Reflection; an important part of the learning process

Giving students the opportunity to reflect on what they've learned, how they've learned it and why they've learned it is an important part of the learning process.

But who has time to set up that kind of reflection?! We hardly even have time to get through the actual lesson!

One teacher with whom I work has an answer. She has set up a reflection procedure with her students which allows them to meaningfully - and consistently - reflect on the learning they've done. Yesterday, I got to see the procedure first hand.

The class is currently digging into the idea that expansion transforms culture over time. During the unit, students are primarily exploring how European expansion into the New World transformed the European, African and Native American cultures.

During the lesson yesterday, the students were still exploring the concepts of expansion, transformation and culture but were thinking about these big ideas through a different context: the current refugee crisis precipitated by the violence, instability and economic troubles in the Middle East and Northern Africa.

To explore these ideas, the teacher lead the students through a Tug-of-War, a visible thinking routine from Making Thinking Visible by Ritchhart, Church & Morrison. She presented the dilemma, "Countries should be required to let refugees settle within their borders," and the students had to generate "tugs" or reasons that support one side of the dilemma or the other. Students then read through the "tugs" as a class, determining the strength of each.

As students did this work, wonderful thoughts and questions were shared and discussed. Connections were made to the push-pull factors the students had learned about when they studied the European Explorers. Students also made connections to the UN Declaration of Human Rights, the treaty signed at the 1951 Convention relating to the Status of Refugees as well as the Ebola crisis last year.

At the end of the discussion, the teacher asked the students to reflect on how their thinking had changed, by inviting them to complete the thinking routine, "I used to think, Now I think," where students reflect on how their thinking has shifted and changed.

The teacher also required the students to respond to the following prompt:

front of the essential elements mat

back of the essential elements mat

Below are samples of some of the students' thinking.

These students simply answered the prompt, identifying two attitudes they demonstrated during the Tug-of-War discussion.

Another student was able to identify more than two attitudes demonstrated during the discussion.

The following students went beyond the requisites of the prompt and elaborated on their responses, explaining how they showed the particular attitudes they demonstrated.

Giving students the opportunity to reflect on their learning is an integral part of the learning process. After reading about how this teacher set up a reflection procedure with her students, how could you or do you give students the opportunity to reflect on what they've learned, how they've learned it and why they've learned on a consistent and daily basis?

Teaching Math in Authentic Contexts

Our staff recently has been examining the question: "What does math teaching and learning look like in a Primary Years Program (PYP)?"

To answer this question, we explored the text "Mathematics in the Primary Years Programme," one of the subject annexes from Making the PYP happen: A curriculum framework for international primary education. In that document, teachers were able to see the clear vision of how math teaching and learning should look like in our PYP.

To document their thinking, teachers created a Practice Profile (a rubric of teacher behavior) based on what they were reading in the text. As primary and intermediate teachers were working in separate sessions, there were two separate practice profiles created and can be found here: KEC PYP Math Practice Profile - Primary and Intermediate.

An important idea that came up during that professional learning engagement was that in a PYP classroom, teachers should provide students with multiple opportunities to explore relevant problems both inside and out of the units of inquiry. The math annex provides some guidance on concepts that might be best suited for learning in context when they say, "data handling, measurement, and shape and space are best studied in authentic contexts provided by the transdisciplinary units of inquiry," because they represent the "areas of mathematics that other disciplines use to research, describe, represent, and understand aspects of their domain," (p. 85 of Making the PYP Happen).

Reflecting on this new understanding of math instruction in the PYP, one G2 teacher planned for her students to create a timeline, an authentic opportunity to explore the abstract mathematical concepts of measurement, subtraction, space, and time. She knew that the timeline would give her students a better understanding of the heroes they were studying in their unit of inquiry, as they were trying to make sense of the big idea that people influence the world in different ways.

First, the students created the timeline using the scale 1 cm = 1 year. The students worked together to create century strips, each measuring a meter (and alternating in color).

Then, the students needed to figure out how long each of the heroes' strips should be. The teacher modeled how to use a number line to figure out the age of the hero they'd be researching. Using the birth date and death date (or the current date for living heroes), the students figured the difference between the two. It is important to mention that the students did pretty well with this since they have been using number lines and open number lines all year for almost every math topic. This shows how effective it is to give students the opportunity to use the same thinking tools and structures over and over again until they become routine.

Next, students used that information to create strips for each of their heroes, again with the scale 1 cm = 1 year.

Finally, the teacher gave students the opportunity to look at the timeline and document their observations, thoughts, and questions using the thinking routine See-Think-Wonder (from Making Thinking Visible by Ritchhart, Morrison, & Church).

This G2 teacher continues to see other ways that math can be learned in meaningful ways during her unit of inquiry. Recently, she used the data they had collected on heroes' ages to introduce median, mode and range. Using the data the students had already collected made it more authentic and engaging.

The students found that their heroes ranged in age from 37 to 95, a range of 58 years. Kids were surprised and impressed because that seemed like a lot. There were two medians and two modes, so that was confusing for their introduction to the idea of analyzing a data set using those tools, but it was engaging nonetheless.

After reading about how this G2 teacher taught the mathematical concepts of measurement, difference, and data in the authentic context of her unit of inquiry, how could you or have you taught math in meaningful, engaging and authentic ways?

The initial stage of an inquiry

In 2012, representatives from the International Baccalaureate evaluated our Primary Years Program. Among the 52 recommendations that came from that report was the following:

The staff review their planning process to ensure pre-assessment, with a variety of assessment strategies and tools, is included in order to consider students' prior knowledge so that learning can build on what students know and can do.

Before new learning can begin, students' current knowledge, skills, and conceptual understandings must be considered. However, this is not the only thing that happens in the initial stage of an inquiry. Provocations should also invite students to wonder and be curious.

At our public school, we do not often guide students through open inquiries, where they can investigate that which is intrinsically of interest to them. Therefore, it is extremely important that we work hard at the initial stage of an inquiry to get kids interested in the concepts/topics taken from the academic standards on which our units of inquiry are based.

In order to pre-assess her students knowledge, skills, and understanding and to get them interested in an inquiry under the Transdisciplinary Theme Who We Are, one third grade teacher lead her students through a Visible Thinking Routine Chalk Talk (from Making Thinking Visible by Ritchhart, Church, and Morrison).

Central idea: Community forms when people realize they have things in common.

An inquiry into:

• Maps
• Why people settle
• Family histories and the histories of others
• A student's place in the world

This teacher posed questions rooted in the Key Concepts of the PYP that fit with the lines of inquiry for this unit. Her purpose for leading her students through this silent conversation was to make their thinking visible so she could assess what her students already knew, were able to do, and understood. She also was inviting her students to think, to wonder, and to be curious about the topics they would be investigating.

As this teacher demonstrates, Chalk Talk is certainly a great assessment tool that gets students interested in the topics about to be investigated.

Below are some additional strategies, tools, and ideas that teachers can use to enter into the inquiry cycle with their students, from different researchers and educators who have created different models of the complex inquiry process.

Creators: Teachers at my school (created during a staff development day)
Initial stage called: Invitation
Teacher:

• Invites students to wonder about a topic
• Visual thinking routine: I notice, I think, I wonder
• Creates a safe environment to take risks/ask questions
• Allows a space for kids to think outside the box
• Fully engages students
• Ignites authentic interest in topics
• Creates a desire to know/understand something
• Captures the hearts, brains, and spirits of kids
• Builds background
• Starts with aspects that are interesting to students
• Identifies topics to study (if based on standards)
• Considers learners’ prior experience and current understanding
• Pre-assess students to learn what they know, understand, and can do prior to the study

Student:

• Wonder about a topic
• What is it like that?
• How does it work?
• Identify what they already know
• Are fully engaged
• Get excited
• Become curious
• Are motivated

Creators: Stephanie Harvey and Harvey Daniels
Initial stage called: Immerse: invite curiosity, build background, find topics, and wonder
Teacher:

• Plans instruction and teaches with central curriculum concepts and focus questions in mind
• Gathers and organizes curriculum materials and resources
• Immerse kids in multiple sources to build background knowledge
• Invites curiosity, questioning, engagement
• Models own curricular inquiry
• Conducts think-alouds with text and materials related to the curricular topic
• Demonstrates how to ask questions about curricular topics
• Facilitates small-group formation to ensure heterogeneous groups with compatible interests
• Confers with small groups and individuals

Student:

• Express their own curiosity
• Explore, experience, and learn about topics using texts, visuals, Internet, artifacts, etc.
• Read, listen, and view to build background knowledge about the curricular topic.
• Talk, write, and draw in response to instruction
• Wonder and ask questions
• Meet with teams to set schedules, ground rules, and goals.

Creators: Kath Murdoch
Initial stage called: Tuning In
Teacher:

• Establishing the 'known'
• Connecting to students' lives
• Create a sense of purpose for inquiry
• Invite first thinking
• First invitation for questions
• Ask:
• What theories do we have?
• How do you already understand this?
• What connections can you already make?
• How could we find out more about this?

Creators: The 5E Instructional Cycle
Initial stage called:Engage
Teacher:

• poses problems
• asks questions
• reveals discrepancies
• causes disequilibrium or doubt
• assess prior knowledge

Student:

• calls up prior knowledge
• has an interest
• experiences doubt or disequilibrium
• has a question(s)
• identifies problems to solve, decisions to be made, conflicts to be resolved
• writes questions, problems, etc.
• develops a need to know
• self reflects and evaluates

I Used to Think ... , Now I Think ...

Making students' thinking visible is important for both teaching and learning. When teachers are able to see what students are thinking about the concepts with which they are working, teachers are better able to understand how they might support their students growth in understanding. Furthermore, making students' thinking visible is advantageous for the students. When they are able to see how their own thinking is growing, shifting, and changing, they're able to better understand their thinking processes, which benefits them in future learning.

In their book, Making Thinking Visible (2011), Ritchhart, Church, and Morrison have included seven Visual Thinking Routines for synthesizing and organizing ideas. "I Used to Think ... , Now I think ..." is a routine that teachers can use to provide students an opportunity to reflect and think about their own thinking (metacognition). It is used "to help learners reflect on how their thinking has shifted and changed over time," (p. 51). Furthermore, it allows teachers to see how students are understanding particular concepts before and after a period of learning, which is important formative assessment data that teachers can utilize as they develop future learning engagements for their students.

Recently, I found myself in a kindergarten classroom with 34 learners. Their classroom teachers were leading the children through an inquiry into how weather influences living things all over the world. During the unit of inquiry, the students inquire into how weather can be observed, recorded, and predicted; how severe weather affects humans' lives; and how seasons can influence living things. As the students learn about these concepts, teachers plan learning opportunities during which their students can engage with the big ideas of change, responsibility, cycles, and pattern.

Understanding this was the direction the teachers were going during this unit of inquiry, I planned a lesson with the students around the concept of "cycles". By working with the seasons at the factual level, I wanted the students to understand that cycles are patterns in the shape of a circle that repeat over and over. Because kindergartners wouldn't be able to articulate that understanding verbally, I was looking to see if they could show me their understanding of cycles by drawing a flow map in the shape of a circle.

Because I not only wanted to check the students' understanding at the end of the lesson, but I wanted to know what they understood about seasons before the lesson began, I decided that the Visible Thinking Routine, "I Used to Think ..., Now I Think" would be a perfect way for the kindergarteners to demonstrate their understanding before and after the lesson.

I began with introducing how a flow map is a tool that allows us to show the order or sequence of something.  I gave students time to show their understanding of seasons using a flow map under the heading, "I used to think". Then, after learning that the seasons go in a cycle (using pictures of a biCYCLE, a motorCYCLE, and the reCYCLE symbol, along with singing the song, "ROUND and ROUND the Seasons Go) students had to show me their new understanding of how the seasons go in a cycle under the heading "Now". Below are some student work examples of how their thinking changed and shifted within the hour lesson.

Student A: This student shows how she understands the seasons run. Notice the linear flow-map, along with the incorrect order of the seasons (spring-fall-winter-summer).

Student A: After the lesson, not only does the student demonstrate her knowledge of the order of the seasons, but she understands the concept that the seasons run in a cycle, not linearly.

Student B: This kindergartner is obviously advanced in his literacy skills. However, he still demonstrates an incorrect understanding of how seasons work.

Student B: After the lesson, the student demonstrates the correct understanding of the cyclical nature of the seasons, along with adjective descriptors of each of the seasons.

Student C: This student demonstrates a correct understanding of the cycle concept before the lesson. Notice how he also labels his graphic organizer "flow map".

Student C: Because the student already demonstrated a correct understanding of how the seasons run in a cycle, he didn't feel the need to draw the cycle again. Instead, he challenged himself (completely independent from teacher direction) and demonstrated his understanding with words - "the sezins (seasons) go in a caieikl (cycle)".

Student D: This kindergartener demonstrates a lack of understanding of print. He was able to copy from the board words and phrases like "flow map", I used to think", "wntr" and "sprg" however they're not in any sort of order and it is hard to understand what his thinking is with regards to the concept of cycles.

Student D: Although this student wasn't able to adequately demonstrate understanding before the lesson, this "Now I Think" demonstration clearly shows he gained not only an understanding of the abstract concept of cycles, but he also is beginning to accurately use print to communicate meaning: W (winter); CC (spring); (su) summer; [backwards] F (fall). Complete with a jack-o-lantern!

Student E: It is unclear what the student understands about seasons or cycles in this "I used to think".

Student E: This student continues to demonstrate a lack of understanding of seasons, cycles, or this particular Visible Thinking Routine.

Although Student E was not able to demonstrate an understanding of the concepts taught, the majority of his classmates were. After this lesson on the concept of cycles, 29 of the 34 five- and six-year-olds (85%) were able demonstrate an understanding of the concept of "cycles". As the classroom teachers continue their study of cycles, seasons, and the bigger idea of "how weather all over the world influences living things", they will have to keep a close watch on those five students who were unable to demonstrate an understanding of cycles and carefully scaffold the learning engagements so that these students too, will be able to access the challenging, significant, engaging, and relevant curriculum going on in the kindergarten classrooms.

After reading about how kindergartners used the Visible Thinking Routine "I Used to Think ..., Now I Think ..." to demonstrate their understanding of concepts, how could you use "I Used to Think ..., Now I Think ..." in your instructional practice?

Chalk Talk

At the beginning of a unit of inquiry, a teacher has the important responsibility of creating a desire within her students to know about and understand a particular concept. During this initial “invitation” phase of the inquiry, teachers need to set up learning engagements where students can feel safe enough to take risks, ask questions, explore, be engaged, share their background knowledge, and to think outside the box. Yes, this initial step is a pre-assessment; it is essential that the teacher knows what the students know, understand, and are able to do as they dive into the unit of inquiry. However, this first step is more than just figuring out what students already know about a particular concept and collecting student questions. It is about capturing the hearts, brains, and spirits of the kids and igniting authentic interest in the concepts & topics being studied. (It is important to note that these ideas about this first step in the inquiry cycle are not my own. They all came from our school’s staff, when we completed the Visual Thinking Routine, “I used to think … Now I think” about the inquiry process at a recent professional development. I simply aggregated their responses to create our unique inquiry cycle: Invitation-Investigation-Demonstration.)

Because this first step in the inquiry process is so influential to the success of the study, the learning engagement that the teacher decides to complete with her students must be a significant and engaging one. Ritchhart, Church, and Morrison have included seven Visual Thinking Routines for introducing and exploring ideas in their 2011 book, Making Thinking Visible. Chalk Talk is one of those routines that teachers can use to “uncover prior knowledge, ideas, and questioning.” The routine is an “open discussion on paper; it ensures that all voices are heard and it gives students thinking time," (p. 51).

Recently, a second-grade teacher was preparing to begin a unit of inquiry with a central idea of: people influence the world in positive ways. During this unit of inquiry, students inquire into the characteristics of a hero, people who have made a difference, one’s own personal strengths, and how people can make a difference in the world. To spark her students’ interest in these particular concepts, she wrote several prompts on large sheets of chart paper and placed them on tables around the room. Her students had markers and she invited them to silently move freely from poster to poster, recording their responses to the prompts. Below are the "finished" products:

With these posters, the teacher not only excited her students about the idea of studying heroes who have made a difference both in the past and in the present, but she was able to efficiently collect valuable information about what the students already know, understand, and are able to do. She can now use this information to tailor future lessons to meet the specific needs of her students.

For instance, during a subsequent lesson, the teacher helped the students aggregate the information they wrote down from the "what is a hero" poster to create a working definition of a "hero".

Now, as students learn about heroes through reading, writing, and viewing a variety of multiple sources throughout the unit of inquiry, they can "test" their definition of what a hero is and continue to adapt it.

Building on the success she had with the original chalk talk routine, the teacher wanted to use the same Visible Thinking Routine, but in a different way. She knew the students already were familiar with the process, so they were ready to apply that familiar process to new content. 

As a way to continue to inquire into heroes, the teacher introduced the students to the poem "Lincoln", by Nancy Byrd Turner. Knowing that the poem was beyond the independent reading level of second graders, her plan to scaffold the activity was to copy each stanza of the poem onto a separate piece of chart paper. She even made the point to the second graders that she divided the poem into fourths (math connection). She then had the students read the poem, stanza by stanza, noting their ideas about what they thought the author was trying to communicate with each stanza.

Since learning about how this particular second grade teacher used the Visible Thinking Routine "Chalk Talk" in her classroom, other members of the team showed me how they have used it in the past with their students. Here are some examples of how other second grade classrooms used this Visible Thinking Routine as they studied communities last fall:

After reading about how members of the second grade team are using the Visible Thinking Routine "Chalk Talk" to introduce and explore new topics and concepts with their students, how could you use "Chalk Talk, in your instructional practice?