Developing Mathematical Inquiry Community (DMIC)

Today we had a PLD on Developing Mathematical Inquiry Communities.

Why we need to develop mathematical inquiry communities?

Only 26% of Maori students and 11% of the Pasifika students are achieving at Curriculum standards at year 8. Yet a high proportion of teachers indicated they felt confident in their teaching and that they are able to engage and meet the needs of their students.
Set our mindset out of the closed stages.

Exploring and challenging our beliefs, values, pedagogy and practices. 
Our beliefs about our students can affect our

• Perception of students status
• expectations of students
• teaching practices and decisions
• learning opportunities we provide

Does streaming in schools help?

Hattie says " we have more streaming than any other country in the world", we also have on e of the widest gaps between those who do well in our schools and those who do worst. The Pisa results worldwide suggest countries that stream less do better overall.

Streaming predetermines children's performance, removing challanges they might have faced in a class of mixed ability, foreclosing the possibility they might be a late improver, permanently lowering, or raising, their confidence in themselves.

Nothing boosts a child's confidence, or lowers it, more than educational comparisons with their peers.

What is DMIC?

• Culturally responsive teaching and learning
• Inquiry learning
• Developing rich mathematical reasoning ad thinking
• Proficient use of mathematical practices
• Social groupings and group worthy problematic activity.
• High ecpectations
• co- constructing teaching and learning.

What are mathematical practices?
They are the specific things that successful mathematic leaners do? These could be-

• Unpacking the problem?
• Applying the strategies to solve problems that may not necessarily be a maths problem.
• Making connections with their everyday life
• Being able to articulate what they understand.
• Using mathematical language
• Making a claim
• Developing a mathematical explanation
• Justifying thinking
• constructing arguments
• Generalisiing a mathematica idea
• Representing mathematical thinking using pictures, material and numbers.

Target students - where to at the end of Term 2

Today we had a Data discussion day and each teacher was required to present their teaching and learning journey for their target students.  All my target students were Maori students. At the end of Term 2 they are all AT the standard for Maths. Have a little peek through my presentation about what worked for my students.

Creativity with Maths - Part 2

Last week was a very busy week with open day at our school and so could not update on what happened to the idea of fraction games in my class. The games that they came up with were -

Quarter King wheel

Material required- A spinner

Students had to find quarters of the number on which the pointer of the spinner landed. This is a game where two students could play and the person who had game the most answers was the winner.

Thundering thirds

Material required: A spinner

Two contenders were required to play this game. The contenders had to be very good with finding thirds of the number. The one who gave the most answers was the winner. Students working on this game needed to find their numbers that could be divided into thirds. 

Four fractions 

Material required - Each player needed 10 counters. Counters of the two players needed to be of different colours.

This was is the game where the players had to choose a question and then answer it. The questions that were laminated were like - What is a quarter of 24? What is the half of 30? If a player knew the correct answer, he/she got to put a counter on the square that has the answer.

Fraction Ladders

Material required : four counters and a dice. If the dice landed on an even number then the player got to play and had to find quarters and halves of the numbers on the ladder. each player needed to complete two ladders. The winner was the one who completed the half and a quarter ladder first.

Students enjoyed trialling these games and felt that they needed to make some amendments to the rules and the numbers printed on the board games. 

I will update you on it in my next post, next week.
To be continued...

Recording and Reflecting

Lots of times Ashley and myself get involved in professional talks about Manaiakalani. This time we were talking about 'class on air'. It is a great way of sharing teaching ideas with the rest of the world.

So we decided to film each other and put our lessons on the blog.

It has been a boon to have two teachers in a class and recording each other was not a problem at all. We do not have great tools like the 360 degree camera and microphone to get the best quality, but we are so motivated that we are determined to record our lessons. 

My lesson was a short lesson on Number Talks. My question to students was " what do you know about 1/4 ( a quarter)? 

 This is my first attempt, so please be kind when leaving comments.

Reflection - After watching the video I realised that one students was dominant in the group. I should have encouraged other students to participate in the discussion as well. I should be incorporating more use Talk Moves.

Maths- Connections and Communication

Maths is a connected subject, but some students think of it as disconnected and isolated  from other subjects. Such students who believe that maths is a set of formulas that have to be remembered is associated mainly with low achievement. 

We use talk moves all the time in class. It allows us to communicate about the topic that we are learning. Since I have started using talk moves, I have noticed that my students are making more meaning of this subject and are becoming enthusiastically engaged in their learning of Maths. 

Today I gave simple multiplicative problems to my students. They had to solve the problems mentally and also explain how they had come to a conclusion. I noticed that some of the students could work out the correct answer but were not able to explain their thinking. One of the girls is very new to New Zealand and can speak only Samoan. There were others who felt intimidated and not so confident sharing their ideas in a large group.  

I wanted to honour these students who had solved the problem but were not able to explain their thinking. So I gave them time to think about mathematics. I put them into groups and gave them an opportunity to think and talk about what worked and what went wrong.

Students felt more comfortable in smaller groups and they could find a way to connect or ask questions about the parts that may be confusing or difficult to follow. 

During sharing time, almost all students in this group could contribute a little to explain their working. I was elated to see that each student who never contributed could gather courage to say something little. Though they were not very explicit but I think it was a huge effort on their part.

 Yes! I thought, 'Little steps at a time can make a difference'. 

  

Group worthy questions

This Term Sue Pine our facilitator for Maths has shown us how group worthy questions can be a great tool to encourage mathematical discussions among students. So Last week I gave group worthy open ended questions to my class.
The question was - There are some bears and they are going to the picnic in cars. Five bears can fit in a car. How many bears are going to the picnic.
There was lots of thinking, discussion and working out of problems using different numbers.  They drew their understanding of the problem on the paper. But as they became confident, they started enjoying solving problems and asked me to give them some pictures of cars. To my surprise they started to make their own questions using their pictures.
Initially,  students started by skip counting in fives and then slowly worked out their way to find answers to problems involving bigger numbers. For example 100 bears can go in 20 cars so 115 bears will go in 3 more cars and that makes a total of 23 cars. Language associated with multiplication like 'groups of' or 'time'  all became very clear to the students and the best thing was that they all taught each other how to solve the problems. it was a great lesson and I felt a very happy teacher. This is what students did in groups to solve the problems.

Number Talks

Number Talks were introduced to us by our Maths facilitator, Sue Pine. These are extremely easy to do and are of an immense value to our daily Maths programme. My co- teacher Ashley and myself devote 10 minutes of our Maths time to number talks everyday. During this time students are asked to work out a problem mentally in their head. It is interesting to find how students derive their answers. It gives an insight into what strategies students are able to use and how efficiently. It is always good to visually represent the different methods used by students as this allows them to learn  other strategies from one another and also allows students to show their mathematical thinking.

Here is what we did in our class to introduce number talks.
We asked our students what do knew about the 1/2.  The answers that we got are in the picture below.

Here is a video  from Jo Boaler that will facilitate the idea of Number talks further.

Getting them Motivated

Maths has become one of the favourite subjects of my students. They are happy to do Maths for a whole block and this is because they have experienced success in this subject. Maths is like addiction. Once you get it, you want to do more. However I have a few students who are not so good at Maths and feel a little bit discouraged because they are not the first ones to solve the problem. I needed to somehow get them motivated to solve problems. So I got this group on the mat for the whole block and started by what they could do. Our topic of discussion was Fractions.
We have been asked to start with a big problem which always got these students confused... so to get them going I started with very easy problems so that they could get motivated. The problems that I gave them were as easy as...
"Show me quarter of 8"
Students worked in groups and were given white boards and play dough to show their working out.
slowly they got what was meant by quarter and sixths and eighths...

Then I gave them the hard problems that I would normally launch to the whole class. The question that I gave is...

Everyone in the group got it.  This group further went on to make their own problems and not only shared them with the class to solve but also helped those who got an incorrect answer.

And they chose not to use equipment any more.

                                                                What a delight!!


                                                            MY REFLECTION

Sometimes it is important to show students what they can do to build up their self esteem.
I am a very happy teacher to see my students intrinsically motivated. Harder problems may throw a spanner in the wheels!