A book I had forgotton..

I suddenly remembered a book I had used a few years ago for ideas for open-ended investigations (It All Adds Up by Penny Skinner).  It includes worked examples from students of investigations and Maths Reports and gives some ideas for pedagogical practices that fit with the course.

Here are some examples you could try:
Addtition
What happens when you add numbers ending in 9 to numbers ending in 3?
Investgate what happens when you add 2-digit palndromes such as 66+ 77 or 77+88+99
Investigate what happens when you add 3 consecutive numbers or  3 consecutive even numbers or 3 consecutive odd numbers:

Investigate what happens when you begin with any 3 digit number, reverse it and add to the orginal. Repeat until you have a palindrome.

Subtraction
Wht happens when:

• you subtract a number ending in 7 from a number ending in2?
• you subtract a number  ending in 25 from a number ending in 26 eg 426-225?
• you subtract a number  ending in 26 from a number ending in 25 eg 525-126?

Using the digits 1,2,3 and 4 once only. make pairs of 2 digit numbers and find their differences eg 43-12. Which pair give the smallent difference and which the largest?

Choose 3 different digits and form a number beginning with largest and finishing with smallest. Write the number in reverse and subtract eg 832-238. Now reverse the answer and add it to the answer, so
832-
238
594 +
495
1089
Try it!

Multiplication
Investigate what happens when you multiply:

• numbers ending in 4 by 6
• a number ending in 13 (113, 213) by 6
• 142857 by any single digit number up to 7
• a number ending in 7 by 13

Investigate multiplying odd numbers by odd numbers, odd by even, even by even
Investigate the series: 11x18, 21x18, 31x18...
Investigate the multiples of 99

Decimals
Use a calculator to convert sevenths to a decimal 1/7=, 2/7=, 3/7= etc.
What do you notice?

Let me know if you want to borrow the book!

Session 4:Teaching for a Growth Mindset

I really liked the idea of agreeing norms around teaching for a Growth Mindset and this would be great for us to discuss as a group- ideas around visualisation (how much do we do that?), around asking children to explain their thinking, to convince others, to persuade and argue.
I really liked the video of the classroom where the students were figuring out 1 divided by 2/3. It really showed the students that were relying on some kind of algorithm and the students that were really trying to visualise the problem.

The idea of the open-ended questioning comes up and of course if we are using inquiry this is nothing new. abut again-how often do we really see it in classes? Often as an assessment at the end, but not always during the actual teaching part of a unit. I really liked the lesson plan about the CCTV camera and think that structure offers a lot for us in Primary to think about-giving the problem individually first, having discussions about the answers, looking at sample answers. I think it can be so vauable for teachers to discuss together student work and try to see what the student was thinking.

Luckily we are not in a school that gives grades or uses setting for abilities but it is good to have this grounded in research. I think we have some work to do on feedback and agian this could be something we begin as a group.

Finally I think it gives us some food for thought about the hidden messages we send children and how mindful we need to be about so many elements of our work- the classroom environment, classroom management, grouping of students, individual vs group work, feedback, etc etc etc.....!

Session 3 : Mistakes and Persistence

I think it is true that students see making a mistake in a very negative light-they can look crushed if they have got something wrong. I think it can be a challenge to turn that round in the upper primary and I think it is a challenge teachers in the earlier years need to rise to- teaching children that mistakes are part of learning. Parents do get the idea though that you are saying it's OK to mke a mistake and not really care about that so there is also a challenge to ensure that the message is that mistakes are OK as long as we work them through. I guess this is linked the second idea in the session around persistence.

The idea of the Didactic Contract was new to me. In some ways it reminded me of the constuctivist idea of scaffolding learning but I guess the message here is that teachers can 'over-scaffold' in order to help students get to the 'right' answer.

I was interested to read more about the role of 'speed' of calculation in Maths and I think many people do think that those that answer quickly are better at Maths. The idea of that being quick with an answer means you are 'smart' is one that resonates with me. I am a slow processor! I like to take my time to think things through. I like to read things at least a couple of times before committing to an answer or an opinion. I think it is so important to give students time and to make sure that those with their hand up first aren't always the ones we pick on to answer- this relies on mindful classroom management.

Session 1 and 2 Reflection

The main ideas that I learned in the first session that I plan on making use of in my classroom are how mathematics is about playing, wondering and imaginations. Students should be playing games, solving puzzles and using their reasoning skills which are more natural mathematical experiences than being told how to do something. Students learn by doing, by having their own ideas, opinions and reactions, by being given a chance to be curious. They will learn far more this way than being told how to solve something. The article at the end of session 1 that framed music and art being taught the way mathematics is taught was really eye opening for me. It made me realise that there is definitely a different way that we could be teaching math. We need to ask better questions that are engaging and allow students to engage in the art of mathematics instead of telling them how things work and letting them plug the numbers in.

The main ideas that I learned in the second session are:

Brain plasticity - all students can achieve the highest levels in math with the right teaching and messages.

Fixed mindset vs growth mindset - how a fixed mindset holds students and teachers back from their potential and how a growth mindset can be developed through effective "mindset messages" and praise that inspires growth.

Also, just the fact that so much research backs up these claims yet it isn't being implemented despite it's significant findings.

I would like to foster a classroom of growth minded learners. It is so vitally important that all students believe that they are able to understand mathematical concepts despite their current abilities. It's exciting to know that research has shown that drastic  changes in mindset (and the actual structure of the brain) can be made in as little as 3 weeks.

Session 1 & 2- Maths & Mindsets

Let's get to the nitty gritty...

1.   Words are powerful and can have a long-lasting effect on students.  Various stereotypes and myths surrounding maths influence how students see themselves, either positively or negatively.   As an educator, I need to be mindful of the messages I share with my students.  Additionally, I need to give qualitative, feedback and meaningful praise to ensure that students feel confident in their math abilities, as it is this kind of encouragement that will help to establish a positive attitude towards maths.

2. The way in which math is being taught in some schools needs to change!  Math needs to be viewed as an open, creative subject, and students need to be provided time to create their own understanding of the concepts being taught. Memorization of math facts and times tables is where you often loose student engagement- keep them interested by providing real life problems to be solved and maintaining a playful, amusing, flexible, and creative learning environment.


In the second session, we were asked the following question:

If your school took on the mindset evidence seriously, what would need to be changed?   

My response to this question was positive... and simple. Although I am relatively new to ISZL and the framework of the PYP, I feel as though the language used in the Learner Profiles and Attitudes already supports the development of a growth mindset.  Teachers and students across the grades are regularly referring to the positive character traits and descriptors, such as risk taker, committed, confident, perseverance, independence, respect, etc. This language is visible in every classroom and as a result, teachers are more conscientious of the language being used to describe learning behaviours... and students become more familiar with the use of positive language to describe their own learning behaviours and experiences. With that being said.... more professional development and training is always beneficial.... so bring on the growth mindset training.

Here are my reflections from the first two parts of the course...

I am excited about this course. I'm beginning to think about the 'messages' my students have already heard about their maths learning and more importantly what messages I may be giving both verbal and non-verbal to my students. I am aiming not only to make maths enjoyable but also accessible to all my students. To have open ended tasks, an inquiry based approach where there isn't just one right answer and where the student's thinking is valued. I think it is important to have the children work collaboratively in varied groups and to present their thinking to others.

I have been fascinated by what I have learned about the brain and the research that supports the fact that every child can do well in maths and that every learning experience can change a child's ability in maths. Working with young children, I feel it is even more important to give them the right messages for a growth mindset, to encourage perseverance that they can learn from their mistakes and to be careful with the use of praise.