## Sunday, 16 August 2015

### Applying Types of Inquiry in Maths Learning

What type of maths inquiry do we employ the most and the least in our classrooms?

 Demonstrated Inquiry Structured Inquiry Guided Inquiry Open Inquiry Posing the question Teacher Teacher Teacher Student Planning the procedure Teacher Teacher Student Student Drawing conclusions Teacher Student Student Student

How can we veer away from the dominating structured inquiry approach in maths?

Looking at our first maths unit this year (below), I wonder what types of inquiry should be employed and when?

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Maths Unit

Central Idea:

Our base 10 number system evolved for a variety of reasons and led to place values that extend infinitely in both directions.

Lines of Inquiry:

° FUNCTION: How our Hindu-Arabic number system place values extend infinitely in both directions

° FUNCTION: How our base 10 number system works

° CAUSATION: Reasons we can multiply / divide whole and decimal numbers easily by 10, 100, 1 000 etc

° CONNECTION: Differences & similarities between our Hindu-Arabic and
other ancient number systems Eg, Roman, Egyptian,
Babylonian etc

° CAUSATION: Reasons the Hindu-Arabic number system was formed

° FORM: What the location of negative numbers in relation to zero is like

°CONNECTION: How we use negative numbers in our real lives

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As a lead in for the unit, we will discuss whether or not numbers really do exist or not. If all the people in the world suddenly vanished, would numbers still exist? I've done this in the past and its fascinating what children think about this and how they support their reasons. The discussion also leads to many questions they generate and quite a few obvious 'light bulb' moments as children realise maths is a concept, its not a concrete entity in their lives.

Then we will share theories we might have of why our number system is based upon 10. (A common and interesting theory is that it is because we have 10 fingers. Later in the unit, we will revisit this idea and the children will create their own number systems based on 3 or 7 etc imagining that is the number of fingers people had)

Presenting the Central Idea to small groups to generate questions they would need to know the answers to to have a deep understanding of the central idea will also allow an inquiry-based learning feel and student ownership to begin to form in their minds. These questions will be displayed beside the central idea and will be addressed as the unit unfolds.

Looking at the planner, perhaps I could allocate a different type of inquiry structure to each line of inquiry.....

Lines of Inquiry:

° FUNCTION:  How our Hindu-Arabic number system place values
extends infinitely in both directions
( Open Inquiry: Give students the beginnings of a number place value line with positive and negative place values. Individuals or small groups generate questions and devise ways to find out how place value works in both directions. Able to use laptops, manipulatives etc to explore. Share what we did and what we discovered)

° FUNCTION: How our base 10 number system works
(Guided Inquiry: Identify elements of our number system by analysing number grids etc. Discuss theory behind having a base 10 number system: 10 fingers. Provocation- What is people had 3 fingers or 7 fingers? Individually or in small groups, create a base 3 or a base 7 number system. How would it work? How is it similar or different to our base 10 number system? Share with class)

° CAUSATION: Reasons we can multiply/divide whole and decimal
numbers easily by 10, 100, 1 000 etc
(Guided Inquiry: Invite some students to show how we can multiply and divide numbers by 10 and 100. Students then enquire into the patterns and changing of place values when we multiply and divide by 1 000, 10 000 etc. Extend this enquiry further with finding out how this works with decimal numbers - money - and negative numbers)

° CONNECTION: Differences & similarities between our Hindu-Arabic &
other ancient number systems Eg, Roman, Egyptian,
Babylonian etc
(Open Inquiry: Provoke student questions by showing parts of ancient number systems. Groups generate questions they want to discover about a particular number system, explore and share enquiries)

° FORM: What the location of negative numbers in relation to zero is like
(Structured Inquiry: Look at temperature readings around the world where there is a negative temperature and explain its meaning using number lines)

° CONNECTION: How we use negative numbers in our real lives
(Structured Inquiry: Brainstorm and ask parents at home to collate ideas together for discussion)

Looking at this, I feel it is fairly student-centred as they will have quite a lot of opportunities to take ownership of their learning and it will hopefully set the tone successfully of the expectations in how their maths learning will be for the year......

1. What year level are you teaching?

1. Hiya, I'm teaching Year 6 (Grade 5). I've done similar with Year 3 before, just simpler version though of course. :)

2. This is great!! I'm looking forward to trying this! Thank you for sharing!

1. Hi Katie, Thanks so much for your kind feedback; I hope it helps :)

3. Graeme, I love the way you've sifted this great central idea for the different degrees of inquiry. I think I've shared before work we've done in Year 4 on this:
http://followinglearning.blogspot.fr/2016/01/how-we-wrote-numbers.html

If I were to repeat it, I'd want to see it through the lens of types of inquiry that you're using.

I found asking students to research and present a different number system or way of saying or writing numbers at home gave us lots of material to reflect on, and as there were families with different linguistic and ethnic backgrounds, often they could call on personal experience, or at least refer back to roots. Others chose to look at ancient number systems. Another thing that kids were really interested in was the soroban, the Japanese abacus, which is available cheap on the internet and basically uses the Roman number system.

What do you think? ...........