Coding enables students to be agents of change

[photo credit http://www.startupdaily.net/2014/03/adelaide-tech-community-teaching-kids-code/]

Alfredo Papesit said in his L2 talk ‘code the change’ that “There is a disconnect between the technology that you have available to you, the problems we are facing in society and whether you know how to use this technology to its full potential.” What is his solution? Teaching students how to code. This is not a new idea, but it is still not something which is embedded within my school or indeed in many schools around the globe.

Papesit states that by knowing how to code “You will have another lens to approach problems and the power to find solutions to these problems. You will have the power to code up solutions which never existed before.”  Papesit gave an example of his students investigating where energy was being wasted in their daily lives and using a hummingbird kit to design a prototype to design a solution to reduce energy waste.

However, for me a far more clear example of students using coding to create a solution were two high school students, who ran their own workshop at Learning2 for teachers and introduced me to ‘appinventor’ by MIT and ‘girls who code’.  These two high school girls had been set the challenge to design an app by their teacher using ‘appinventor’ by MIT. They could design any app they wanted, provided there was a gap in the market for it. They chose to create technology to improve their community and the biggest problem they identified in HCMC was trash disposal. They wanted to solve not just the issue of recyclables (such as cans and plastic), but to also help community members to reuse items and furniture from expat families as they move to their next posting. The two girls created the app and explained the empowerment they felt as they were designing a solution to a very real problem.

The two girls also introduced me to ‘girls who code’ a foundation aimed to close the shockingly real gender gap in technology. Tech jobs are the fastest growing industry in the world, yet only 18% of computer science graduates in the US are women and by 2020, women are on track to fill only 3% of computing related jobs in the US. (Statistics taken from https://girlswhocode.com/about-us/)

[photo credit http://www.tiffaniestanard.com/news-events/new-partnership-with-girls-who-code/ %5D

‘Girls who code’ sets up immersion programs and after school clubs around the US to get girls coding. On their website are endless examples of what girls are doing to create change. Here is one example of a 17 year old girl, Margot Richards, who created a game to raise awareness on gun control laws called ‘Gun Cleaners’.
“With code, I was able to create a video game to raise awareness on gun control laws. The video game is called Gun Cleaners, and players use the up and down arrows to collect the assembly’s votes to help pass the gun control bill while avoiding being shot by guns. With a fun and addicting video game, we were able to help raise awareness about one our society’s most pressing problems.”

[photo credit https://www.linkedin.com/company/girls-who-code]

There are many skills which our students need to create change in our world and to take action. They need research skills, communication skills, thinking skills, visual literacy (we still see terrible posters being displayed around schools!) to name just a few… These skills are all explicitly a part of the PYP, MYP and IB curriculum, but it seems obvious to me that coding skills should also be a part of our curriculum, starting from KG in the PYP program.

 

I was truly inspired by these two highschool students who led their coding workshop at Learning2 and here are some questions which I have been asking myself since my experience at Learning2:

• How can we implement a coding culture at ISHCMC? Where do we start?
• What other skills do our students need to be agents of change in their community?
• What organizations are there in HCMC that our students can be involved in?

  References
  Alfredo Papesit’s L2 talk ‘code the change’ https://youtu.be/WiZ0q5NOaKQ
  https://girlswhocode.com/about-us/
  https://code.org/

Fostering inquiry mindsets in Maths

An inquiry teacher is someone who is more curious about how the students develop their thinking,  rather than the actual answer itself.  Many PYP teachers recognise what this should look like in Units of Inquiry, but how does this translate to Maths? Many teachers would argue that, in Maths, of course the actual answer is of vital importance and those teachers might place the emphasis on their students reaching one answer, using one method and achieving computational mastery.  However, structured and purposeful inquiry is supposed to be the main approach to teaching and learning mathematics in the PYP.  So how do we build a bridge between these two approaches?

Lana Fleiszig  (@lanafleiszig), the Numeracy Co-ordinator at an IB Primary Years Program school in Melbourne, has been a mentor for us at ISHCMC over the past few years and has helped us to change our mathematic practices in order to become more inquiry based.  Through her guidance, each Grade team has written units of Math inquiry for all the number strands.  These units have a central idea, lines of inquiry, key concepts and are shared with the students.  Within these units we embed all the number standards from AERO and create a sequence of understanding, which are based on Math Strategies identified in GLoSS (The Global Strategy Stage interviews from NZ).

Here is an example of a unit in Grade 2 for addition and subtraction:

Our central idea is “There are many mathematical strategies that help us to solve addition and subtraction problems”.  

Our Lines of inquiry are:

• Understanding and applying mental strategies (Function)
• Different ways of knowing (Reflection)
• The place value of numbers help us to understand addition and subtraction (Form)

At the start of each number unit of inquiry, we use provocations to spark curiosity and to promote an inquiry mindset in Math.  These provocations might involve a story book, games, a photo, a video, a statement, art or manipulatives arranged in a certain way.  the provocations should generate data for the teacher to identify the students’ level of understanding.  We often have a week of provocations at the start of a unit so that teachers know what strategies the students are already comfortable using and what concepts they understand so that we know, as teachers, what the next step should be to develop their mathematical thinking.

Here are some examples from our provocations from week one, the problems were related to the real world, they built on student knowledge of place value, it involved discourse and the students had a variety of ways to record their thinking (from using manipulatives such as base ten blocks, numicon, sketching, whiteboards and written strategies).

Through my professional development with Lana, my Grade 2 team now places greater emphasis on: the mathematics process, using a variety of strategies, connecting mathematical concepts, using manipulatives to make maths understandable, real-life problem solving, finding out what students already know and building on these understandings and using mathematical discourse.

By using an inquiry lens, students can link concepts together and as a result we find that our students gain deeper understandings.  We frequently use visible thinking routines, such as claim-support-question, see-think-wonder or tug-of-war to enable the students explore and dig deeper into ideas.

Lana taught us the value of opening up math tasks to create open-ended questions, these questions are a great way to differentiate mathematics instruction and to enhance learning. The research center of NRICH (Cambridge University) which I first discovered when I did my masters degree at the Cambridge faculty,  were possibly the first group to coin the term’Low threshold, high ceiling’ tasks.   These activities are problems which everyone in the group can access and then work on at their own level, which includes possibilities for challenging math. By using open ended math activities it promotes a positive classroom culture because the whole class does maths together.

George  Pólya, a Hungarian mathematician, said that it is far more beneficial to solve a problem in many different ways, rather than solving one problem.  When students work on open ended math problems, they can reflect on their practice and identify the most efficient strategies.

There are many elements to fostering inquiry mindsets in Maths with your students, as well as with your colleagues and, in your own practice.  My colleague, Tiffany Eaton, just shared this powerful graphic from Jo Boaler (@joboaler) on Twitter and I think it is a great visual to remind us of some of the ways to foster inquiry mindsets in Maths:

Connecting with nature in a concrete jungle

A simple interaction in the corridor sparked the Grade 2 team to rewrite our upcoming unit of inquiry for How The World Works.

What happened?  A butterfly landed on a Grade 3 student and every child around her ran around screaming, the girl panicked and was on the verge of tears, teachers had to step in to calm down the students.

Later, I spoke to a Grade 3 teacher about what had happened and she said it wasn’t surprising, that they see those behaviours alot when they go on camp.  Higher grades reported similar trends on their camps.  Why is it that some of our students are feeling such a disconnect and so uncomfortable with nature when it lands on them?

My feeling is that it stems from the fact that they rarely stop to observe, notice and appreciate the nature around them.  Even in a concrete jungle such as Ho Chi Minh City, nature is all around us.  Some of these students spend too much time in shopping malls and some told me they have never even owned a potted plant.  Nature isn’t just about beautiful mountains or stunning lakes, its on your walk from the car park to the school grounds, it’s the heavy rain of monsoon floods, it’s the crickets you hear at night from your terrace. Nature is all around us, yet our students are visibly disconnected from it.

Our HTWW unit was about plants, the lines of inquiry focused on how they grow and how plants are used.  Whilst this unit had benefits such as being a hands on unit with a strong scientific underpinning, we now feel there was a gap which our students needed, which was a stronger connection with nature.

In planning this unit on nature, the Grade 2 teachers wanted to create a really authentic unit for the students, which was based entirely on what the students were curious about.  We changed the central idea to: Curiosities about nature can lead to discoveries. On day one, we planned only the provocation, nothing else, we needed to see what our students were curious about.

Our provocation was a series of three nature walks in our school and the students were amazed at what they found, snails, flowers, tall trees, roots which stood out of the ground, leaves with little buds on them, ants living in a tree, butterflies, dragonflies, holes in the soil… the list goes on.  From here, some students had inquiries for which they were ready to inquire into.  Why do leaves change colour?  Why do insects have blue or green blood?  Do all flowers make pollen?  What do leaves do?  Why do clouds change shape?

Every morning we write a journal about ‘How I connected with nature yesterday’ and our students are becoming more and more comfortable with this.  One morning, during mindfulness a student opened his eyes and saw an insect on the window, he quietly picked up the camera and photographed the insect up close.

When he shared his photo and his curiosity with the class afterwards no one screamed or said ‘ugh’ instead everyone had questions “Does it have wings?” “What is it doing?” “Can it see us?”  “Does it feel scared?” “Does it wash its hands like flies?”.

There are many ways of knowing and students are learning which ways are suitable for their questions.  They are recording their direct observations,  internet research, book research, investigations and microscopic photographs in their nature journals.

Sometimes we need to look beyond our reflections from last year and consider the needs of our students, right here, right now.  That’s what teaching in time is all about.  We need to ask ourselves this when planning upcoming units of inquiry: what do your students need and how are you catering for it?

Natural born philosophers

Here is a link to the article I wrote for Oi Magazine

Oi-August-2016-Vacation-Bound page 93

What do you look for when data mining in Maths?

As teachers, we all keep vast amounts of data, reading data, writing data, math data, behavioural and social data, data on conversation skills, a vast variety of formative assessment.  But what do we most often do with this data?  We store them in excel spreadsheets or we set individual targets for our students.  In our school we use google sheets so that they can be shared and access by others, such as admin and student support services, so that anyone can track individual students.

However, I find it difficult to connect with data when they are kept purely as an excel spreadsheet. I have begun to see real value in actually pulling my data outside of the excel spreadsheet in order to see the bigger picture, spot patterns and reflect on how my teaching practice needs to change to enhance the learning of all my students.

 

Let me share an example:

In our school we do GLoSS interviews, these assessments show which mathematical strategies your students are using and they give teachers a clear set of strategy expectations for each grade level (these assessments come from New Zealand).

We assess our students on entry to Grade 2 and on exit of Grade 2.  During the course of the year, the  level of strategy expectations increase from level 4 to level 5.

To really analyse our data, my colleague and I decided we needed to take the data out of excel and work on paper.

• We created Venn diagrams to compare the three different skill sets: addition and subtraction, proportion and ratio, multiplication and division.
• We created two Venn diagrams, one for students below grade level expectation (blue paper) and one for students exceeding grade level expectation (yellow paper).
• We repeated this process twice, once in September on entry to Grade 2 and now again in May, on exit of Grade 2.

 

Entry to G2: above grade level expectation is stage 5 and above

 

This visual really allowed us to see big patterns in the data across the whole grade level. By colour coding each class, we could easily spot patterns and strengths within each other’s classes as well as across the grade level.

By presenting the data in this way, the most resounding observations are:

• On entry, we had 22 students exceeding expectation in any area. Now upon exit, we have 73.  That is a huge increase.
• The number of students exceeding in all 3 areas has grown from 13 to 21 students.
• Our strongest area of teaching is Addition and Subtraction, this section has grown from 4 students exceeding grade level expectation at entry to 26 students on exit.
• Overall on entry, we had 35 students of concern in any area. Now upon exit, we only have 27.  The majority of these students of concern are below grade level expectation in proportion and ratio.
• Another indicator that our weakest area of teaching in G1 and in G2 is proportion and ratio is that we didn’t have any students exceeding solely in proportion/ratio on entry to Gr. 2 and on exit, we still don’t have any.

So…

Firstly, we  need to consider how we can improve our Math unit on fractions, percentages and decimals (proportion and ratio).  Next year, we will need to track  all the students’ progress through this unit more closely next year. This unit is a 6 week long unit in November / December and as a team, we are considering how to revisit this unit during the year to keep these skills retained, so that students don’t forget their skills, strategies and knowledge?

Secondly, we need to follow up with our Student Support Services team to ensure that students who are under or above grade level will be flagged and tracked in G3 to ensure that they are given the appropriate support and extension.

 

 

Is planning ahead a restraint to student inquiry?

My biggest strength is my organisation.  You can ask anyone on my team.  I am very organised.  But I am learning how this is a strength, but can also be an obstacle, as I increasingly try to hand over our units to our G2 students.

The question I have been asking myself lately, is:

Should you map out the teaching of writing within units of inquiry months in advance?

My Grade 2 students are nearing the completion of a research based unit, inquiring into how “Communities play a role in preparing for and responding to natural disasters?”.   The writing genre, which has been mapped into our unit since September, is informational reports.  And indeed informational reports have been a relevant genre for half of my class, but not for everyone.

Students have research question templates, writing templates and peer assessment checklists to ensure high quality and focused writing.

This unit was co-written by the students and their teachers, based on student curiosities, so it naturally invited student inquiry.  The students had lots of driving questions, but narrowed these down and created focus by choosing the one they were most interested in for their inquiry.

I shared the inquiry model with my students to help them monitor their own progression in their inquiry.  During the ‘finding out phase’, my students interviewed members of the ISHCMC community, they researched on kiddle.org (a child friendly search engine) and then they drew their own conclusions from all the data gathered.

Once they had all their data, I noticed that their questions varied largely in terms of what type of writing they would publish.  Take these questions for example:

• How does a city warn people when a tsunami will strike?

This is a question for an explanatory text, because it will tell us how something happens.

• What are the best ways to prepare for a cyclone?

This question is best suited to a procedural text.  Procedural writing instructs others how to achieve or do something.

• How did the communities help after the landslide in Seoul (2011)?

This is research is best suited to be published as an informational report.  Informational reports classify, organise and describe information.

Organisation: All student questions are colour coded according to research groups (type of naturally disaster) and placed into columns based on writing genre for explicit teaching groups.

 

By allowing the students the freedom to choose their own inquiry questions, I also had to give them freedom in terms of what genre of writing would follow as a result of their question.  During the ‘Making conclusions’ phase of the inquiry, I had three different writing groups and each had explicit teaching into one of these three writing genres: explanatory, informational and procedural.  As a grade level, we prepared three different writing templates to help scaffold the students during the writing process.

Of course, we cannot let our students get to the end of the year and only be able to write one genre, but I believe that there must be a balance.  We must be open and flexible in our planning, especially when we map out our literacy genres across the whole year.  Sometimes units change and so they should, if we are truly basing our units “on each student’s needs, interests and competencies” (Making the PYP happen, Page 10).

An interesting trend that I found in my class was that my highest level writers had more complicated questions, which were most appropriate for the more complex genre of informational reports.  Such as, “What kind of earthquake preparedness systems does Japan have that Nepal does not?”

Whereas, my lower level writers had more simplistic questions, which were most appropriate for procedural writing, which is a simpler genre to write.  Such as, “How can people be safe in a tornado?” Hence helping my students to choose the most appropriate genre for their question was also a means of differentiation.

When you plan your next unit, how often does the writing of the central idea and the lines of inquiry actually involve your students?

In my case, not yet, until now.

Normally, I work collaboratively with a group of teachers, we redefine or write entirely new units.  It takes a long time. We ponder over the units and we deliberate over the development of the central idea “Is this wording overly subjective or does it implement judgement?”  “Does it invite student inquiry?” “Are a range of responses possible?”.  We, as teachers, do all the thinking. Then we deliver the unit to the students and we expect them to be curious, to take action and to make independent inquiries.  My PYP planners too often include comments such as “Next unit needs to provide more opportunities for independent inquiry” and too often my student reports include comments such as “Needs to develop his natural curiosity and to explore concepts independently.”

Clearly I’m doing something wrong.

Every time that I come back and read ‘Making the PYP Happen’ I find something new.  This time, I didn’t get past page 14.  It states that PYP units “should be based on each student’s needs, interests and competencies” (Making the PYP happen, Page 10).  That “Each unit should be engaging of interest to the students and actively involving them in their own learning; relevant linked to the students’ prior knowledge, experience, and current circumstances.” (Making the PYP happen, page 14).

This got me thinking, that to create an authentic student-driven unit, it needs to be created by the students.

Our next unit transdisciplinary theme is Sharing The Planet and the topic is natural disasters.  We wanted this unit to be a research-based unit where our students are independently inquiring, right from the start of the unit.  But in order to make this unit truly engaging and of interest to our students we have written it WITH them.

We started our unit with a provocation and used the Philosophy4Children framework to frame the student’s thinking and to get their input.

1. Our stimulus was a guest speaker, someone who had been in a natural disaster. We had four guest speakers for all four classes to ensure breadth of responses from the students.
2. The students identified the main concepts and the big ideas.  These included: Preparation , Protection,  Safety, Damages and Rebuilding, Disaster, Working together,  Cooperation, Danger, Fear, Loss , Risk of death, Friendship and communities, Bravery, Communication, Warnings.
3.  The students generated one deep, conceptual question which they were interested in discussing further, based on one of the concepts identified.  Here are some examples of their questions:How do people keep safe in natural disasters? How and why do disasters happen?  Why do people need to be careful about preparing for natural disasters? How can communities reduce the risk of death? Why are there risks in life? Can you be fearless and brave at the same time?
4. Through a series of steps, the class voted on one question and we discussed it for 15 minutes.

 

Do we give our students enough opportunity to learn in their mother tongue?

During student led-conferences at ISHCMC we all give our students the opportunity to share their learning with their parents either in English or in their mother tongue.  Not surprisingly, many of our ESL learners choose to present in their mother tongue as their parents may not have a high level of English, or because the student and parent are more comfortable speaking together in their familiar home language.

However, this got me thinking…

Do we give our students enough opportunity to learn, to speak and to share their understandings in their mother tongue in class?

And if not, then why not?

During our student led conferences, I saw my students explain the phenomenon of day and night through the rotation of the Earth on it’s axis, the concept of months through the Moon’s revolution around the Earth (naming the moons at each stage of the cycle) and the concept of years measured by the Earth’s revolution around the Sun.

Some students chose to share in English and some in Korean, Vietnamese, Spanish or French.  Whilst I could only understand my student speaking in French, it was clear to me how much more confident, at ease and fluent some of these students were in their mother tongue.

Whilst of course we need to encourage our students to express themselves in English, we also need to allow them time to learn in their mother tongue and to tell them explicitly that this is OK.

My French student was struggling in Maths with counting concepts, such as skip counting or counting on.  When I asked her what she was doing in her head, she told me she was counting in English.  By asking her to count in French and by frequently reminding her that this was OK in our lessons, she made fewer errors.

I also have a Spanish student who is a beginner learner in English.  His parents wanting to immerse him in English and to give him the best opportunity to learn this new language, withdrew all opportunities to read in Spanish at home.  As a result, he felt frustrated by the reading process.

Learning a new language requires balance.

As teachers, we cannot ignore how important it is to allow our bilingual or multilingual students to think, read, speak and write in their home language.  We should help our parents and students to see the value and importance of fostering both languages.  We must also see the importance of balancing both of these in our classroom too.

 

Conceptual understandings require time.

In order for students to reach deep and conceptual understandings they require time. Time to explore concepts, time to think, time to build connections.    I regularly use the thinking routines by Project Zero, which are designed to:

“Slow down the pace of the classroom to make space for deep observation and wonderment.  That happens by talking and discussing objects or systems in the everyday world.” (Schwarz, 2014)

There is great value in slowing down the pace of the classroom in order to reach deeper and more conceptual understandings.  A common misconception is “We don’t have time, we have so much to cover!”.  But by teaching and learning in a more thoughtful and slower way, you actually save time in the end.  By establishing solid understandings you are eradicating misconceptions, which you would have had to re-address later on, had you just rushed through.

I want to highlight this point with an example of my students learning about TIME and how to ‘tell the time’ in our current UOI.  The line of inquiry which we are exploring is “How people organise and measure time”.

Telling time is often taught as a rote skill and with this comes deep misconceptions.

Traditionally, teachers often start with teaching the full hours “When the big hand points to 12 and the little hand points to 1, it is  1 o clock”.  Then onto half past 2 and then onto  quarter past and quarter to the hour.   But when our students learn time in this way, they do not have an understand of “the duration of time and its relation to the numbers and hands on a clock” (Thompson and Van de Walle 1981), nor do they have a true conceptual understanding of time.

Before designing my lessons on telling the time, I did some research.  And, no, I did not consult Pinterest, instead I went on the National Council of Teachers of Mathematics website http://www.nctm.org/ and within 5 minutes I had a series of investigations designed to:

“provide opportunities for children to investigate time units, experience events lasting set amounts of time, and develop personal referents for standard time units” (Mc Millen and Hernandez, 2008).

These investigations by Mc Millen and Hernandez (2008) were different to other approaches I had read and observed,  these researchers  highlighted the differences associated with the two hands of an analog clock and why these two systems should be taught separately at first. In these investigations  students worked with two types of one-handed clocks, a minute clock and an hour clock, to meaningfully discover both differences and connections between the two clock hands.

By spending a little amount of time doing some research, I saved myself a lot of time in planning.

In the first lesson, I gave my students time to investigate time units such as 1 second and 1 minute, in order to help them to develop personal references for standard time units and to discover the relationship between them.   My classroom was loud and noisy.  We were building towers, bouncing balls, doing star jumps, burps and … you name it!

 

In the second lesson, the students investigated what can be determined about time when a clock has only an hour hand.   We built our own clocks and learnt how to tell the time with these simple phrases, its “o’clock” its “a little past five.” or “a little before five o’clock.” or its  “between four o’clock and five o’clock”.  The students worked in partners and had a number of partner activities to do, which they greatly enjoyed.

In the third lesson,  the students then investigated clocks with only a minute hand.  This lesson focused on connecting  minutes to an hour.  We started by matching ‘groups of five minutes’ to the clock face and built minute clocks in our classrooms.  I encouraged my students to use efficient counting strategies to tell time, eg, skip counting by 5s: 5, 10, 15, 20, then counting on individual minutes 21, 22.  By the end of the lesson, all my students were all able to count the minutes past the start of an hour with their partners.

The hour clock

In the fourth lesson, my students  “investigated the motion and location of the minute hand as it relates to the hour hand” (Mc Millen and Hernandez, 2008).  My students then connected their knowledge together, they counted the minutes first, then found the hour, and finally combined them.    At this point I exposed my students to analogue clocks with both hands, and after some discussions “Which comes first, the hour or the minute?” My students were all quizzing each other “Guess which time this is?” and telling the time to the minute.

It took 3 lessons (4 hours in total) before I even introduced my students to a real clock face with two analogue hands.  Yet, my students were able by the end of that 4th lesson to tell the time accurately and to the minute.  This is my 4th year as a Grade 2 teacher, and never yet have I seen students learn the time faster.

What can I conclude from this experience?

It pays to give students time, time to understand concepts deeply and in the end, well … you might even save time.

If you are interested in any of the sources mentioned here, they are referenced below.

McMillen, S and  Hernandez, B (2008) Taking Time to Understand Telling Time.  The National Council of Teachers of Mathematics. accessible at http://maccss.ncdpi.wikispaces.net/file/view/Taking+Time+to+Understand+Time.pdf

Schwatrz, K. (2014) How Dissecting a Pencil Can Ignite Curiosity and Wonderment. MindShift. accessible at http://ww2.kqed.org/mindshift/2014/12/08/how-dissecting-a-pencil-can-ignite-curiosity-and-wonderment/

Thompson, C and Van de Walle, J (1981). A SingleHanded Approach to Telling Time. Arithmetic Teacher 28 (April 1981): 4–9.  cited in McMillen, S and  Hernandez, B (2008) .

 

 

Listening to and trying to understand student thinking which has been made visible

The school in which I work strives to create a culture of thinking. By adopting many of the simple, yet hugely effective strategies from http://www.visiblethinkingpz.org/ we can make our student’s thinking visible.

Unless encouraged to do so, most of our student’s thinking is invisible, sometimes students explain how they reached an answer, but often they do not.  But by making their thinking visible, they can build on each other’s ideas and understand concepts better.

However, for a large part, this rich data gets lost somewhere in the classroom and visible thinking risks becoming just ‘one of those’ classroom activities which we do.

As teachers, we are all busy, but how often do we stop and reflect on the thinking of our students which we have made visible?

I have the rare opportunity of having a trainee teacher in my classroom, who already has heaps of classroom experience, yet who is eager to learn more.  At the start of our unit, we spent 3 days gathering as much information about our student’s prior knowledge before we began our unit on time.  We used the visible thinking strategy of ‘Headlines’ along with 8 different card sorts.  We recorded 14 different discussions using the Harkness method.

Then, most importantly, my colleague and I spent over 1 hour over reviewing, analyzing, discussing the ideas, knowledge and misconceptions of our students which we had gathered.  This final step is the one which is most often neglected.  But this is the most important step of all!

We lay out all of our data on the floor, and we examined each student one by one…

One of our most surprising findings, was a conversation by two young boys over the moon cycle:

We actually saw, how through discussion, this one child was able to change his own thinking and overcome his own misconception.  At the beginning of the discussion Juan stated that the moon cycle changed every day “This is the beginning (points at crescent moon) when it’s morning, then as the sun gets bigger the moon gets bigger.”  Two big misconceptions there.  But wait, here is the turning point, after an interesting conversation with his peer, who states “I know that the full moon gets bigger and bigger up to TET and then it gets darker and darker again.” Juan then says “I see a full moon every month… I now think it takes 30 days”.  For me this conversation showed that Juan did not have a large amount of prior knowledge about the topic, but that his reasoning skills and his ability to make connections to make sense of information is incredibly strong.

As a teacher, the understanding that we can reach through listening to and actually reflecting on the data of each of our student’s thinking should not just be considered an opportunity, but rather as an integral part of the ‘visible thinking’ approach.