5 steps to teach concepts ... in math

Last year, I shared a blog post with friends and colleagues on Facebook entitled "Are You Doing It Wrong? How to Introduce Telling Time" by Cindy Lee of Ainslee Labs (which has since been reposted here: Avoid the biggest mistake teachers make when teaching time ).

It caught the attention of my second grade colleagues and now together, we're trying to figure out how to put Ms. Lee's ideas into practice with students.

Traditionally, students are introduced to telling time by first learning time to the hour. Next, students learn to tell time to the half hour, then to the quarter hour, then to the nearest five minutes and finally to the exact minute.

Ms. Lee has experience that shows this way is confusing to kids (I've had that same experience!). We first teach kids to look wherever the short hand is pointing to to read the hour. But soon thereafter, this understanding becomes a misconception.

To address this confusion, Ms. Lee suggests using a clock graphic colorfully divided into twelfths, teaching the kids that each hour has an area or space that belongs to them.

Below, I've detailed how I used my five-step concept-based lesson framework to introduce this idea to the students.

1. Start with a concept.

Before the lesson, I decided on three related objectives to make sure that my lesson was three-dimensional (to learn more about 3D curriculum and instruction see anything by Lynn Erickson).

Concept: The students will understand that you can't achieve your goal if you use the right tool the wrong way.

Knowledge: The students will know that the hour has an area or space that belongs to them on the clock.

Skill: The students will be able to read the hour on a clock, regardless of how many minutes have passed.

Although I was specifically concerned with students gaining mathematical knowledge and skill during this lesson, I was equally interested in them learning the timeless, abstract, universal and transferable idea that even if you're using the right tool, you need to use it the right away to be able to reach your goals. Striking a balance between teaching and learning knowledge, skill and concept objectives is paramount, in concept-based teaching.

2. Pick a specific, concrete example of a person, place, situation, or thing that illustrates that concept & 3. Create an opportunity for students to explore that concrete example.

To introduce students to the concept of using the right tool the right way, I brought in a tool box, a hammer, a small board and my lanyard.

I told them I had a goal of making a lanyard hanger so that it wouldn't get tangled on my shelf at home. We first chatted about the right tool I'd need out of my toolbox. When we decided that a hammer was indeed the right tool, I tried to hammer in the nail with the end of the hammer. When that didn't work, a student suggested I use the top of the hammer. When that didn't work, someone suggested I used the circle part of the top.

As the nail went into the board, so too did the idea into the kids' brains that you need the right tool used the right way to get the job done!

Then I introduced them to another tool - a clock.

"When we use a clock as our tool, what is our goal?" I asked.

As one girl offered (and all the second graders agreed), we use clocks to read the time.

So, I asked the students to write on their whiteboards what the time was on each of the following clocks:

All the students were able to accurately tell me the time. We all agreed that to read the time on those clocks, you just needed to look where the hour-hand was pointing.

"Okay," I said, "now tell me what time it is."

We counted together that 55 minutes had passed and they all had to read the hour by themselves. Just like clockwork (pun completely intended) all but 1 or 2 students said it was 2:55.

Then, we had a conversation about how we had been using the right tool to tell the time, but we were using it in the wrong way.

Next, I showed them the clock face with the partitioned hours (thanks again to Ainslee Labs for the free clock face. Want to pay for her whole telling time kit?).

We used this clock face to practice telling the time with various times. Over and over again, the students had no trouble identifying the correct hour, even when the hour hand wasn't pointing directly to a particular number. Eventually I removed the gray numbers inside the clock and 100% of the students were able to read the hour on a clock, regardless of how many minutes have passed because they knew that the hour has an area or space that belongs to them on the clock.

4. Check for understanding by having them write a concept statement. 

(This step is very similar to the thinking routine Headlines found in Making Thinking Visible by Ritchhart, Church, and Morrison, p. 111)

Since I was confident that the students had reached the knowledge and skill objectives of the lesson, I asked, "What did you learn today about how you should use a tool to achieve your goal?".

I gave the students a chance to write down their individual responses on their whiteboards and then one-by-one we shared until everyone's ideas were represented in our statement. Below is the sequence of revisions that our conceptual statement when through. My prompts are highlighted in yellow.

"What do you have to remember about tools when trying to achieve a goal?" First child responds:

"Does anyone want to add anything?" Second child adds:

"Does anyone want to add anything?" Third child adds:

 "Is this true just when we're telling time?" Fourth child adds:

"Who needs to do all of this?" Fifth child responds:

"That doesn't sound right." Sixth child corrects: 

The students were comfortable that their conceptual statement encapsulated all the learning they had done up until that point, so we ended the lesson there.

Often times when crafting conceptual statements (sometimes called generalizations, central ideas, or enduring understandings) we create hard-to-understand statements that don't sound like how we normally talk. Concept statements should be written in language that is easy to understand to all who read it. One way to do this is let the students craft the statement, as we did together in this lesson.

5. Reflect on their thinking and decide next steps.

Moving forward, I would want these students to continue to practice reading the hour using this partitioned clock. Eventually, I would want them to independently be able to read the hours and the minutes first with the partitions and then after slowly taking away that support.

Conceptually, I would want to explore other tools and discuss the correct way to use them and contrast that with the wrong way to use them. This conversation would fit in wonderfully with any beginning-of-the-year guided discoveries that students experience as they are exploring the learning tools of the classroom.

After reading how I used a clock lesson to teach a timeless, abstract, universal and transferable concept to second graders, how do you teach these BIG IDEAS to your students?

Teaching 21st Century Skills with Minecraft

In an attempt to help students who struggle in the areas of literacy and math, our school hosts Learning Academy, a before-school academic support class where students are able to practice and refine skills taught during the school day.

Students are invited to attend Learning Academy when they show they have a deficit in literacy and/or math skills, but it important to remember that these students - nay, all students - also require time and opportunities to develop thinking and communication skills, some of which have collectively become known as 21st Century Skills or the 4Cs: communication, collaboration, critical thinking and creativity.

http://fargopublicschools.areavoices.com/files/2014/09/21st-Century-Skills-4-Cs-graphic.jpg

To foster and support the development of these 21st Century Skills, I invited some of the Learning Academy participants to take part in a @MinecraftEdu class after being introduced to MinecraftEdu at a workshop presented by Alan November (@globalearner). MinecraftEdu is a "school-ready remix of the original smash hit game Minecraft." It builds on the excitement and engagement generated by the game-version of Minecraft to give students an environment in which they can develop and refine various academic and social skills.

Students worked together in worlds downloaded from the MinecraftEdu World Library that other users had created. We worked in the following worlds: Tutorial World, Multiplying Decimal Numbers, and The Island. In these challenging worlds, students worked on mathematical skills such as understanding coordinate systems, multiplying decimals and long division while exploring, hunting and navigating through adventurous worlds full of obstacles and pitfalls.

After working for several weeks in those worlds, I created a (very simple) world of my own, where I gave students tasks that would allow them to continue to practice mathematical concepts while also giving them the chance to create and build. Below, is a short video showing the students' work on one particular mathematical task I had set up in this world.

Now that this first group of kids has been with me for several months, it is time for the students to move on and a new group to start learning with MinecraftEdu. The week before I said goodbye to this first group of students, I asked them if they could write up a reflection of what they learned, how they learned it and why they learned it. Below are their reflections. 

After reading about how I used MinecraftEdu to help students develop skills of communication, creativity, and creative & critical problem-solving how do you help your students develop these skills in your classroom?

He who does the talking, does the learning

All of us learn in different and multiple ways. As a teacher, it is important for me to remember to strike a balance in the way that I teach, so that my students have the opportunity to learn in different and multiple ways.

The Learning Pyramid below suggests that relatively little learning is done when students are just listening, but that students learn and retain more when they have the chance to teach others about the concept they themselves are learning about.

https://www.washingtonpost.com/news/answer-sheet/wp/2013/03/06/why-the-learning-pyramid-is-wrong/

Ironically, this specific graphic comes from a Washington Post article that critiques The Learning Pyramid.

Although there might be problems with the pyramid above, many will agree with the underlying concept: the more students are engaged, active and put in charge, the more learning that takes place.

Recently, one of my colleagues shared a gem of a quote from Jen York-Barr: "The person doing the talking is often the person doing the learning." This saying falls in line with the idea that when students are active participants in the learning process, the more they will learn.

Trying to capitalize on this idea, in my morning Minecraft class, I learned that a student wasn't able to easily and quickly multiply 9's because he hadn't mastered "The 9 Trick".

*Please note: I understand that math tricks, shortcuts and 'helpful' phrases are sometimes damaging to students' understanding of mathematical concepts. But, sometimes they can offer students a bridge as they construct their understanding of these complex and abstract concepts.

After giving him a mini-lecture on how to use the trick and giving him multiple opportunities to practice doing the trick with different kinds of equations, I asked him to prepare a short demonstration that would help teach others about the useful trick with multiplying by 9.

Below, is a recording of his demonstration.

At a talk I attended in August, Alan November (@globalearner & @NLearning) advocated for more of this kind of "students-teaching-students" approach. As an example, he shared with us the website http://mathtrain.tv/, which is a free, educational "kids teaching kids" project from Mr. Marcos & his Students at Lincoln Middle School in Santa Monica, CA. The idea isn't solely to show our students these videos (some are very helpful), but to also have our students create teaching videos for an authentic, international audience.

Often times, teachers ask students to turn and talk with their partners to share their thinking and teach others right beside them. With devices that record video and audio that can then be instantly uploaded to the web, how could we put our students in charge of the teaching so that they feel empowered to teach others around the globe?

LET 'EM CHOOSE! Using Academic Choice Literacy Stations in the Elementary Classroom

We want our students to acquire the skills necessary to make good choices in their future. In order to develop those skills, a trusted colleague told me that we must create safe places where students can make mistakes.

Ruth Sidney Charney, in her book Teaching Children to Care, echoes this sentiment when she writes, "Children are growing up in a world with frightful persuasions and terrifying problems. Rather than providing prescriptions for them, we need to give them choices. Decision making must be part of the expected curriculum. There are many kinds of purposeful choices students may make in a regular school day." (p. 374)

One authentic way students can develop these decision-making skills is by giving them the power to choose how they'd like to spend their independent literacy learning time while the teacher is meeting with a guided reading group.

But when planning out the choices we'll give children to independently complete, what exactly can be classified as an Academic Choice Literacy Stations? Conversely, what isn't an appropriate option during this time of the school day? 

To answer these questions, I turned to the teachers with whom I work. Their responses are below:

Academic Choice Literacy Stations are:

• permanent, but not always.
• set aside for specific learning purposes.
• physical spaces, but not always.
• task-oriented with clear expectations.
• more task oriented/hands on for younger students, older students need less task-oriented/hands on.
• open-ended inquiry!
• spots with ongoing routines.
• organized and labeled.
• introduced one at a time.
• meaningful literacy.
• able function w/o teacher assistance.
• flexible and provide variety.
• targeted to instill a love of reading and learning.
• heterogeneously grouped.

Academic Choice Literacy Stations are not:

• a closed-ended exercise.
• new every day (teachers shouldn't feel under pressure to create new lessons each day!)
• done without practice, students shouldn’t be expected to do independently until they fully understand it.
• changed too often or all at once.
• busy work.
• fill-in-the-blank worksheets.
• meant to sit idle.
• activities that require a lot of planning by the teacher.

*The responses above are based on a reading from Guided Reading: Good First Teaching for All Children by Fountas and Pinnell.

Once we build Academic Choice Literacy Stations into our classroom routine, how do we keep students accountable? How can we assess students' efforts during this lengthy time?

One teacher developed the rubric below that her students will use to reflect on the choices they made while she was working with a small group. (Click the rubric below to go to the Google Doc that you can copy and edit for yourself!)

Rather than providing prescriptions for students, what choices do you give students throughout the day, but especially when they're learning literacy strategies, skills and dispositions? 

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?

The (lucky) 13 benefits of reading aloud to your students

Delivering reading instruction in a comprehensive model requires a balance of student and teacher responsibility.

YOU DO IT: Reading independently and working/thinking through literacy stations are both necessary parts of any balanced literacy approach. During those two components, students are completely responsible for employing the strategies and skills taught to them during whole- and small-group instruction.

WE DO IT: During the SHORT whole-group mini lesson and during guided reading, students have considerable responsibility, but the teacher is there to scaffold the experience for the students to varying degrees depending on the task and the student's unique needs.

I DO IT: The one literacy event that the teacher should continue to hold the majority of the responsibility is the sacred "READ ALOUD". This essential part of the balanced literacy model shouldn't constitute a large part of the instructional day, but it is nonetheless crucial that students be read to, regardless of their age.

To learn more about the balanced literacy model that we're using at the school in which I work, click here: Balanced Literacy Expectations.

On September 10, 2015 I participated in a Twitter Chat (#ILAchat & #GRA15) that focused on reading aloud to students. The chat, sponsored by the International Literacy Association (formerly the International Reading Association), allowed me to think about the benefits of reading aloud to students. Below are 13 benefits I was able to capture from that discussion.

Benefits of Reading Aloud

1. To allow students to focus completely on understanding the story instead of decoding the print.

2. To improve listening comprehension.

3. To read books at a higher level than what they independently can.

Reading aloud benefits everyone, especially our non- and struggling readers because it allows them to develop high-level thinking skills, even though they cannot (yet) fluently decode print. Allowing students to build these critical comprehension habits, skills and strategies is essential - even if they're not yet reading themselves, because they'll need them once they eventually break the code.

4. To build background knowledge of the concepts studied during the other parts of the day (like in the Unit of Inquiry in a PYP school).

5. To expose students to a variety of vocabulary.

6. To kick-off a mini-lesson.

It is no secret that we teachers are busy and there is a lot to get through! So why not make our read aloud an integrated part of the learning we're doing, rather than a random selection, separate from the other learning we're doing in the classroom?

7. To build community through a shared experience.

Especially at the beginning of the year, everything we do must be done to build relationships, establish trust and create community. Reading the same text, having shared discussions and contemplating together what will come next builds community in our classrooms.

8. To develop a love, enjoyment, interest, desire & motivation for/of reading and books.

9. To hear a model of fluent reading.

10. To see the authentic contexts in which particular strategies are used by thoughtful readers.

11. To understand the rewards of reading.

Our students look up to us. It is inevitable that we're their role models. Reading aloud to students allows us to show them through our actions that we're good readers and we're passionate about reading.

12. To honor diverse populations and establish an appreciation of others.

13. To recognize students’ own experiences, lives and struggles by reading books to which our diverse student population can relate.

The books that we choose to read aloud are important. As authors write and publish texts that better represent the diversity that mirrors our students and their lives, it is essential that we pick texts that reflect the students in our classroom. Our hope is that these choices lead to acceptance, empathy and tolerance.

Through the Twitter chat with ILA, I was able to gleam 13 benefits to a read aloud. But what do you think?

• In your opinion, what are the benefits of reading aloud that I missed?
• What are books you plan on reading aloud to your students this year? What have you read in the past?
• Who wants to be a part of the Global Read Aloud: one book to connect the world?

Know Thy Impact

Those in education understand that new, innovative ways of doing things are popping up all the time. Especially now, as savvy educators connect on social media platforms like Pinterest, Reddit, Facebook, Blogger and Twitter, there is a superfluity of new things to try out with students.

"Try this! Now try this! Look at this new thing! How about this new graphic organizer?! What about this new thinking routine?!"

All promise to increase student achievement. But John Hattie, a researcher who has authored various publications on maximizing teachers' impact on students' learning, says in this video that, "there is hardly anything we do as teachers that harms kids." He continues that, "95%-98% of things we do to students enhances achievement. All you need to enhance achievement," he jokes, "is a pulse."

But we cannot settle for simply increasing student achievement. Since virtually everything we do to kids will undoubtedly increase their achievement, what we need to do is carefully select the interventions that have the greatest impact on students' learning. In Hattie's language, those treatments with an effect size of .4 or more are desirable. Hattie explains that an effect size of .4 is about a year's growth and he argues that in order to have a remarkable, systematic, positive impact on kids, we need to be doing things with students that will increase their achievement more than that.

So, how do we know what we're doing is working and working to the level that we need? How do we know the strategies, interventions, activities and learning engagements we're doing with kids are growing their achievement more than a year's growth? We must answer Hattie's invitation to "Know Thy Impact".

When we're working with kids, we must look for the evidence that what we're doing with our students is working. We must ask, "what are our kids doing, saying, and thinking that shows they are learning ... and learning a lot about big ideas that are timeless, abstract, universal, and transferable? How can we prove that what we're doing is actually improving their lives? 

If we can't prove that students are learning with evidence, it isn't their fault: it is ours. It is our responsibility to change what we are doing, so that they can be successful.

To learn more about Hattie and his research, start here: Hattie Ranking: Influences And Effect Sizes Related To Student Achievement & Hattie's 8 Mindframes.

The concept of impact has been on my mind a lot in the last 36 hours, ever since I heard that my dear Auntie Judy passed away unexpectedly. Judy, or Ms Higbea as she was known to literally thousands of students, was an educator for 50 years. I learned so much from my aunt; among them, the continual need to question and reflect on what is best for students.

The very ironic thing about a teacher like Judy who is continually asking, "What's my impact?" is that they will never truly understand the impact they have. It is those teachers who aren't just increasing students' achievement scores. And they're not even just increasing students' learning. They're improving the quality of the lives of students, their families, colleagues, and those in the larger community.

As news spreads of Judy's passing, those that were impacted by her are voicing their shock, heartbreak, and words of comfort and appreciation. Through Judy's formal work with the Freeport school system, Freeport Community Services, Wolfe's Neck Farm and her informal interactions, she impacted the lives of many different people in many different ways. Many are sad. Many are grateful.

Judy would probably think it obnoxious of me to be writing about her in such a way. She was quite humble - one of her many lovely qualities I didn't "inherit". But if by her example, we all can continually question, "what's my impact?" her impact on us and on our students will continue.