Teaching as Inquiry: Maths Mentoring

Staff Meeting Spirals of Inquiry 13/2/18

Today I was mentored by a maths expert. She observed my use of Developing Communities of Mathematical Inquiry and gave great recommendations to improve my teaching. See the next steps below!

Attitudinal Data - Draw how you feel in Maths time

    

Almost students drew themselves appearing happy, and some drew their partners, also with happy faces. One drew and said "bored, angry and sad" (child with additional needs); one drew himself happy but his partner (mentioned prior) as angry; one drew a frown with "too easy." I have adapted my prompting to better extend or support individual children, and altered two partnerships as a result of the attitudinal survey.

Teaching Focus	Active listening Discuss and role-play active listening. Use inclusive language “show us”, “we want to know”, “tell us”. Emphasise need for individual responsibility for sense-making Affirm models of students actively engaged and questioning to clarify sections or gain further information
Big Idea	Students may use using words, numbers, symbols and pictures. to represent grouping and counting strategies (L1-L2 Equations & expressions) Students may count by one or count on (L2 NUmber strategies) Numbers can be partitioned and combined to solve simple addition and subtraction problems (L2 Number strategies)
Problem	There are 10 ducks in the pond. 6 are green. How many are blue?
Conjectures: Possible strategies/ solutions/ misconceptions	* Students may count all or count on * Students may not be aware that the final number is the total amount * Students may know number bonds to ten * The commutative property e.g. 4+6=10 so 6+4 =10 (those highlighted are ideas that the children showed) What also happened:  *Some children are still developing an understanding of partitioning and recombining (i.e. they said “there are 6 blue ducks,” but needed support to add on 4 more and reach the total of 10)
Independent	Pairs use materials and make combinatinos to ten using only green and blue (penguins, blocks, beads). How many different ways can you make 10? Day two: students to discuss and draw a scene e.g. ocean, farm, etc
Formative Assessment	See Notes - hard copy
Reflections & questions	After day 1 * I am concerned about anxiety e.g. E& P: P said "I feel worried because I don't understand" Partner understands and tries to explain, but P still confused. * Chln are not readily discussing the problem, e.g. one leads other follows but doesn't understand - A& A: one understands, the other, "The ducks went out in the rain" * Independent group was unfocused and noisy. Tomorrow I will try and active listening drawing task for them and model taking turns, listening and agreeing decisions together. * Distractions e.g. E& D: E drawing faces (independent time) FOR THE FOLLOWING LESSON 20/2/18 Independent activity: discussing and drawing a team picture/scene This was beneficial. We modelled what great groups look like: sharing pencil, talking, listening, taking turns NEXT STEPS ·       *   Provide lots of restating in a positive way e.g. “Say it again” “there were how many ducks?” bring active listening into other areas in my teaching ·        * QUESTIONING/REPHRASING: not “what is the problem,” but “what/when/how many were in the STORY?”. Do more resharing/explaining e.g. ask multiple times, “so how many green ducks?” “how many altogether?” etc ·        * Have a clear idea of the possible big maths ideas e.g. for the duck problem, it could be that there are various ways to make ten OR counting all OR counting on OR writing a maths equation to show your thinking OR the commutative property. ·        * Use the children’s learning in sequence when sharing e.g. have the children who drew and counted all share back first, the ones who counted on share back second. It is ok to annotate and expand on the teacher whiteboard, once students have shared. ·        * It is ok to jump in on the teachable moment, e.g. the mentor saw a child writing 6 and 4 = 10, so drew the plus sign for them and explained this. ·        * Be clear about the group NORM at the start of the session. I would love to develop these with the team, but ideas include: sharing the pen, listening and responding to what your buddy says, not getting distracted with socks/pens, explaining to your buddy at the end, asking your buddy to explain it back to you. Revisit the NORM at the end of the lesson. ·        * If one child is dominating the pen and the other sitting back confused, give the pen to the child who is sitting back and say to the other child, “you can tell him/her what to do and explain as you go” and observe. ·        * TOMORROW: Re-ask the question to focus on the commutative property. “There were 6 blue and 4 green ducks yesterday. How did we show that? Today there are 6 green. There are 10 ducks altogether. How many are blue?” Our norm will be avoiding distractions.

25/2/18 Term 1 Week 4 Co-teaching and co-planning with Dorinda
We are trailing a shared planning approach, and then co-teaching our students. We have the shared norm of active listening. We have brainstormed and selected independent activities, and will adapt to ensure students are on task with Maths work and that the noise level is acceptable.
Reflection with students after day 2 of co-teaching:

1/5/18 Term 2 Week 1 Mentoring with Liana (DMIC Advisor)
Liana's comments are in red.

New planning framework

Math Focus Classroom Norm	Place Value: naming and ordering three digit numbers (H,T,O) * Shared responsibility for sense making * Turn taking (talking, listening, using the pen) * Explaining ideas back to the group/partner Liana commented that I did this cohesively, linking the big idea and the classroom norms with a game (adding fingers to ten) in buddies. Inclusion was provided as all students were actively using the norms, and many were called on to share their strategy or reasoning back to the group.
Big Idea	Digits in any column are worth ten times as much as those in the column to its right, for example a 7 in the tens columns represents 7 tens, or 70, while a 7 in the ones column is worth 7 ones, or 7. An understanding of the decimal system and how to use place value is an important part of all further number understanding (NZ Maths Key Ideas)
Problem	Some of the numbers have fallen off a number line. Use your knowledge of hundreds, tens and ones to put them back in order. Discuss: number line, order (high to low).  Next time I need to use a known context and create a story e.g. some runners were racing. They each got a number for the order they finished in. Line up the numbers in the order they finished. A story gives the children context and familiar language for discussing the maths at hand.
Conjectures: Possible strategies/ solutions/ misconceptions	Students order using correct place value Students focus on the largest single digit e.g. 298 vs 892 Students are unsure how to name 3 digit numbers Other things that came up in the session:  * Two students were challenged with naming numbers e.g. 798 was read "7 - 9 - 8" rather than 7 hundred and 98.  * Some students used the end number to order e.g. saw 289 as higher than 982.
Independent	Students are given a selection of 3 digit numbers to order. Making Connections: I need to work on adding this section into our maths sessions. Students need to start making connections to the big maths idea at hand (Similarities/Differences; Generalization; Introduction of Strategy, Addressing Misconceptions)
Formative Assessment	See hard copy
Reflections & Next Steps	*  All pairs worked well together, taking turns with pen       * Some needed prompting to talk as they wrote down their numbers i.e. say why they were putting it where they did using place value language        * I will explore making numbers using base 10 materials, then naming and ordering with students later this week, to clarify misconceptions        * Future learning in line with needs: naming numbers; naming ten more/less than a number; naming how many hundreds/tens/ones in each number; trading; counting on from largest number when adding               Work towards a shared discussion / debate next, where students justify and argue their reasoning for ordering numbers in the way they have.