Math Problem Solving Series #1: Classroom Procedures

Posted on October 29, 2012 by Janet Abercrombie

If you are like most elementary and upper elementary teachers, you are a generalist. You didn’t major in math. You know that teaching math with a textbook won’t help your students achieve the Problem-Solving standards of the Common Core.

Here are just a few common questions teachers have:

How do I get started teaching problem solving?
Is there a magic curriculum that will help me help my students?
How do I manage students when some can do the whole process in their heads and others need step-by-step guidance?
How do I know students are progressing toward the standard?
How do I challenge students that find Problem Solving easy?
How do I help students and parents understand that there is more to Problem Solving than getting a correct answer?

This series aims to answer those questions and more. Today I’ll address a classroom instructional procedure that has worked for me and others I have coached.

An Opportunity to Understand the Question (5 minutes)

I’ll elaborate on conceptual understanding in my next post. For now, just know that students with low reading levels don’t have a chance of solving the problem if they don’t understand the question.

Make sure that student problem-solving scores are not a reflection of reading comprehension. You want to see their math thinking. Ideally, questions can be posed in videos like those presented by Dan Meyer. As an elementary teacher, you’ll probably have difficulty finding real-life situations that can be easily compiled into video (but please share ideas of videos if you can!).

Read the question aloud. Let students draw. Translate the question into students’ first languages, if necessary. Show them the situation with hand puppets. Let them throw the whole paragraph into Google translate. Students need to be able to state two things:

What I know (my students abbreviate it W.I.K.)
What I need to know (W.I.N.K.)

For language acquisition, ask students to think and write the math vocabulary that might help them get started.

Silent Think Time (5-10 min.)

Students need time to think about the numbers, play with different options, fail, succeed, and/or extend. Give them access to manipulatives such as tiles or chips – anything they need except their neighbor.

During the silent time, focus in on your students who excel at problem-solving. Problem-solving extensions for talented/gifted math students come in the questions you ask.

For example: Last week students needed to make a table of numbers and/or find patterns in order to determine the number of polygon tiles that would be in the 8th row of a sequence. While most students were diligently drawing out the pattern, I rolled my exercise ball next to a student, sat beside her and whispered, “I need for you to predict how many of each kind of polygon will be in the 100th row.” She looked at me, nodded, and went back to work.

My favorite extension questions for Grade 5s, which you can modify for your grade:

If you turned that pattern into an equation, what would it look like?
I see you have a series of numbers and outcomes. How might you plot those on a line graph?
Can you draw me a picture to show why that works? Some may want to use legos or pile up erasers. Whatever they need to do to visually represent their thinking…
Is there a more efficient way to get to the answer?
What would happen if…?
How does this problem relate to what we’ve been doing in our math journals? What vocabulary words seem to fit?

Pair Share (5-10 min.)

Students who have come to an answer need to cover up their answer. Pairs should discuss the strategy or procedure they used. It’s as important that pairs share what didn’t work as what did work.

Pairs can share patterns they found. They can ask each other questions like “How did you get from this part to that?”

Sometimes it’s helpful to have pairs join with another pair for additional sharing.

More Independent Work Time (5 min.)

The next question: “Based on what you heard, what would you add to your work or change?”

Consensus (2 minutes – 2 weeks)

Resist the urge to tell students the correct answer. If you don’t know, don’t look it up. In this last part of the process, students need to come to consensus on the answer. The process goes like this:

Solicit all the answers students have gotten. Write them on the board. Answers only, no explanations. Other students are not allowed to comment on answers. When someone offers and answer, simply say, “Thank you.” Add the answer to the list until all have been covered.
Ask, “Are there any solutions on this list that we can eliminate?” Often, students realize they didn’t answer the actual question. They’ll ask that their answers be removed before others comment. Students verbalize, “I don’t think ___ is reasonable because…” Then ask, “Does everyone agree?” If so, eliminate that answer. If even one person still insists on that answer, leave it on the list.
Continue this process. If students disagree with an answer, they can ask a question, but they cannot disagree without offering a reason or a question. This forces your high students to listen to others and find the logical fallacies. Keep asking, “Does everyone agree?” or “Give a thumbs up/down on whether you agree or disagree. What is holding some of you back?”

Be fully prepared to say, “Well, it looks like we can’t reach consensus today. Take some time to think about the reasons behind your answers. We’ll come back to this tomorrow.”

The Fun

If you leave a problem overnight, you’ll probably have students who will come to you later in the day to explain their thinking or try to cajole you into confirming that their answer is correct. Again, resist the urge to confirm an answer. Have the students anticipate questions the others will ask.

Put the problem on your class blog and let the debate continue.

What procedures do you use to teach Problem Solving?

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photo credit: <a href=”http://www.flickr.com/photos/rbbaird/5073748911/”>rbbaird</a> via <a href=”http://photopin.com”>photopin</a> <a href=”http://creativecommons.org/licenses/by-nc/2.0/”>cc</a>

How to Help Students Develop Passion for Writing

Posted on July 19, 2012 by Janet Abercrombie

In an earlier post, I included a video that can be used to introduce students to a Writer’s Notebook. After two weeks of working with a new group of students, students have written more than ten entries and have reflected on their writer’s journals.

Here are some student reflections:

Individual Lessons

Each writing lesson provided students with a different writing idea to try, but no lesson required students to write in a certain way. My “ideas to try” came from a few sources:

Ralph Fletcher’s A Writer’s Notebook
Lucy Calkins’s Units of Study for Teaching Writing, Grades 3-5
Various picture books.

The Overarching Goal

It’s easy to get caught up in a cycle I call product-based learning. In a product-based learning classroom, teachers focus student lessons toward the final narrative, the final essay, or the final whatever.

Using only the Lucy Calkins materials, students work on three to six exploratory journal entries before choosing and working on a final piece. The exploratory journal entries include thoughts about important people, places, objects, memorable events, important “firsts”, and more. Ralph Fletcher offers more suggestions – to write lists and wonderings and memories and observations and…

For additional journal entries, consider inspiring students through mini-field trips. In my case, classes walked to the beach in order to make observations along the way, play, and then write observations, memories, and experiences. Students took “mini field trips” around the school. They visited the school fish pond and were introduced to the turtles on the ground floor (most students didn’t know the turtles existed). The science lab hosts a butterfly garden – which many had never seen. The group also walked along a small section of the hiking trails surrounding the school.

Other schools might have students take “trips” to the roof of the school in order to get a different perspective on “ordinary” settings. They might write along the periphery of the playground and write about observations or memories. Ordinary field trips can include intentional writing time at the site or writing during lunch at a park. If possible, arm students with an iPod Touch to take photographs.

When students begin having fun with writing, they are better equipped to be independent writers – working in a workshop community envisioned by Donald Graves. They also begin to know themselves as writers.

Common Core Considerations

It might be easy to dismiss the idea of a writer’s notebook since no particular Common Core Standard specifically states that students “free write” or “develop a collection of writing.”

Yet a writer’s notebook does two things to directly support all of the CCSS writing standards:

Notebooks provide a foundation for more formal pieces of writing. Writer’s notebooks are places where students explore ideas for the formal opinion, narrative, and research pieces they need to write to achieve Common Core Standards. Notebooks lessen the “I-don’t-know-what-to-write-about” time.
Notebooks provide a place where students can practice writing fluency – getting thoughts down on paper in an efficient way.
Writer’s notebooks allow teachers to better personalize the instruction of Common Core Writing Standards. Assuming teachers use a workshop model of instruction, the key is to develop a checklist of standards and address those standards through individual student conferences and small group instruction.

Say, for instance, you have a student like the boy who produced Sample 2 (above). This student is obviously interested in science, especially science having to do with animals and insects. After a month or so of writer’s notebook entries, begins to steer the student toward research and informational writing about an insect of his choice. Later in the year, he might write an opinion piece on the use of pesticides to control that insect. Still later, you might challenge him to write a story using A Bug’s Life as a mentor text. What would a day in life of that particular bug look like?

When you begin the year with a writer’s notebook, you slow down temporarily by putting off the “formal” curriculum – but the notebooks allow you to go faster later.

How do you help students develop writing ideas?

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Teaching Oral Reading Fluency to Older Students

Posted on July 4, 2012 by Janet Abercrombie

My father taught me to read with fluency and expression. He didn’t know he was doing it. Every Sunday afternoon, my brother and I would sit with him by the heater or on the porch and he would read us the Sunday comics. Characters such as Beetle Bailey, Charlie Brown, Dennis the Menace, and the Wizard of Id each had their own voices.

If you walk into a Lower Primary grade classroom, you’ll likely see students reading aloud to teachers who explicitly teach them to read more smoothly and read with expression. Do Upper Primary and Middle School teachers need to focus on oral reading fluency? If so, how can upper grade teachers explicitly instruct students on fluency without it feeling “childish”?

How does Oral Reading Fluency Fit into Common Core Standards?

The Common Core standards include oral reading fluency as part of the Reading Foundational Skills. Until grade 2, foundational skills focus on students understanding print features, translating print features into words, syllables, and sounds. Until grade 6, foundational skills comprise phonics, word analysis, accuracy, and fluency as they support comprehension.

Does this mean teachers can stop teaching oral reading fluency after grade 6? Probably not. While Common Core Reading Foundational skills are discontinued at Grade 6, Middle School teachers still need to know the following:

Are the students recognizing at least 95% of the words they are reading?
Do students use phrasing, punctuation, and italics to pick up on author’s intent?
Do students differentiate between characters by hearing the characters’ different “voices”?

Oral reading fluency does not necessarily align with silent reading fluency, but oral reading fluency can indicate what happens in students’ heads when they read silently.

When students read fluently, they are better able to analyze of the impact of word choice on meaning or tone. Students who read fluently can better analyze poetic and musical tools in poems and stories (Grades 6 and 7 Reading Literature Standard 4).

Students who differentiate character voices more easily analyze ways in which authors develop and contrast points of view of different characters. (Grade 7 Reading Literature Standard 6).

How to Teach Fluency Without It Feeling Childish

Comics and Graphic Novels: Almost all of my struggling readers gravitate to comics like Garfield and Calvin and Hobbes. In the context of reading fluency, those books are a good place to start. How would Calvin’s voice be different from the voice of Hobbes? Have students record some of their favorite strips or pages. The listener should be able to hear the difference and the recorder should be able to defend why he/she chose the particular type of voice. Let the student “ham it up.” Then move the student to graphic novels.

Plays: Like most other skills, fluency and expression come with practice. Plays allow students that practice. The difficulty is that, unless well-planned, play reading becomes another form of round-robin reading that can quickly disengage students. Also, cold readings of plays set up lower-fluency readers and second language students for public scrutiny. I recommend the following progression of activities:

Before assigning parts or having anyone read aloud, have the students read the play silently. Ask about the characters. What type of person is…? What do you think his or her voice would sound like? How would specific characters sit? Stand? What kinds of clothes would the characters wear? Hairstyles?
Find out if anyone is particularly “attached to a part”. If two or more people want the same parts, you can delegate in whatever age-appropriate way you deem best (rock-paper-scissors), dual recordings (multiple girls play Broadway’s Annie). Consider challenging higher readers to play (and understand) the character they identify with the least.
Highlight the importance of practice. Line. By. Line. Model mistakes and re-takes until the line is perfect. Model how you decide which word in a sentence should be emphasized – and how sentence meanings change slightly based on the emphasis (let students help you decide which sounds best).
Give students recording devices to record, listen, evaluate, repeat. They should keep/save recordings of the best “take” of each line or section.
Pair up students who listen to each others’ recordings and offer advice.
Then meet as a group to read the play orally. Record. Garage Band is a great recording tool. If someone makes an error, they can pause then read the line over again. Errors are easily erased.

If you’re teaching fluency to two or more groups, allow the groups to compare the line interpretations. How did someone else read the same part similarly? Differently? Why do you think they made those particular choices?

Morning class:

Afternoon class:

Modifications for English Language Learners

When listening to the podcasts above, you will notice that each podcast features a student who has limited English. Consider recording lines with the students who struggle with English pronunciation. Then, transfer the practice session to iTunes (or .mp3), and have students practice reading with the recording.

End With Reflection

When I started doing class news videos, I realized that students could easily tell me what they did, but had a harder time telling me what they learned.

Take the time to ask students what they learned about reading fluency. What was difficult at first? Which lines needed the most practice? Why do you think the [tongue-in-cheek mean/crazy] teacher would ask you to do this? How might these skills be valuable when reading other texts?

If you are unfamiliar with the workings of Garage Band, see this tutorial:

…but you don’t need Garage Band. Here is a tutorial on iPad Voice Recorder (also featured on iTouches):

In what other ways might older students practice reading fluency?

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Classroom Management Essentials [Podcast]

Posted on June 30, 2012 by Janet Abercrombie

A few times each year, I have the pleasure of visiting my colleagues’ classrooms. As my division focused on the implementation of Word Study, I signed up to watch Barry Mernin’s classroom in action.

Yes, his Word Study procedures were excellent. More amazing to me were the absolutely seamless transitions his 4th grade students made from one activity to another.

I had to see if this was a transition practiced for guests or if it was the natural way his classroom worked.

The next morning, I surreptitiously hiked up to the 7th floor and tried to hide outside Barry’s door. He saw me.

My mind raced with possible excuses for being there.

“Can I watch?” I asked, not knowing what else to say.

“Come on in!” he said in his strong Bostonian accent.

The bell rings. Students move. No one talks. Each student has a place. No one lags behind.

I gawk.

They must be robots, I think. But the students are smiling. They’re leaning in to hear the morning devotion. They listen intently and ask insightful questions.

When faced with the brilliance of colleagues, a teacher can go one of two ways:

Waffle for a week (or month or year) fighting multiple inferiority complexes, or
Enlist the colleague as a mentor and advisor.

I chose the latter.

This week I interviewed Barry. Whether you’re a new teacher or a veteran hoping to tighten up procedures, the podcast below may be the best 16 minutes of professional development you have this week.

Please share any comments or reactions below. If you’d like to contact Barry directly, you can find him at @LarryHermanHK.

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Category Archives: Anecdotes (My stories)

Top 10 Posts of 2012

Math Problem Solving Series #1: Classroom Procedures

How to Help Students Develop Passion for Writing

Teaching Oral Reading Fluency to Older Students

Classroom Management Essentials [Podcast]

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