How often do you think about what students might be thinking about when they are learning?
If you’re like me, the extent of your thoughts might be limited to what the students will ‘do’ in a particular task, not what they are thinking about while they are doing the task. You might even be thinking…
Is there even a difference between the doing and thinking?
Surely kids are thinking while they’re doing?
Stick with me, but consider this statement…
Do you remember learning to drive? Recall how intensely you were thinking and concentrating on each and every gauge, the pressure on the pedals, how close cars were in the adjoining lanes, how low the radio needed to be to concentrate The task of learning to drive is an excellent example of repeatedly thinking about things and committing them to memory.
Daniel T Willingham’s expands on this important idea in his book, Why Don’t Students Like School? He notes,
To teach well, you should pay careful attention to what an assignment will actually make students think about (not what you hope they will think about), because that is what they will remember.
While it goes without saying that we cannot control what the students are thinking about, it begs the question, are the tasks that you are planning, planned with consideration of what the students will be thinking about while they are doing the task?
I am wondering whether we help or hinder our students in the pursuit of creating that perfect rich, open and challenging mathematical task? I have seen many tasks where their clarity has been muddied because the mathematics has gone missing in amongst distracting information and unnecessary requirements.
One of the ways we may consider this is the use of a Mathematics Activities Analysis Page – a planning template that teachers can use to be purposeful about what we want the students to notice (and think about) during a particular task.
An insight I have when I am asking this question or responding to the question myself, is that it often reveals the task to be a performance task or a learning task.
Is it necessary to make this distinction? I believe yes.
In tasks where students simply perform, they often aren’t using, or being given the opportunity to use, their acquired skills to think deeply about the content and transfer to a new context.
However, tasks where students are encouraged to think more critically, creatively and make connections, that is, tasks where the challenge is desirable, the likelihood of retaining learning is greater. In the same way as learning to drive a car on a busy street, such tasks are desirably difficult.
There are a few things that I’m attempting (albeit in a clunky way) to convey.
1) We need to be thinking deeply about the tasks to be able to remember them at a later point.
2) In planning, it is worth thinking about what the children might be thinking about while they are engaging with the task.
3) Tasks need to be desirably difficult for us to attend to them.
The following is an email that I have sent to all K-4 staff at school. I’ve been moved by an experience I saw during one of my visits into a Stage 1 classroom and felt compelled to put some words to it.
Good afternoon all,
This week’s mini-PLM comes in the form of a quote from Reuben Hersh, an American mathematician and academic. He maintains that Mathematics has a front and a back. He notes,
“the finished product of mathematicians belongs in the well-ordered and more-or-less highly polished front of mathematics while the back is the area where mathematicians are busy engaging in but often practically fruitful activities of mathematicians.”
While it may be difficult to think of our littlest students or even most vulnerable students as mathematicians in the vein of Rueben Hersh, his point was at the fore of my mind after hearing a S1 girl grapple with her understanding of faces on 3D shapes, in particular a sphere. It was clunky, with moments of dialogue between students and teachers. There was silence, coupled with sentences that began small snippets of conjecture. All equally enabled by the students, teachers, the class environment, and curiosity.
It would have been far cleaner and easier to grab control of a such a conversation and steer it directly, but my point is, this was true mathematicians work. In this experience, each learner (teacher, too) had access to the front and back of mathematics. And it didn’t come through a pre-loaded worksheet where the content and process was delivered by teacher to the ’empty student’.
My final thought is this: do we value and make space for both the formal, precise and abstract front , AND the messy, intuitive and often clunky back side of Mathematics?
Enjoy your week.
Hersh, R. Experiencing Mathematics: What Do We Do, when We Do Mathematics?American Mathematical Society (2014). p.35.
This is the second of my personal reflections based on Jim Knight’s ‘Instructional Coaching: A Partnership Approach to Improving Instruction’. Jim outlines seven principles that frame the work of partnership instructional coaching, which are:
Engaging in dialogue
Today’s thought is about ‘Respecting choice: Teachers should have choice regarding what and how they learn’.
One of the things I have been wrestling personally about myself as a developing coach, is to what extent are the teachers who I am working with reflecting upon and naming their own next steps for learning. If it is truly a partnership approach, my actions and words must begin from a perspective that each person in the partnership is equal and that knowledge can be co-constructed through dialogue.
So has choice looked like in the context of my role at St Luke’s?
In prepping to work with teachers at the beginning of the term, staff had the opportunity to reflect on an area of their practice that they felt as though needed developing. For some, this looked like developing mathematical tasks that was both challenging and open. For others, it was more about how to launch an investigation without “talking the children out of their curiosity”. Whatever their self-identified need was, my next step was meeting with staff individually or in small groups during planning time to unpack the why behind their goal. More often than not, it was an area that I had also identified. Through collaborative discussion, we named:
what evidence we may collect to determine success;
what time will there be for modelling and observation; and finally
when will we reflect on the process to determine our next steps.
At the first instance, choice was provided. The path forward was shaped together and co-constructed to honour the professionalism that is inherent in our Foundations staff. Without the choice the professionalism is bypassed and there could be a breakdown in the ownership of the goal, process and consequently lower student learning outcomes.
This term has been effectively my first coaching rodeo, or at the very least, the first where I have strategically thought about the process of coaching. These posts may seem like fragmented ramblings where I am trying to make sense of the duty, calling and honour it is to lead staff in such a manner, but it just seems so morally correct to begin from the platform of relationship in leadership.
Have you worked with someone who has operated from a platform of relationship where choice and equality were pillars in the relationship? How did it feel?
Conversely, what about times where choice has been withheld or taken away? What did it feel like?
Do you know how many students in your spaces are learners of ESL/EAL-D backgrounds? What percentage would it be? 20%? 30%? 40%?
In our particular context at St Luke’s, it is more like 50-55%. This has significant implications for the planning, teaching and learning of Mathematics in our spaces. You cannot separate the teaching of mathematical content from the language demands of Mathematics. To plan for, and teach, mathematics with the greatest chance of learning, you will need to acknowledge the challenges that this proportion of students brings.
In short, good teaching of reading and writing is not enough for the development of literacy skills. The better these children can speak and understand English, the better they can read and write it. You may have even heard of the saying, reading and writing float on a sea of talk.
Consider this statement, “By some estimates, ELLs (English Language Learners) spend less than 2 percent of their school day in oral interaction. Teachers must find ways to engage them in productive talk.” (Walqui and Heritage)
This begs the question, what does productive talk, i.e. talk that has depth/rigor, is student led and talk that is sustained, look like in the your Numeracy block?
One way that we can not only support EAL/D-ESL learners, but all learners is through Talk Moves. Talk Moves help faciliate productive talk opportunities and can be used across the curriculum. I have attached a bookmark that you may keep close to you in your programming or print and place near your numeracy work area.
Your challenge is to reflect on your practice in mathematics, and plan to use one or more of the moves this coming week. I’d love to hear your thoughts and how the students responded.
Meaningful Classroom Talk-Supporting English Learners’ Oral Language Development by Aída Walqui and Margaret Heritage
Let Them Talk To promote ELLs’ literacy growth and content-area achievement, don’t neglect their English oral-language skills, by Wayne E. Wright
Talk Moves: A formative assessment strategy for fostering productive probe discussions by Page Keeley
I am trialling some alternate ways to distribute information that may help the programming and teaching of Mathematics with our staff. This week I emailed and shared in our Google Community, Noticing and Wondering- one of my favourite routines in the school day, not the least in the Maths block.
Wondering what noticing and wondering is? So is this guy….
Put simply, there should be opportunities for children to be noticing and wondering and verbalising these in the course of the mathematics experience. Amie Albrecht defines this routine beginning with “asking two simple questions: ‘What do you notice?’ and ‘What do you wonder?’. These are powerful prompts to engage students. ‘Notice and Wonder’ helps lower the barrier to entry for all students. It encourages sense making. Students are more invested because they are connecting their own thinking to the scenario and are generating questions that they are interested in solving.”
While a bit old now, this video greatly encapsulates the power in encouraging questions that engage curiosoty, such as in the notice and wonder routine. And I love the theme, our children are just waiting for us to ask.
Where can you include the notice and wonder routine? In your warm up, in one-on-one discussions with children, during reflection time. Anytime is a good time to notice and wonder!
OPTIONAL CHALLENGE! Show your students one of these images, and ask “What do you notice?” “What do you wonder”. Try not to do much of the talking- simply listen. Share your noticings and wonderings with me when you’re done.
There were many things that I needed to have certain in my mind for me to be successful in the role of Numeracy Instructional Leader- K-4. I knew that I could always be more sharp in my content knowledge, and I had recently developed an interest in common misconceptions in early years learners.
I had heard the term ‘learning coach’ before. I had heard the term ‘instructional leader before’. In reflection, I probably had been doing elements of these roles in previous leadership positions. But now I was officially an instructional leader. My mind boggled with questions and wonderings…
What does it mean to be a coach or IL?
What type of IL will I be? A good one? Will I know if I am not very good?
What if people won’t work with me?
How do I listen better?
Where do I start when working with teachers?
What if I don’t have an answer to questions?
How do I have tricky conversations with people?
Then by happenstance, I began following someone called Jim Knight on Twitter. I followed some chats through the hashtags #educoach #instructionalcoaching, and there was a great buzz about Jim’s works, and in particular a text authored by Jim Knight. I ordered it, and read it over the duration of the Easter holidays. The book is titled, Instructional Coaching: A Partnership Approach to Improving Instruction (2007).
In order to understand my role as a leader and a coach, I was looking for something to have as a theoretical platform in my new position at St Luke’s. One of the opening chapters called ‘What does coaching look like?’, Jim features a quote from Devona Dunekack, an instructional coach in the USA.
“I am first a teacher. My job hasn’t changed, but my audience has. Now I teach teachers to use strategies and routines. My job is to still impact kids, but now I do it by helping teachers be as focused and effective as they can be” (p.19)
I . AM . FIRST . A . TEACHER
There it was. Words that I wanted to still be told, to hear and believe. I had spent 10 years learning to teach children, with the last 3-4 being the most influential years of my career thus far. Upon reading those words, the Instructional Leader shirt began to feel a bit less uncomfortable and more like one that I can really see myself wearing.
Jim’s book details the essential skills required to be a coach, and while not definitive, they do give me a great starting point. As a part of this starting point, I will be beginning a series of reflective posts in response to one of the main themes in the book- The Partnership Philosophy. This philosophy represents seven principles underpinning instructional coaching. The principles which “we base our actions on have very practical implications” (p.38). and help to provide “a conceptual language” (p.40) to frame the work of coaching. These principles are:
Engaging in dialogue
My thoughts today will focus on the first principle: recognising equality.
In this section, leaders and teachers are equal partners in the work they do to drive student learning. Without believing that teachers are professionals who have valid and equal thoughts, ideas and opinions, and instructional leader cannot be in ‘partnership’ with their colleague. The playing field is uneven, heavily skewed towards a relationship where the leader is all-knowing and the teacher is awaiting the one-way, controlled flow of information from the coach. This relationship (if it can be called this), has been a professional learning model adopted the world over, and unsurprisingly hasn’t always succeeded. Furthermore, CEDP has created a document entitled Transformation Journey where it acknowledges that teachers and leaders are learners, affirming this with the words, “Each school is a learning community and a community of learners”.
My reflection is that knowledge can be shared and co-created when partners recognise the equality in the relationship. Where one may offer mathematical content knowledge, the other may offer the intricacies of dynamics amongst students in this class. Together, through the shared knowledge, new understandings are created. One was not more important than the other, and each needed each other.
Remembering that I am first a teacher will ground me in the understanding that I can learn from my colleagues, as much or if not more, as they may learn from me.
Knight, J., 2007. Instructional Coaching: A Partnership Approach to Improving Instruction. SAGE Publications.
On Saturday 30th April, I and two others from SLMP attended the MANSW Primary and Middle School Conference. The theme appealed to me as soon as the advertising began to roll out.
With speakers like Dr Paul Swan and Katherin Cartwright, I was hooked. What I wanted most was the language to speak, promote and lead the unpacking of reasoning back at school.
What is reasoning?
From the rationale of the NSW Syllabus…(emphasis added)
“Mathematics is a reasoning and creativeactivity employing abstraction and generalisation to identify, describe and apply patterns and relationships. The symbolic nature of mathematics provides a powerful, precise and concise means of communication. “
From the Mathematical proficiencies, found in the Australian Curriculum, again emphasis added…
“Students develop an increasingly sophisticated capacity for logical thought and actions, such as analysing, proving, evaluating, explaining, inferring, justifying and generalising. Students are reasoning mathematically when theyexplain their thinking, when they deduce and justify strategies used and conclusions reached, when they adapt the known to the unknown, when they transfer learning from one context to another, when they prove that something is true or false, and whenthey compare and contrast related ideas and explain their choices.”
A generated word cloud allows one to see the core skills behind what it means to reason.
Through the power of nifty visuals, it is neat to see that the term reasoning is at the centre alongside the word students. But are our students actually reasoning? Do we recognise their moments? Are we even creating the environment for reasoning to occur? From here on, I am going to discuss how to promote dialogue as a means of reasoning. I acknowledge that there are a number of other areas, such as classroom culture and learning environment design, and planning challenging tasks (all of which are interrelated with dialogue) that also help engage reasoning skills, but for the purpose of this post, reasoning through communication will be explored.
Planning for reasoning through communication
During the planning phase, teachers make decisions that affect instruction dramatically. They decide what to teach, how they are going to teach, how to organise the classroom, what routines to use, and how to adapt instruction for individuals
Fennema, E., and M.L Franke. “Teachers Knowledge and Its Impact.” In Handbook of Research on Mathematics Teacher and Learning, edited by D. Grouws, pp. 147-64, Reston, Va: National Council of Teachers of Mathematics, 1992.
It makes sense to view the planning stage as the field in which to sow the reasoning seeds. However, this comes with a rather large caveat…don’t expect children to reason if you’re doing all the communicating or you are restricting the ways in which the students can communicate their understanding. You could even go so far to say that communicating is the channel in which reasoning can occur.
It is known that teachers ask many questions in the ebb and flow of the day, and I dare say that we probably think we are asking ‘good questions’, but are they really the right kind of questions? Are these questions that encourage high-level thinking? One of the most powerful instructional shifts an educator can make to increase the amount of reasoning occurring in their classroom is to specifically plan to ask questions are “discussion-generating questions, probing questions, and questions that make the mathematics visible” (5 Practices for Orchestrating Productive Mathematics Discussion, 2nd Edition, Margaret Schwan Smith and Mary Kay Stein, 2018, p.89). Using a framework such as the revised edition of Bloom’s Taxonomy to craft question styles will be helpful to scaffold and promote hard thinking. Further thinking about questioning will lead to the understanding that asking questions serves different purposes as this link from the University of New South Wales demonstrates. In short, knowing which questions to ask is an important skill set to be continually honing as a teacher. Some of my favourite questions to generate discussion and probe understanding are:
Tell me more about this;
I’m interested to know more about what you’re telling me; and
Convince me that this is the only possible answer.
My goal when asking questions such as these is to understand what the student knows how they are doing it and why. I want the student to do more of the talking, and I in turn, more listening so that the instructional shifts I make are precise for that particular student. Here is an example of a template that I may use in the planning stages to help articulate questions or prompts to promote reasoning through dialogue. Click the image for a copy of the planning template.
Asking questions is a large part of the generation and cultivating of mathematical discourse in the classroom. Shifting the dialogue in the classroom however, must focus not simply on asking questions, but truly listening when students are talking. Marilyn Burns describes the critical nature of listening in an interview on her blog, Math Solutions. She notes,
“I’m always listening, not for what they don’t know; I’m not looking for their deficits. I’m looking for where they are, so I can have something to build on, so it can inform my number talks, so I know what kind of questions I might ask that could be developing understanding for some kids, while it’s cementing for other students, and while it’s extending for even others. Listen, listen, listen! I learn, and then I get to be a better teacher.”
Marilyn’s words sent me into a deep spiral of reflection, especially in regards to my own practice. What if we respond by asking questions that we think we should be asking and missing the opportunities to ask the questions that the student needs us to ask to help drive their learning forward? Someone once said to me that if you value something, you make time for it. I wonder do we actually value listening to students when they are talking about their learning. Granted, it can be near impossible to make the time to listen to every student for everything across the day, but being strategic about who to listen to and when is important. Consequently, I believe it is as powerful to plan for listening moments as it is to plan for questioning. Listening purposefully and responding accordingly is perhaps the truest sense of formative assessment- noticing, listening and acting.
In our diocese, many teachers encourage and promote dialogue through a framework called ‘Talk Moves’. Talk Moves help facilitate student discourse by placing the teacher as the conductor of powerful discussion by supporting and modelling mathematical discussion. The Talk Moves are explained in the image below and can be easily planned for, but even harder to implement. I have walked into many classrooms and have seen the teacher have a small printed version of this image on the side of their workstation or whiteboard.
In summary, for students to be able to reason they need to be given the opportunities to talk about their learning and experiences. Perhaps in future posts I will add further to the conditions that help promote reasoning, but I hope for now I have been able to place the spotlight on dialogue and purposeful listening as necessary platform for students to be able to reason.