I am definitely one of those dissatisfied teachers that people talk about; in a good way! I love what I do, but always feel that I could do better. On many occasions I have walked out of the classroom laughing about something great that happened during the lesson, while also thinking about something else I would do differently next time.

I have been lucky enough to be involved with Ithaka Project, which began in 2004 2003 with three Melbourne schools who came together to give their teachers an opportunity to reflect on and improve their teaching. The project has grown and evolved over the past seven years and has been much influenced by Ron Ritchhart (Ritchhart, R,2002) and his colleguescolleagues at Project Zero, Harvard Graduate School of Education. [For more information, see http://ithakaprojecthistory.pbworks.com] During my four years of involvement with the Ithaka Project group, I have been givenhad many opportunities to think about my teaching, my classroom and the learning of my students. Every time I attend a conference, hear a presentation or read an article, I realise there are just so many areas and practices that I would like to improve; to the point that I often become overwhelmed.

Early last year I was invited to be part of this Stories of Learning Project. At our first session Ron gave us a couple of prompt questions about expectations:

•What expectations guide my teaching practice?

•What expectations change and develop my teaching practice?

•How do these expectations influence my current struggles, focus, wonderings and grapples?

•

He then asked us to write for an hour in silence. How often do we teachers have the luxury of such time? And so the day continued; prompt questions followed by generous blocks of time to simply write and reflect.  By the end of the day, not only was I exhausted, but my head was swimming with all the changes I would love to be making in my classroom and to my teaching.

Generate….

•Connections – deeper understanding – embedded understanding – understanding the hows and whys rather than looking for a “correct answer”

•Using peer and self reflection

•Improve the feedback I give my students

•Different approaches to how I teach

•The use of Thinking routines

•Helping students explicitly state their thinking

•Developing resilience in my students

•Engagement – I want my students to be excited about maths and what they can achieve and understand

•How do students feel in my maths classroom?

•The importance of the language of maths to help them discuss and explain their understanding and their questioning

•

Where to start? Literally theThe more I thought about it all, the more there was to work on. So to combat those feelings of it all being too much, my plan was to try and focus on one main goal each year. Admittedly I have been known to get distracted from the goal, but at least it made me feel better in those moments of reflection and planning! I began by sorting through some of my goals, which was a task made more difficult because of the interconnectedness of so many areas.

Sort….

•Connections – deeper understanding – embedded understanding – understanding the hows and whys rather than looking for a “correct answer”

•How do students feel in my maths classroom?

•Improve the feedback I give my students

•The importance of the language of maths to help them discuss and explain their understanding and their questioning

•Helping students explicitly state their thinking

•The use of Thinking routines

•Using peer and self reflection

•Engagement – excited about maths and what they can achieve/understand

•Different approaches to how I teach

•Developing resilience in the students

•

Last year my main focus was on pre-testing. I have come to really value pre-testing in the last few years. It is important to build on what students already know. Pre-tests have helped improve the focus of my teaching, as well as helping me differentiate my teaching for different groups of students. However, when I took a closer look at my pre-testing last year, I realised how I had been focusing on skills and processes, rather than on connections and understandings. For example, if a student wrote the wrong answer to a multiplication of fractions question, was it because they didn’t know how to multiply fractions, or had simply forgotten, or made a silly mistake?. After trialling some different combinations of extended answer questions, open-ended questions and skills questions, I developed several pre-tests that I am more confident help me to identify what students do and don’t understand. I also use them to help students begin to engage with the new topic; I make sure to include questions that all students can answer (to some extent). For example, at the start of the measurement pre-test I ask students to list things we measure, and how they are measured. These are questions that all students can access at their own level. (You can read more about my pre-testing journey at (give a reference to the online version of your story!)

http://storiesoflearning.com/Middle_School_Stories/Entries/2010/12/6_And_in_the_Beginning__Rethinking_Pre-Testing_in_My_Maths_Teaching.html)

At the end of my year of focussing on pre-testing, I was reflectingreflected that my students commented to me that there were a lot of tests in my class. I guess they were pretty right, when I considered pre-tests, surprise quizzes (the use of the word quiz instead of test didn’t really fool them!), notified tests and end of term tests. With the help of a colleague, I’ve now come up with the new name for my pre-tests: WITIKAs (What I Think I Know About). It is surprising how quickly the new name has caught on with my class this year. At the start of each new topic in the second half of the this year, the students will have been asking “Are we doing a WITIKA today?” I like the idea that a WITIKA is really about connection; I am helping students to connect in with what they already know (or more correctly what they think they already know).

While I do have many facets of my teaching that I would like to continue to improve, the more I think about it, most come back to connections in one way or another. Pre-tests are really about students connecting back to previous learning. And at the beginning of this year I decided work on helping students make the connections within and between topics in my class.

In the past couple of years I have been using a version of the Generate, Sort, Connect, ElaborateGenerate-Sort-Connect-Elaborate thinking routine (http://pzweb.harvard.edu/vt/VisibleThinking_html_files/03_ThinkingRoutines/03d_UnderstandingRoutines.html )(link to Visible thinking website with the page for GSCE, just the first time you refer to it) to help students make connections within and between topics. So I have considered the question:

Can the use of thinking routines like generate, sort, connect improve students’ understanding of connections within and between topics in maths?

Towards the end of Term 1, as we concluded our Number unit, I began a Generate, Sort, Connect, ElaborateGenerate-Sort-Connect-Elaborate with my Year 7 Maths class. Together we made a list of all sub-topics we had covered in the Number topic; there were quite a lot when we began to list them! I found this an invaluable exercise on its own; encouraging students to remember how far they have travelled in a few short weeks. Students were then asked to sort each of the sub-topics based on their importance to the Number unit. For example, if they felt understanding Factors was integral to the Number unit, they were asked to write Factors very close to the word Number in the centre of their page. If they thought that Place Value was not so important, they were to write it closer to the edge of the page. Students were then asked to draw lines between sub-topics that they believed were connected. For example, if they thought that they needed to understand Multiplication and Division to understand Multiples and Factors, they would draw a line between these sub-topics.

Students spent some time in class beginningbegan their sorting and connecting in class, and were then asked to finish the task off for homework. As students began their work in class, I wandered around the room asking them to explain their placements. Some students were more confident with their responses than other studentsothers; some need guidance with their decisions and help to remember what each of the subtopics were about.

Some of examples of the student work from late Term 1:

Example 1

Figure 1: Student example work Number 1

I think this student has shown some good thinking and connections. She made the connection between Multiples and Square and Cube Roots, which not all students were able to see. However, she has missed the conenction between Multiples and Index Form. I wonder if part of the reason for the students missing this connection is that she has listed them on opposite sides of “Number”.

Figure 2: Student example work Number 2

This student has not made any of the connections yet. While I generally agree with his sorting, it would now be interesting to see what connections he can make.

Example 3

Figure 3: Student example work Number 3

It is interesting that this student has not connected Estimation, Place Values or Other Number Systems with other sub-topics, but has been able to make connections between many of the other sub-topics. I think she has made some good initial connections, and shown a good understanding of most of the sub-topics, but there are still many more connections she could make.

Ideally I would have liked to spend more time on this exercise. I would have liked students to pair up the following lesson and share and compare their sorting and connecting. I would have then given them an opportunity to amend their own work, if they had wished to. Finally I would have asked some of the pairs to share with the rest of the class. I think it would have been interesting for the students to compare their answers as a group, and have a discussion about why they thought different pairs had different answers, and was this ok? Unfortunately, the follow up lesson never tookdid not take place. I definitely have it on the agenda for next year!

During Around the middle of the year, I took the opportunity with my Year 7 class again to consider all the topics we had visited so far during the year using Generate, Sort, Connect, ElaborateGenerate-Sort-Connect-Elaborate again. As a class we again generated a list of the units we had covered. This time in pairs, students sorted, connected and started to elaborate on their connections. As there were fewer units than there had been sub-topics in the Number Unit, the sorting was much quicker. Students then began to consider how the units were connected. For example, in our Measurement unit they decided you needed to use knowledge and understanding gained in the Number unit (basic operations, place value, order of operation etc.). The conversations within and between pairs were very interesting; they very quickly began to discuss connections that had not occurred to me.

This was quite an exciting moment for me. If students could begin to understand how units of work were connected to each other (not all units with each other, but that there definitely were connections between many of the units), I felt like we were answering that always niggling question “Why are we learning this?”, without having to explicitly give an answer. Students were beginning to make those connections for themselves!

Some examples of student work from early Term 3:

Example 1

It is interesting that this pair has effectively listed Decimals and Fractions as one topic, when we listed it as two topics as a class. The pair has, however, also noted how they are connected. I wonder if this in an indication of how closely connected the pair believes the Decimal and Fractions topics are. I think this pair is shown the initial signs of some very good connections (eg Algebra – coded numbers/patterns/unknowns).

Example 2

Again, there are some interesting initial signs of connections (eg both Algebra and Measurement use patterns. It would be good to further explore this pair’s understanding of Decimals and Fractions; I wonder what they mean by Decimals and Fractions are “part of a number”.

Example 3

It is interesting to note how far away from “Math” that this pair has written Algebra. I wonder how their understanding of and confidence with Algebra has impacted on their decision to list it so far from the centre.

Although it wasn’t really one of my intended focuses for the year, the other area that has caught my attention (I did mention in the beginning that I can get distracted from the original goal!) is the idea of connections within the class; as inin other words, how students feel in my classroom. I don’t know that I havehave never ever intentionally planned how I would like students to feel when they are in my maths classroom. However, in recent years, as more teachers have been in my classroom for one reason or another, many have commented on how supportive and warm my classroom feels. People have even asked me how I created this. And to be honest, it was only then that I began to think about it, and be more intentional in my creation of the environment in which I teach. Part of the conclusion that I have reached is that it is all about connections. Students need to feel connected to each other and to me. This does not mean that they all need to be best friends, or that I need to be “friends” with them (as such), but rather they need to feel known, valued, supported and, ultimately, connected to that class.

Connect……

Elaborate……

During this year I have been lucky enough to be part of new program that my school launched late last year. I was invited to spend three weeks in outback North Western Australia, at a studio school set up in partnership with the local community. The studio school is built on 1.3 million  (REALLY??) acres of land. It was an incredible experience, on many levels. During the visit, we created a new community made up of some 20 students from Melbourne, 19 local Aboriginal students, and 12 staff. While we did not try to run “normal” school lessons, we did run several “sessions” each day. Trying to encourage the local students (who in the main do not attend school regularly) was a real challenge. However, there was also so much to be learnt from their reactions. On reflection, it was really like the reactions of students in any classroom at my school in Melbourne, but magnified. If a local student felt insecure about taking part in something, rather than just hide hiding in the back of the classroom, they deflected, walked off, or gave us a few harsh words. What came across as aggression, was really their sign of insecurity. When one of the skilled staff members took time to coax, explain, help, and scaffold, most students would reengage. Trust needed to be built. The local students needed to feel comfortable, confident, connected. Much more so than Melbourne students that I know, the local students did not want to be seen to not know, stand out or need help. It was only after creating moments of success, connecting what we were doing to what they knew and creating connections between people, that we slowly gained some cooperation from them.

My experience in Western Australia is really the subject for another time and paper, GOOD _ NEXT YEAR?? but there were definitely lessons and reflections from my time away there that have connected back to my teaching in Melbourne. Students everywhere are really not that different. Emotionally all humans are wired similarly, the fact that students are alike wherever we find them should not be surprising. As Sylwester (Sylwester, R. (1994) asserts “we know emotion is important in education-it drives attention, which in turn drives learning and memory.” How a teacher is able to make any student feel is important; only when the student feels comfortable and connected are they able to learn as effectively as possible.

While we were in Western Australia, the Executive Director of the Studio School, Ned McCord, wrote and shared a story about Coacher Mustering with us. As well as his work with us, Ned also runs a nearby Cattle Station, and while he does an amazing job helping drive a very new endeavour in education, he is much more comfortable talking about cattle than students. However, the analogies he draws between the Coacher Mustering and student learning are very insightful.

“The aim is to mob up the cattle so that they can be educated to move as one mob….To start with you have a mob of quiet cattle, meaning cattle that have had the opportunity of having had some education. We call this mob the coachers…..It is important that they can work together and that there is cohesion in this mob of cattle. It is also equally important to remember that the staff and horses you have been allocated to do the job will contribute to the success or failure of the muster…….As we move the coachers or educated cattle around the paddock strategically to cover the area that is to be mustered, the free range cattle are brought in….At this point, the Coacher Mob have to open up and let the free range cattle join the mob. Once the free range cattle are part of the mob, the coachers have to accept them for who they are and where they have come from….Every now and again you will get a calf that runs away from the mob. One must learn not to chase it as it will only run further with fear. It is better for the coacher mob to stay together and the calf will not run far and will soon realize it is safer with the mob than on its own and will return to the safety and comfort provided by the mob.” (McCord, N. (2010)

FABULOUS

Students have the potential to have much influence on each other. As a teachers, it is our job to try and harness this influence to improve the students’ learning and understanding of our students. There will be times when a student loses their way, feels lost or separates, but if the culture of the classroom is united, focussed and engaging, the lost student is much more likely to connect back into the group.

In conclusion, as each new group of students come into my classroom, with their different experiences, feelings and understandings, I too approach each new class with different hopes and focuses. While the list of what I would like to achieve with, and improve on, in my teaching is long, taking the time to sit down and think about what is important to me as a teacher and why, and then prioritising that list, has helped me feel like I am more focused on doing one task effectively. In the past I have been more inclined to try something new for a little while and then quickly move onto the next thing; whereas now I am more likely to trial and refine, revisit and reflect on, improvements that I really see as valuable.

My trial of using of Generate, Sort, Connect, ElaborateGenerate-Sort-Connect-Elaborate was a good beginning this year, but I would have liked to have given more time to it (but such are the demands of a busy school life). Next year I will use Generate, Sort, Connect, ElaborateGenerate-Sort-Connect-Elaborate again in my maths classroom. Even inf the short time that I gave the routine this year, there were invaluable discussions. Hopefully, by finding more time to give to the routine next year, I will create the opportunity for students to further develop connections and to be  able to do so more independently.

I believe that connections are a major key to success in any classroom. Students need to be able to create and see connections within the learning that is happening in any given subject. However, they also need to feel connected to that class emotionally. Whether those students are in the outback or in a private school in Melbourne, their fundamental needs are not that different; connectedness is definitely one of those needs.

While I have begun to explore connections this year, I would definitely like to give this concept more thought next year. However, I think I will move on, knowing that my next focus is probably connected to connections anywayNext year, . I am ready going to explore this concept in relation to consider feedback; how I give feedback to my students; the he different methods I use I use, how effective it is and how I make themstudents feel when they receive it. There is much more for me to learn and explore as a teacher, and to help achieve this unending goal, it is important that Ito continue to focus on connecting the connections.

References:

McCord, N (2010). Yiramalay Coacher Mustering.

Ritchhart, R. (2002). Intellectual Character: What it is, why it matters and how to get

it. Jossey-Bass. San Francisco.

Sylwester, R. (1994). How Emotions Affect Learning. Educational Leadership Journal.

Websites:

http://storiesoflearning.com/Middle_School_Stories/Entries/2010/12/6_And_in_the_Beginning__Rethinking_Pre-Testing_in_My_Maths_Teaching.html

http://pzweb.harvard.edu/vt/VisibleThinking_html_files/03_ThinkingRoutines/03d_UnderstandingRoutines.html

http://ithakaprojecthistory.pbworks.com/w/page/34244604/The-Ithaka-Project