Mathematical Teaching Inquiry: Building on Students Thinking 2014

2014: My Mathematical Inquiry is centered around
Chapter 3 - Building on Students Thinking
Effective Pedagogy in Mathematics

This is a years roll out...
Starting January 2014 - December 2014
Please be patient as you scroll to the latest update.
It just seem odd to blog it all backwards!

I mentioned my  2013 Math Inquiry on this blog when I was first wondering about the potential legacy that Sugata Mitra's ideas may have on 21st century teaching and learning practice. This years inquiry has me working towards being more explicit in my understandings. The greatest difference between 2013 and 2014 Teaching Inquiry is my establish maths program called Maths Like a Pirate

The Inquiry process as a pictorial:

Questions I think about are:
What does building on student thinking mean?
Who does the building?
Questions of student agency
What is being built? 
Whos knowledge is being valued?

Theses questions remind me of Michael Young's talk titled
Powerful Knowledge, Knowledge of the Powerful 

When I think about building on student thinking I am wanting to maintain constant focus on the role of the digital trends as explicitly identified by CORE Education
Further to the digital trends is a powerful and thought provoking blog post  by 

The three questions are:
1. What kinds of things do we focus on for our inquiry?
2. Do we all have to use the same platform to share our learning?
3. How do we chose what to capture as evidence of our e-learning inquiry?

As my Math Teaching Inquiry is using e-learning in multiple ways, I'm thinking about the three questions as I work towards a dynamic relationship between my program Maths Like a Pirate and e-learning.

Remebering, as  Karen States:
" The tech is merely the enabler - the engine-  while the curriculum and pedagogy are in the drivers seat."

For this teaching Inquiry, my understanding of 'Building on Student Thinking' has two pathways....
1. Starting from the knowledge that the a student has and through 'learning progressions' building individual thinking.
2. The second understanding is about the importance of building student thinking with others. The key is to create something new by working with others. 'Utilizing the third space' The spaces in between. Taking into consideration the role of knowledge in the 21st century.

Both understandings are needing to nudge into play the understanding that Students are no longer consumers but producers of knowledge.

I am reminded that Bereiter, C. (2002) 
Believes that if education
 is to participate in the knowledge age then,
our conceptions of "knowledge and mind
need to change."

My Inquiry Question:
How can I use students mathematical knowledge to engage in tasks and conversations that relate to everyday experiences and problems?

Questions (from Te Toi Tupu)
Focus on the Inquiry
What should my students achieve?
Where are they in relation to the school's goals and priorities?
What do they need to learn next?

Teaching Inquiry
Which teaching strategies will support the students to achieve the identified outcomes?

Learning Inquiry
What learning happened for the students?
What will we do next to ensure that they continue to achieve?

How will you address the Inquiry in your class? 
What steps will you take?

Continue explicit improvement of online maths collaboration  Maths Like a Pirate

Term one:2014

T1Wk:1 Preparation week

Circumstance: Making buns.  Asked where is the Maths. They replied counting. Probed asking What did that sound like. Used 1:1 match only
Action: Placed an equation on each tray eg 2+2+2+2= Can you make the buns on the tray look like this equation?
Result: Groups raced each other to make 4 groups of 2 on the tray. As well as students counting in 2s. One student decided counting in fours was going to be alot more fun, the result was the others followed!

Circumstance:  Students not able to explicitly talk about where they see maths in the living world.
Action: I showed the class our movie trailor Epuni Gardens, Lower Hutt, Wellington 
I asked where is the Maths?
Result: Students immediately saw patterns in sunflowers and in the numbers of seeds. A highly distractable student ran out of the classroom and brought back a large dried sunflower head and the class made many maths knowledge connections. 
Kupu Hou = He Kai ‘aahuhanga’ Geometry!

Circumstance: Students doing Number problems in small groups. I asked How did you find your solution? Their constant response was in my head. I guessed. And yet.. their solution was correct.
Action: I tried one of the questions offered to me by our facilitator Phoebe from Cognition Education to help nudge this inquiry.  Q. What other way can you solve this problem?
Result: A roll out of speaking of different strategies by all the students. Inspired by student voice!

Circumstance: During Pirate Challenges students language was limited when reflecting on the questions afterwards.
Action: Showed the Pirate Movie Trailer Seussical Pirate Challenge Movie created by @ugafrank & @21stStacy. We then looked at the images from when they did the challenge. Asking what is the same what is different in how we all did the challenge. And.. Why do you think the two classes  have done things differently?
Result: Stunning result with students completely engaged with language around same and different. As well as applying inference when thinking about why.

Circumstance: a little unsure what best to focus on during Pirate Challenges:
Action: Explicit about what is being assessed when doing Pirate Challenges. Focussing on CORE Education conversation about Student Centered Approach To Assessment
Result: I was able to distil responses to the challenge. Focussing on problem identification and improving ideas. Students starting to say..” I can see a problem with…”

Circumstance: Regardless of stage/ ability Students are forgetting to start from the largest number when using addition.
Action: Students created a Mathematical art work 9I was remembering the importance of STEAM) The art work was of Sharks. Each Shark had a different set of silver teeth. Each set of silver teeth are set as even numbers.  The art was to amplify  the importance of counting on from the largest number. I told the students a story about pirates going fishing to catch two sharks to make fish and chips for the crew.  Pirates Remember, Always catch & count on from the shark/mako with the largest number of silver teeth!
Result: Students focussed and discussing the silver teeth. There were conversations around doubles of numbers which was led by the students when creating their Shark. As the art was worked on independently through out the day, I heard students taking maths! I was surprised and very excited. I have learnt and somehow forgotten the importance of using art to communicate number knowledge.

Tweet tex

Circumstance: Students starting to use Math language 'count on from the biggest number' as well as using the strategy. However, still requiring practice.
Action: Chose to continue practicing using the context of sharks teeth and made contact with @SharkyJillian A Shark expert on twitter. To ask how many teeth did sharks really have. To see what numbers were we really dealing.
Result: @SharkyJillian has offered to take a Math lesson on Sharks! Exciting Term 2 Maths Planning Number Knowledge and Strategy 
Context: Sharks!
Let me know if anyone else is keen to join us. As we will use @SkypeClassroom

  • you can email me and we can connect for a sharky math lesson!

  • T1Wk:9
    Circumstance: Students had difficulty in identifying small and large numbers. 
    Action:  Used lego blocks to show a number. eg. a tower of five blocks, a tower of 10 blocks. Which number is biggest? Which tower is biggest? Increased the numbers. Replaced the word biggest with the word largest. Made this into a game.
    Result: Students showed increased confidence when  identifying small and large numbers. Students had alot of fun!

    Circumstance: I realized students did not know that the words biggest and smallest were part of mathematical knowledge
    Action: Created a daily Mathematical vocabulary brainstorm as part of morning 'hotspot'. 
    Result: Students contributed the following words: square, circle, plus, minus, less, difference, measurement. Students were very unsure about mathematical vocabulary and almost shy to contribute.

    Circumstance: Students continue to be unsure of their mathematical vocabulary.
    Action: Continue with Daily Mathematical Vocabulary brain storm in the context of their Pirate Challenges!

    Daily increase of identification and use of mathematical vocabulary! Huge Success!
    Will do this activity for a whole week, every third week of term 2.

    Base line vocabulary at start of the week - 16 words

    and then there was...

    Term Two 2014

    Circumstance: Students who I expected to be settled were unsettled.
    ActionDecided to do a JAM assessment on students who were the most disengaged. Needed to check was the base line data still correct.
    Result: Base line data indicated a need for extension

    Circumstance: Attended a Key Note Address to the Wellington Mathematic Symposia by Suzzane Chapin. Focussing on the importance of mathematical language.
    Action: Based on new base line data I started fractions with my students. I asked my students to use the word fraction in a sentence. Or to use the word "quarter' in a sentence.
    Result: Ihaia said. "If I had four squares and I chopped them all into quarters how many squares would I have?" I had no idea Ihaia knew how to apply fractions.

    Circumstance: Students were showing signs of becoming disengaged with the weekly 'bun making'. Placing the buns into rays eg 2 + 2 +2  / 4+ 4 + 4 / 5 + 5 + 5. This has been a very effective way of students applying theri number knolwedge. However, I am wanting to maintain application of Math knowledge as motivating and energizing.
    Action: Shifted bun making with focus on number to making pizzas with the focus on fractions.
    Result: Students talking about cutting their pizza into 1/2, 1/4, 1/6. Students cut cooked pizzas into their desired fraction! Stunning response. 

    Circumstance:  Using @googlehangouts_ the class connected with @MsLombardoClass in CANADA. 
    (We use  @googlehangouts_as it is more stable than Skype and is cost free for CANADA.) 
    We played two games. Guess my Math number, focussing on the language Greater than / Less Than and Guess my Math Word.
    Action: @MsLombardoClass chose a word we did not know. The word was 'odd number'.
    Result: Students wanted to know what an odd number was and after the 'Google hangout' conversations continued about what was odd about a number. Our next learning steps were introduced to us by our new friends in CANADA. We were all a little bit excited and started talking about just how far away is CANADA? So we did a little bit of standard measuring!

    Circumstance: Following up from term one. Time to collecte base line data on knowledge of Mathematical vocabulary.
    ActionBase line data of Mathematical Vocabulary colected through out the week.
    ResultsDaily increase of identification and use of mathematical vocabulary! Huge Success! Largest number compiled was 57 words in ten minutes! 
    Will collect again in week nine of this term.

    Circumstance: School closed for most of the week due to teaching staff attending EDUTECH in Australia.
    Action: NA
    Result: NA

    Circumstance: During the Math Pirate Challenge,'Build a Bridge' students were asked to use their language and knowledge about fractions.
    Action: Students started talking about their bridge in relation to fractions! They also started talking about how they were building parts of cubes!
    As evidenced in captured student conversations.

    "I started creating my bridge by folding a piece of paper in half." - Ihaia

    "There are 18 eggs in total on our bridge. Half of 18 is 9. We know this because there are the same amount on each side." - Leah

    "Ideas for designing this bridge came from @MsEsClass in CANADA. Our Bridge works with fractions. Can you see a half? " - Devin

    " You've got a bit of a cube going on here." Ihaia

    Result: This Math Pirate Challenge was one of the best pirate challenges to date. Students were successfully applying their knowledge of fractions and attributing the start of their ideas to influences out side of the classroom. The students are starting to realize that using their Math Knowledge they can start to improve on other students ideas.

    Circumstance: Extending Fractions work into number knowledge. Context making model pizzas.
    Action: After students made pizzas from dough, students then  made card board models of pizza that were sectioned into fifths. Each student given 10 paper olives and 10 paper tomatoes to share evenly on each fifth of pizza.
    Result: Students who understood the activity talked it through with the rest of the group. Answering questions. Students who understood  were able to use language that referenced back to when they had pizzas with their families and the importance of sharing the toppings. When asked how many tomatoes on one fifth of their pizza most students knew there needed to be two.

    Circumstance: Based on the importance of idea improvement and returning to a similar task. Students continued with new pizza models. This week the Pizza model was in thirds.
    Action: Each student was given a pizza divided into thirds, with 6 paper olives, 6 paper tomatoes and 6 paper pieces of salami to divided evenly amongst the whole pizza. Each student completed the activity confidently. As an extension, each child was then given a different number of pieces of cheese to divide evenly over the pizza. Eg. 24 pieces of cheese. (depending on the students number knowledge abilities)
    Result: Students speaking confidently about pizzas and fractions. Specific conversation arose from the kinds of fractions commercial pizza shops cut their pizzas and how the topings are shared. There was alot of debate about wether the local pizza shop cut pizza into eighths or sixths! Math vocab from this activity was written down and placed around the interactive white board.

    Circumstance: During the Math Pirate Challenge Building a Bridge WK 6 I asked a group how did they come up with the idea of using a structure of a cube to help create the bridge. The answer was, "We mixed our ideas together and we started to make a cube." - Leah. Based on the idea of change I wondered what else the students could work with where change would occur. Aim: To be explicit in our math about change / shift.
    Action: Introduced a "Matariki- Maori New Year" paper folding activity that involved working with fractions. A piece of paper started as a rectangle and changed into a diamond. Four diamonds, placed together create a star!
    Result: Whilst doing the activity students were able to identify mathematical language used during the activity. eg centre line, half, quarters, corners, line. Students used the math vocabulary to explain the instructions to their peers if they were unsure of the next step.

    Completed Star images are on their way.
    Watch this space!

    Term Three 2014
    My Mathematical Inquiry is centered around
    Chapter 3 - Building on Students Thinking
    Effective Pedagogy in Mathematics

    My central objective for term three is for each of my students to improve in their additive strategies.
    All the students are wanting to get faster at their basic facts.
    Base line data = JAM test and anecdotal evidence. 

    Students first day back from holidays and I wanted to find an activity that would allow them to use their fractions vocabulary and introduce them in a playful way to their term of  'amplified additive strategies.'
    Made oragami, guess my lucky number games with simple single digit addition and subtractions inside.
    Students spent 20 minutes testing each other.It was Maori Language week so they played the game using maori language vocabulary.
    The second result was,  when folding the paper they used their math vocab from term 2. Vocab used: line, half, centre, corner, quarter, triangle, square.

    No launch pads. A happy math humm.



    Circumstance: The students find subtraction difficult. 
    Action:  Created number problems using their marshmallow challenge images.
    Result: Students were fully engaged in working out the difference in the number of marshmallows used to build a tower. I will continue this strategy - it was an energetic lesson with a lot of laughter form the students and a lot of effective problem solving.

    Circumstance: Whole class playing online mathematical games. Sometimes children say the games are too easy.  I heard two children talking together about how they can do these number problems in class but not on the computer and why is that?
    Action: I was very excited to hear them recognize their learning needs. The game I had set for them were subtractions of less the 10. I talked with them about their discovery of their learning.
    Result:  The two students understood they needed to practice and apply their number knowledge in lots of different contexts. The students communicated Increased optimism as they could see they were working towards improvement.

    Circumstance: Students are working on place value partitioning. They are learning to expand two and three digit numbers and are getting a bit confused.
    Action: Introduced Bubble Gum Maths. I mimed chewing and stretching bubble gum and talked about how bubble gum and maths had a lot in common. I said we were stretching numbers today, making them look long! That the other word for stretching was expanding!
    Result:  Tremendous discusion about bubble gum, 100% instant accuracy when expanding three digit numbers, that they asked for four digit numbers! So I tossed a few in. It was one of those beautiful moments in maths when everything just made sense. 

    Circumstance:  Every Wednesday students  engage with  an online math programme called SUMDOG There is an going conversation about the learning choices we all make.
    Action: Before logging in, I asked the students: 
    Why do we play SUMDOG? 
    What do you think would be the most useful activities for you to play and why do you think that?
    Result: Students talked about prioritising hard games over easy ones. Furthermore, students said they were going to work on the games that used plus and minus as they knew they wanted to get better. One student asked, Why is it I can do all my basic facts in class but can't do them so well on SUMDOG? I was excited to hear my students thinking about their learning and realising that there was value in practising the same skill in different contexts.

    Circumstance:  I am unsure if a couple of my students are really seeing the patterns of numbers. I often ask how did you get to a particular answer and they  reply it was just in my head. With further probing it is often difficult for students to find the mathematical vocabulary to discuss their work. I also wonder how much they can image. Although achieved within a JAM assessment I feel a need to keep checking in on this skill. I am reminded of a slide in a Fractions presentation by Phoebe at Te Toi Tupu Cognition Education. The movement from materials - to imaging - using numbers.

    The Strategy Teaching Tool

    Action: This week we worked with double digits using blocks of ten and single blocks. As well as sticks of old fashioned chalk and a lot of carpet space.

    The two students I was concerned about were able to identify and build two digit numbers and see patterns using their addition skills. All the students were engaged and enjoyed doing their number work on the floor. When using their mathematical vocabulary there appears to be a mix up in understanding what a set is and what a group is. The interchanging of these words may be acting as a speed hump to moving forward. How many groups of ten are in the number 22?
    The other result: Cleaners were not so happy. Next time use white chalk and do it outside!
    Will certainly be doing this activity many times in different ways. 
    A great warm down may be to show a number using cubes and students to find it on the hundreds board.

    Circumstance: Participated in a Place Value (PV)  Workshop by Phoebe at Cognition Education
    Action: Played a, fast paced, stunning PV game with Playing Cards. Called Pyramids.
    Result: Played PV Pyramids as the warm up and students were completely engaged with the fast paced nature of the game and quickly started using their mathematical language to describe, ones, tens, hundreds.  My students would say I have the biggest number. My number is 623. My number has 6 one hundreds,  2 tens and 3 ones. 
    (I will find the game instructions and post here - this game is an absolute must. Great game when all you have is a pack of cards and so easy to extend into larger numbers and decimal work.)

    This photo is off seniors playing the same game. 
    The game is extended by adding a decimal. NOTE: little plastic pig = decimal! 

    I need to add here in WK 8  
    The class participated in THE DOT CLUB International dot Day.
    finding fractions and number patterns  using dots for

    "My number is 12. 
    1/6 of my dots are blue". Leah

    Circumstance: A class in Canada, who we connect with in @MathsPirates wanted to  Mystery Skype the class. (Its a new school year in Canada, so new children) My first thought: Ok, so where is the maths? How can I make this work as a valuable activity to be doing in our Math time?  Answer: Students to focus questions around, Measurement:  time, distance, seasons, temperature and money m
    Action: Students wrote mathematical focussed questions.

    Result: Students took turns asking Questions using their mathematical vocabulary. One student at the end of the Mystery Skype said we could have added a Geometry question. We could have asked what shape is your country. Is your country look like a square or an oblong? I was very happy that students were again seeing that Math is every where and time and its relationship to world time clocks is a significant part of our lives. Students talked at length that when it was a 9:00am on a Spring day in NZ it was the end of a summer afternoon in Canada. Mystery Skype with Math focus was stunning!

    Circumstance: The whole term has been to focus on increasing basic facts. I'm also interested to learn what  Term 2 Mathematical Vocabulary has been retained.
    Action: This week - Basic Fact testing and daily Math Vocabulary warm ups. (JAM and 5 minute word blats)

    Here is where I dropped the ball.

    No comments:

    Post a Comment