Category Archives: Instructional Strategy

Fascinating Data: One step closer to a thinking classroom


Are your students lacking motivation to begin a task?  Does their typical discussion involve headphones and iPhones?  Do they stop working at the first sign of trouble?

If so, read on…

As is often the case, I Googled one thing and found myself several links later reading  Peter Liljedahl’s research on thinking classrooms and was fascinated. His research included 300 teachers, the majority of whom taught 6th-12th grade, on the elements that supported or impeded a thinking classroom.

“A thinking classroom is a classroom that is not only conducive to thinking but also occasions thinking, a space that is inhabited by thinking individuals as well as individuals thinking collectively, learning together and constructing knowledge and understanding through activity and discussion. It is a space wherein the teacher not only fosters thinking but also expects it, both implicitly and explicitly.”   ~Peter Liljedahl, Associate Professor at Simon Fraser University, Canada

One of the elements Liljedahl found impactful was the student workspace.


And this is where it gets interesting.

Liljedahl  looked at five different workspaces.  He gave each group of 2-4 students only one pen to ensure group work, then gave students a task to solve.  The five workspaces included:

  • a wall-mounted whiteboard (vertical, non-permanent (i.e. easy to erase))
  • a whiteboard laying on top of their desks or table (horizontal, non-permanent)
  • a sheet of flip chart paper taped to the wall (vertical, permanent (i.e. can’t erase marks))
  • a sheet of flip chart paper laying on top of their desk or table (horizontal, permanent)
  • their own notebooks at their desks or table (horizontal, permanent).

Eight data points were collected to measure the effectiveness of each of the surfaces.

  1. Time to task
  2. Time to first mathematical notation
  3. Eagerness to start (A score of 0, 1, 2 or 3 was assigned with 0 assigned for no enthusiasm to begin and a 3 assigned if every member of the group were wanting to start.)
  4. Discussion (A score of 0, 1, 2 or 3 was assigned with 0 assigned for no discussion and a 3 assigned for discussion involving all members of the group.)
  5. Participation (A score of 0, 1, 2 or 3 was assigned with 0 assigned if no members of the group were active in working on the task and a 3 assigned if all members of the group were participating in the work.)
  6. Persistence (A score of 0, 1, 2 or 3 was assigned with 0 assigned if the group gave up immediately when a challenge was encountered and a 3 assigned if the group persisted through multiple challenges.)
  7. Non-linearity of work (A score of 0, 1, 2 or 3 was assigned with 0 assigned if the work was orderly and linear and a 3 assigned if the work was scattered.)
  8. Knowledge mobility (A score of 0, 1, 2 or 3 was assigned with 0 assigned if there was no interaction with another group and a 3 assigned if there were lots of interaction with another group or with many other groups.)

Here is the data:


Non-permanent surfaces outperformed permanent surfaces in almost every measure. Are students more willing to take risks when they are working on non-permanent surfaces?

Vertical surfaces outperformed horizontal surfaces in almost every measure.  The act of standing reduces the ability to hide.

Vertical whiteboards decrease the amount of time it takes students to get something on their surface;  from almost 2 1/2 minutes down to 20 seconds!  Eagerness increases when moving to a vertical whiteboard – a perfect 3!   And, Participation and Discussion jumped from less than 1 with a notebook to close to 3 with a vertical whiteboard.

How cool is that?!  This is impactful data!  

Get some white boards, people! Get them on the wall! Get them now!!  

And, let me know how I can help!


P.S. If you are in need of super cheap whiteboards, just laminate a piece of construction paper or tag board!

P.S.S. Find a concise summary of Liljedahl’s research of the 9 elements of a thinking classroom here.

Two trains are heading in the opposite direction…: Teaching problem-solving

I’ve always hated the train problem; you know, the one in the title?  I’m not sure why; I think because I would typically read through it once and become defeated since I couldn’t immediately come up with an equation I could apply. Therefore, it must be hard.  My experience has been that most students feel this way about problem-solving.  The STEMtistic below says it all.


Our education standards for mathematics expect that students are engaged in problem-solving.  The National Council of Teachers of Mathematics (NCTM) Principals and Standards for School Mathematics has verified that problem-solving is an integral part of learning.  OK, then how do we rewire students’ brains so that they don’t fear math problems?  How do we help students access the math?

To start, we need to teach our students how to read like a mathematician. 

We need to teach our students how to bring the linguistic and math clues to the surface.

We need to engage students in understanding the problem before they try to solve it – or worse, freeze and dismiss it all together.

Close reading is eduspeak for reading deeply for a purpose. It is more than just skimming. In the literacy world, close reading includes three phases:

  1. Reading for Key ideas
  2. Rereading for craft and structure
  3. Rereading to integrate knowledge and ideas.

I’ve been to several trainings on how to close read science and social studies texts and articles, but I have never been trained on close reading in math; I didn’t think it even applied.

Then came those 5th grade classroom teachers I was privileged to visit last month. During one of those visits, I saw close reading . . .  in math!

The close reading strategy was called the 3 Reads Protocol. In this protocol, students read the problem three times, each with a particular focus. While the strategy was used in a 5th grade classroom, it can be used just as effectively at the middle school and high school levels.

Below was the problem given to the 5th graders:

On the first read, the problem was read chorally (as a class) then covered up and students were asked, “What is the problem about?” Students talked to their study partners about what they remembered of the situation – not the math, just the context. Students answered that the boy in the problem was doing some of his homework before dinner and some after.

Next, students read the problem aloud a second time with their partner and were asked to determine the key quantities and key words from the problem.  After 2 minutes of partner time, the teacher listed the quantities and words on the board.  The students answered with the obvious fractions, then included a smattering of words such as completedbefore, after, remaining, dessert, and the rest. Students were asked why these words were important and how the quantities were related.

The third read,  again with a partner, focused students on the question, What is the problem asking us to find out?  After determining this, students were asked to draw a diagram that included the quantities and their relationship. Some students started with a tape diagram, others with an area model.

Only after these three readings and active thinking did students begin to actually solve the problem in partners. There was a lot of math discourse happening around the room that continued for a good 15-20 minutes.  During this time, the teacher walked around the class, listened in, asked questions about student thinking, and noted which students she would call on during the whole class discussion.

Students were then brought together as a class.  The teacher asked specific partners to share the models they had drawn.  As each model was shown, the teacher asked questions of the class such as:

  • How does _________’s diagram show 3/7?
  • Where is ¼ in ________’s diagram?
  • How are ¼ and 3/7 related in this diagram?

She made sure to ask students who had made models that had taken a divergent path to explain their thinking and asked the same questions she had asked the students with the correct models. Once the teacher went back to the class list of key words, the class came to an agreement about which model (s) made the most sense and the answer that was correct.


After whole group discussion

We want kids to learn how to solve problems on their own. We need to give them strategies to do it!   Like any skill we want to master, teaching kids how to read closely in math will take time, practice, and coaching – especially if we want to change attitudes about word problems in general.

So, try the 3-reads protocol in your math class! Like most new strategies, it is not likely to go super smooth the first time. Don’t give up! Try it again and get your students out of the bathroom and cleaning up in math instead!

BTW:  I solved the train problem…eventually!

Train Problem - SOLVED!




Warming-up: Just do it

As I age, I’ve noticed that warming up before exercise is becoming more and more important. Walking a couple of blocks before I start jogging really does help me get my body and mind ready for the task ahead and avoid injury. When I think about applying the metaphor to school, it makes sense: I may not get “injured” in the academic aerobics in which I participate, but it’s certainly helpful to take a bit of time to reset and remember, before engaging in new learning. Thus, whether anticipating physical or mental exercise, I am a proponent of warm-ups.  Like preparing myself for a run, I find them to be a way of refocusing my students’ minds on math during the first five minutes of the period.  The key word in that sentence is “five.”  Unless I set a timer for myself, that five minutes can easily turn into 10 or 12. Like when I run, if I don’t push a little harder, my progress is going to be slow.

Forty-five minute class periods do not allow teachers to be as effective as we would like to be with our students.  When trying to figure out how to structure that precious time, we have to think hard about what which pieces have the greatest impact on student learning.  One piece that is often under fire is the daily warm-up; I’m here to remind you: it’s worthy!

...but warm-ups are!

…but warm-ups are!

Beyond using warm-ups to review the concepts of the previous day and/or to preview the day’s upcoming lesson, Jessica Bogie a high school level Geometry and 6th grade math teacher (and blogger – Algebrainiac),  proposes that warm-ups are good for conversation about math ideas – a worthy idea! Jessica hosted an episode on  Global Math called Warm-ups = What Are They Good For? .    She suggests a two-week rotating schedule of warm-ups:

Two-week warm-up rotation idea.

Two-week warm-up rotation idea.

I’ve blogged before about my love for Estimation 180 here and here  and Would you Rather here, so I was happy to see both in her 10-day rotating schedule.  I love the Visual Patterns site and Math Mistakes well and will likely blog about them in the future.

With much buzz about Carol Dweck’s Mindset theory applying in education, having a Mindset Moment Monday every month is  a great way to continue the conversation all year.  Check out the list of short videos that Marisa from the blog, La Vie Mathématique, posted on the topic.

Another warm-ups resource Jessica mentions, is Lisa Bejarano’s Filing Cabinet of Warm-ups on the Crazy Math Teacher Lady blog.  Lisa teaches Geometry and blogs about the lessons she teaches. This list repeats some sources I’ve listed but offers new ones as well.

So, praise be to warm-ups; just as physical ones get our bodies ready for the exertion of exercise, these mental ones get our minds ready for the hard work of learning!

Rigorous Reading Across Content Areas: Text-Dependent Formative Tasks

Back in February, I had the opportunity to attend the Oregon Reading Association’s Winter Institute, featuring Douglas Fisher and Nancy Frey. For a self-professed literacy geek like me, this experience was akin to IT folks hearing from Steve Jobs, Classical Violinists spending a day with Itzhak Perlman, or Craft Brewers (hey, we are in Oregon) being addressed by Fritz Maytag. It’s not often we get to see our professional mentors live and in person, at the Holiday Inn PDX Airport, no less.

Screen Shot 2015-04-07 at 11.15.35 AM

Their presentation provided guidance for teaching complex texts and raising the level of rigor in the classroom, which are Common Core literacy cornerstones. A bonus of our participation in the session included walking away with a copy of Fisher & Frey’s 2013 title, Rigorous Reading, 5 Access Points for Comprehending Complex Texts. Although each access point is worthy of its own blog post , the one this post is devoted to is Access Point #5: Demonstrating Understanding and Assessing Performance. In this section of the text, the authors posit the need for after-reading “Text-Dependent Tasks” such as the following:

Perspective Writing: Perhaps too often, we teachers assume the role of audience for a student’s writing. Writing from differing perspectives or to a different audience can stretch students’ decision-making powers. Who is the audience? What then is the purpose of my writing? What register must I employ in my style?

Many teachers have heard of and have used the RAFT strategy developed by Santa and Havens (1995) requiring students to understand the Role, Audience, Format, and Topic for each piece of writing. Fisher & Frey resurrect it here as a strategy for formative assessment. In one example they cite, an English teacher learns she needs to review author’s purpose and the introduction to The Metamorphosis because her students don’t show evidence of understanding beyond the literal level when presented this RAFT:

Role – Gregor Samsa

Audience – Mr. and Mrs. Samsa, his parents

Format – Note

Topic – Why don’t you notice me?

Though, RAFT is not only for the realm of the English Teacher. Apply RAFT after reading a famous historical speech, such as Susan B. Anthony’s “Women’s Rights to the Suffrage, 1873.”

Role – Participant

Audience – Susan B. Anthony

Format – Letter

Topic – Reaction to this speech

In Science: After reading the article, “West Coast starfish are dying, but why?” convince Congress that the plight of sea stars is farther reaching than just one species:

Role – Researcher

Audience – U.S. Congress

Format – Speech Talking Points

Topic – Explanation of metaphor: “…starfish are sentinels about conditions in our oceans….”

Here are a few other Text Dependent Task ideas to include in your repertoire:

  • Admit Slips: Akin to Exit Tickets, students instead respond to an assigned topic as they enter the classroom. “Describe the water cycle.” “Why are irrational numbers important in science and engineering?”  “What factors motivated the character to commence her journey?”
  • Found Poems: As students reread a text, have them find key phrases to arrange into a free-verse poem, linked with connector words (articles, conjunctions, “to be” verbs, etc.)
  • Yesterday’s News: Summarize the information presented the day before, from a film, reading, lecture, or discussion.
  • Write a letter to people who have made a difference. Write to Albert Einstein about the negotiations for a present day nuclear deal in Iran. Write to an author about his/her influence on a particular topic (TC Boyle on the environment; Roald Dahl on imagination, for example).

Students beginning some of these tasks may need a reminder to go back to text and quote or paraphrase in their responses. Sentence frames to introduce text are helpful aids to guide students:

  • (author) states, “….”
  • In her book _______, (author) maintains that, “….”
  • X disagrees when he writes, “….”
  • According to the text, “….”

Supplemental frames to assist students with explaining their evidence can prevent the infamous “hanging quote,” when students mistakenly think that quoted text speaks for itself:

  • Basically, X is saying _______.
  • In other words, X believes ________.
  • X‘s point is that ________.

Finally, writers also need to make a distinct connection, identifying the reason for including the quote/evidence. Simple connector frames could be:

  • This statement is important because ______.
  • This relates to _____.
  • This contradicts _____ because ______.

Perhaps May isn’t the time that you’re thinking about doing “heavy lifting” in the classroom, but consider these ideas seeds. Let them germinate over the summer if you’re not ready to harvest them today. You never know what you might reap in the Fall.

Academic Vocabulary, Language, and Math

Ask yourself this seemingly simple question: What’s the difference between Academic Vocabulary and Academic Language? They sound similar, right?  We not only need to recognize the similarities and differences of these two concepts, we need to provide opportunities for all students to engage in both in our classes, including Math. Earlier this month, I had the privilege of collaborating with our district’s Sheltered Instructional Coach, Maranda Turner, and six of our talented high school math teachers doing just that.

Our work was centered on deepening our understanding of instruction that supports all students, particularly students struggling with language and literacy in math. We walked away with a solid understanding of the difference between academic vocabulary and academic language, along with engagement strategies to help us plan specific activities aligned to research based strategies to help all learners succeed.

Vocabulary Word Box used during the session.

Illustrated Vocabulary organizer used during the session.

The first part of our morning was spent making sure our next unit was aligned to the Common Core Learning Targets in our pacing guide. Research by John Hattie shows students make academic growth when we communicate and engage our students in learning targets. Besides students being able to really answer their parent’s age-old question: “What did you learn at school today?” they also have a defined purpose for doing the work being assigned to them.

Algebra 1 Semester 2 Unit 7

Algebra 1 Semester 2 Unit 7

The rest of the day we zeroed in on the particulars of academic vocabulary (words specific to the content area) and academic language (how to communicate the vocabulary in a “math way”). Each teacher pair chose 2-3 priority academic vocabulary words for the next unit, determined an appropriate activity, identified opportunities to practice the academic language, and establish where it would fit into the unit. Activities included the use of Illustrated Vocabulary Boxes, Frayer Models,  (low/no prep) Word Sorts, and Sentence Stems and Sentence Frames.  We discussed the importance of allowing students plenty of written and spoken rehearsals as they worked to use new academic language.  

Academic Language Frame for Math.

Academic Language Frame for Math.

After each instructional component (learning targets, academic vocabulary, academic language), teachers were provided 30-60 minutes to plan these tools into their instruction. It wasn’t nearly enough, considering the work needed in all units, but it’s the right work, and teachers appreciated the supportive start.  We know that when change is hard, we must narrow the path.  Consider this: take one strategy; use it once or twice a week in one course. How soon would the strategy become automatic and in all courses?   

Let me know if you are interested in spending some time working on how to support kids in their math language and literacy. I know a coach….


Targeting Conventions Through Listening

I can’t really remember how we got on the subject. I stopped by Springwater Trail High School last week and dropped in on a few classes, including Paul Kramer’s. I was there around lunch, and Paul took a little time to give me a sense a what’s going on in his English classes. That’s when we talked about the change he’s made to his approach to teaching conventions.

Paul explained he first took his conventions frustrations to colleague Aaron Ramsey to brainstorm. Kramer described how he hated teaching conventions and his students hated learning about them in the traditional “skill and drill” format. More importantly, he wasn’t seeing student growth; transfer from worksheets and quizzes to student writing wasn’t happening. He was looking for something different; so, he and Aaron collaborated on another way to focus on conventions that could better mimic real-world writing. What they came up with was Conventions Dictation.

Conventions Dictation is a more authentic way to learn these important skills through differentiation, as well as a way for students to take responsibility for their learning. Paul started recording himself using the app Audacity, already installed on his MAC. (Garage Band and even Quicktime will do the trick, if like me, you’re not finding this app already available). What did he choose to record? Engaging book jackets! Student buy-in? You bet! Recordings are less than a minute in length. He reads articulately yet fluently, so students can hear the pauses that often indicate the need for some kind of punctuation. There are differentiated levels of recordings, depending on the length and complexity of sentences: basic, intermediate, and advanced.

Paul uses district late-start Wednesdays, when classes are a bit shorter than normal, to focus on writing. Conventions work has become a cornerstone of these class periods. Here’s how it works for the first opportunity of the semester:

  • Students pick up a laptop from the mobile cart and login to Google Drive. (Can be done in a computer lab or, if allowed in your building, through BYO student-owned devices).
  • Kramer shares a .wav file of the recording (m4a files work, too).
  • Students don earbuds, listen, and transcribe the recording by hand. Transcriptions are done in writing, not on the computer because Kramer wants students to be purposeful in their decisions.
  • Students can take as much time as needed to transcribe, working at their own pace. Most generally complete the task in one class period (about 40 minutes on late-start days).
  • Students are encouraged to take the time to edit after they “unplug” and before they turn the transcription in.
  • During the editing process, students are allowed several resources: use of a dictionary (print or online), the classroom Writer’s Guide (a print resource compiled by Kramer with targeted conventions rules and examples); or a host of online resources he’s culled onto a Google Doc, also shared with students.
  • Students submit their attempt for a grade.
  • Kramer scores student work on a rubric he’s designed tied to CCSS Speaking & Listening and Language Standards to assess skill proficiency.
  • Students who pass the proficiency can move on to other transcriptions to improve their grade or move on to other writing options.
  • Students who don’t pass, need to make corrections (again accessing the resources available to them), and confer with Kramer for targeted instruction. In addition, other options are available for students to demonstrate their proficiency in conventions once they’ve attempted at least one dictation.

The proof of this method’s benefits is in the pudding, as they say–in this case, in the students’ writing. I had an opportunity to informally interview students in one of Kramer’s Junior Language Arts classes. Individually, students reported they felt their own writing had improved because of this approach to conventions, as evidenced by higher scores on that trait. Kramer is the first to admit this is still a work in progress, but providing a meaningful way to engage students in the technical aspects of writing is a most excellent first step!


Strategies and Activities and More, oh my!

“Lions and Tigers and Bears, oh my!” is a familiar quote to many from the Wizard of Oz. It’s come to represent the speaker being fearful of a rumored threat. But, we also know that Dorothy locks arms with Tin Man and Scarecrow and plows forward with them in the face of fear and ultimately conquers it (picking up the Cowardly Lion in the process). Perhaps distinguishing strategies from activities isn’t quite as intimidating as encountering wild animals in the Haunted Forest of Oz, but it has leant itself to some uneasiness.

So, let’s extend this analogy a bit: Dorothy’s ultimate goal is to return home to Kansas. In order to do that, she has to employ research-based strategies by engaging in a variety of activities. The first strategy we witness is Feedback; she confers with Glinda, the Good Witch of the North and learns she needs to go on a quest to reach the Wizard. Armed with this new information, Dorothy sets off and soon employs Cooperative Learning as she picks up Scarecrow, Tin Man, and the Cowardly Lion. She collaborates with her partners to follow the Yellow Brick Road, reaching the Emerald City and the Wizard. Optional extension: continue the metaphor with a partner or on your own; for the rest, here comes the connection!

A couple of weeks ago, Shannon and I teamed up with building admin to deliver PD to middle school teachers in our district on this very subject: distinguishing Strategies and Activities (not The Wizard of Oz). In order for our students to achieve positive academic results, we need to engage in activities that employ research-based strategies to better their performance.

Once the foundation was laid, we targeted one specific strategy: Non-Linguistic Representation (NLR) and a specific activity: Concept Mapping. We briefly reviewed Dual Coding Theory, namely reminding folks that we take in information in two ways, linguistically (word-based) and non-linguistically (sensory), concluding that the more we employ both systems of representation, the better we are able to think about and recall knowledge. Following, we facilitated an activity using a jigsaw process in small groups to complete a Concept Definition Map.

Working in content area groups, teams then brainstormed other types of NLRs that would be applicable to their field. Below is an example of one such list:

NLR ELA examples

Let’s take a look at a few of these NLRs that might be transferrable to various content areas:

The 4-Square is often used for vocabulary and as part of the writing process, but it isn’t the sole property of English Language Arts. Students can help solidify new vocabulary by not only defining it and writing about it, but by also supplying a picture to represent the word. When writing, students may benefit from a structured graphic organizer that helps them organize their thoughts and reminds them to incorporate transitions, details, and a summary conclusion. The designs are many and modifiable, too–truly versatile.

Haiku Deck is a presentation software students can use for a variety of purposes/projects. Check out this Haiku Deck Sample. They also provide a simple introduction video you can access on their home page.

Comic strip templates can be used for visualization activities with difficult text or to explain a process in a visual way. I had sophomores in small groups create a strip for the classic poem, “Lady of Shalott” stanza by stanza in order to “see” the action unfolding, which aided their comprehension. Again, if you are tech-minded, there are several comic strip makers and animation apps free online or for tablets, such as Bitstrips and Toontastic. Scientific processes and historical events, among other adaptations, seem like they would be a natural fit to such an activity.

Roseanne Roseannadanna

So, it’s like Rosanne Rosannadanna says, “It’s always something. If it’s not one thing, it’s another.” Either Dorothy gets bumped on the head, dreams of traveling to the Land of Oz and has to get back home to Kansas, or we have students in our classrooms who have their own dreams of success. Regardless, employing researched-based strategies, engaging students in effective activities, and providing multiple ways of gaining that knowledge is best practice.