lake. Two of them few away. How many ducks are left?

(open) The answer is 8. Create a story-problem to get this result. (Again, the students can choose not only a variety of mathematical operations, but also easy or difficult numbers to play with.)

b). PARALLEL tasks

Although the core question is the same, the students can choose, again, the difficulty level. This way you don’t hold back some children or push others far beyond their current ability. Besides, their own choices reflect what they are comfortable working on – use that as DATA to inform your future teaching.

E.g.  Option 1: There were 23 students in a class. 10 of them went to the library. How many are left in the classroom?

Option 2: There were 223 students in a school. 123 left for field trips. How many are now in the school?

2.      Math Matrix

The students can go any direction so long as they go through the middle (your key task, your lesson focus) – they will complete just 3 tasks out of 9. (See example from my 2nd grade math class – click on picture to enlarge it)

matrix

3.      The Ladder

Simply create a 4 -5 “ladder” with increasingly difficult tasks. The base is compulsory (again, it is your lesson focus and all students should do it).  Allow students to choose level (see another example from my 2nd graders).

ladder

*You can color-code tasks, too, but I try not to use that strategy – some children might find it threatening and will always choose easy levels, even below their capacity just to make sure they do not fail. (More on motivation here)

4.      Menus

I am sure everyone is familiar with it:

Main menu – 1 task that all students need to work on

Side dish – 3 tasks and students can choose 2 of them

Dessert – 3 tasks and students *may* choose one (or none at all)

*See sample

Math

5.      Math stations

Although students go through all math stations (below you have several examples on place value), each station has “challenges”, too, so that students can work with more difficult tasks if they choose to.

pizap.com13791849320221 - Copy

COLLABORATION

Practical ideas:

1. Design a challenge (with partner/group) for another team
2. Create a math test (student LOVE this – besides, it saves me time to create a test!)
3. Think and build a math project 
4. Teach your peers (see previous post)

*See pictures – student-created challenges, I printed them and posted them around the room. Each kid could go and solve any and as many as s/he could within a certain amount of time (it was Halloween hence their funny outfits!)

pizap.com13792474939941

PRACTICE

Obviously I cannot list all the possible ways but here are some:

  1. Math stations (for instance, just for place value understanding we had 10 different stations)
  2. Games (class or online games)
  3. Group problem-solving
  4. Peer practice (like number facts that I talked about in my previous post)

………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………..

Humor, of course, should not be missing. Being a good thinker does not prevent one from smiling!

Photo5036

……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

A few people I recommend following are listed here with their Twitter handles – you will also see their blog links in the profile. They were the ones that inspired me and made me think.

You can also read my post on provocations – there is a math example there, too.

  1. Love the open questions, 7 is the answer, what’s the question. It could go on all day. All week even!

  2. A broken calculator is useful, take away one or two buttons for example ‘x and 2’ can you show 3×2? Any standard problem will require new thinking.

    Mr E (North Yorkshire, Eng).

  3. Great provocation, Mr. E. I’ll challenge my students to do exactly that.

  4. […] class is full of lively conversations, games, open-ended problems, and  inquiry. See some of that here  or here […]

  5. […] 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). […]

  6. […] Open-ended tasks and questions are ideal for that ( I wrote about them here and here). […]

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: