Tag Archives: CCSS

Problem Solving Series #3: What Teaching Resources Should I Buy?

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So far, this series has included…

  1. Classroom procedures that help students explore and construct problem-solving strategies.
  2. Ways to make sure your low readers and second language students are not at a disadvantage.

Is there a perfect Problem Solving teaching resource?

Bad news: Instructional materials are only as good as the instructor. More bad news: Materials from the major textbook companies will probably not be adequate – even if their representatives tell you otherwise.

In 2003 and 2007, two representatives of a major textbook company tried to convince me that the problem solving activities attached to the summative assessments were adequate in helping students develop problem-solving skills. My first issue: One problem solver per unit means that students get 12 opportunities during the year to build these skills. Students need more than that. My second issue: Students have had no scaffolding throughout the unit that would make them successful.

Students turned in their assessments with looks of shame and defeat.

One representative claimed there was research defending the position that problem solving strategies need not be explicitly taught. Given enough time, students will develop strategies on their own.

I have scoured the research. Can’t find it. The only research I can find post-millenium states that students with disabilities benefit from explicit, repeated instruction.

Look for materials that explicitly teach strategies.

If students are going to transfer problem solving skills to real-world problems in a different context, Grant Wiggins suggests students must make four cognitive moves:

  1. independently realize what the question is asking and think about which answers/approaches make sense;
  2. infer the most relevant prior learning from plausible alternatives;
  3. try out an approach, making adjustments as needed given the context or wording; and
  4. adapt their answer, perhaps, in the face of a somewhat novel or odd setting

Students must have a mental portfolio of plausible, alternative approaches. Without a mental portfolio of possible strategies, elementary students will tend to do one of the following:

  • randomly add, subtract, multiply, or divide numbers – hoping they pick the right operation.
  • tell you they are using the “guess and check” method. Their paper will full of random computational guesses. One of the guesses will be circled.

If you spend at least a few lessons each year explicitly working with and repeating strategies, students have a mental portfolio of approaches from which they can draw.

Give them a chance to explore one type of problem using the procedures I outlined in the first part of this series. Give them a similar problem the next day. Then give them a homework assignment using that strategy. The fourth time, almost all students can independently use the strategy.

…but don’t name the strategies.

In the next entry, I’ll get on my proverbial soapbox about the “pick a strategy” step in the frequently-published ‘problem solving process.’ Rather than say, ‘This kind of problem is solved by [name the strategy]‘, you still want students to construct a strategy or two that works.

When students find something that works and defend their strategy, then you want them to solidify the conceptual understanding in different (but similar) problems.

Who cares what they call it? If students are going to name things, ask them to connect vocabulary from other math strands to the patterns they are finding.

Collect the strategies in a journal, notebook, or portfolio.

Math journals help students keep a record of previous lessons. Some of the best journals I’ve seen are found at Runde’s Room.

During a lesson where a new strategy is introduced, expect the journal pages will be rather messy. The students will start well, including sketches and bullet points showing their understanding of the scenario and the question. Then, to construct meaning, students need to try different things, collaborate with classmates, change approaches, then collaborate some more. They will cross things out. They will erase until the page tears (although I discourage erasing). They will repair pages with scotch tape. They will use white-out strips. They will circle things and use arrows when explaining work to others. This is a good thing.

The second day, students will get to an answer more directly because they can refer to the procedures that worked the day before and apply them in the new and different situation.

The homework that follows might be given as a worksheet. Rather than collecting the homework for grading, have students take the work out at the beginning of the lesson, compare their answers in small groups, and come to consensus.

If changes need to be made, students can make the changes in a different color pencil. Then, students write a short “things to remember” note and paste the homework in their journal.

Wean students off of the repetition.

At some point, the types of problems should spiral more than repeat. Questions for students: Does this problem resemble any you’ve seen before? How does it relate to prior knowledge in other areas of mathematics?

Some will benefit from looking back at the journal for ideas. Others will not need that step.

Remember that not all the students will need repetitions of strategies.

Once a student demonstrates the ability to independently use a strategy, there is no reason to give him or her more of the same. You will have students that catch on the first time and immediately apply the strategy to new situations. These students will be held back if you require them to have them do the same problems as the rest of the class.

Try giving these students a problem that is at least a grade level higher. Assuming the student has no trouble with that, move him/her on to a project.

What materials help teach problem solving strategies?

I’ve had the best luck with The Problem Solver - with reservations that I will explain in the fourth part of this series.

The real power of the Problem Solver comes when teachers can match Problem Solving strategies with the conceptual ideas of a mainstream curriculum math unit. Some examples:

  1. Students need to find all the factors of numbers. They learn the Rules of Divisibility and continually ask themselves Is 1 a factor? Is 2 a factor? Is 3 a factor? This unit provides a great opportunity for the strategy ‘Make an organized list’. In both situations, students need to think about and organize numbers in a more systematic way.
  2. You are teaching a unit on fractions. Fractions combine well with the ‘Working
    backward’ strategy.
  3. If students are learning to graph coordinates on a plane, they might also practice ‘Make a picture or diagram’.

Mathematical strands that tend to match Problem Solving strategies.

Think of problem solving as an umbrella that covers all the mathematical strands.

No hard and fast rules exist to match problem solving with other mathematical strands – only experience will help you make the matches. Also, problem-solving strategies overlap. Many students begin a problem with a picture or diagram. Why stop there? An organized list might lead to a pattern that can be graphed. Celebrate when students find the overlaps!

If you’re new to a mathematics series or to problem solving instruction, here are some general guidelines:

Conclusion

Find a set of materials that explicitly teach problem solving strategies. Teach the strategies for a decent chunk of the year. Don’t rely on teaching strategies the whole year, but give students enough background knowledge and confidence that they can approach a scenario with a few tried and true options.

Do not force repetition on all your students because some will not need it. An initial problem or a pre-assessment might be the same but the follow-up problems need not be.

Connect the strategies with other mathematical strands.

Have you found any research on the pros and cons of teaching strategies? What materials have you found that help teach problem solving? Please share!

If you like what you read, please subscribe to Expat Educator. You’ll have instant access to subsequent posts in this series. The next post: What the Problem Solving Process is Missing.

photo credit: Marquette La via photopin cc

Are We Confusing Standards with Standardization?

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Standards, not standardization

My soap box. Here I go again…

As I write this, I’m ducking behind my screen, ready to dodge virtual tomatoes. Please bear with me as I question some assumptions we are making with regards to standards and standardization.

We educators use terms and acronyms, assuming that all people have the same understanding. First, I will clarify terms. Then I will ask questions.

Clarification 1: Textbooks are not curriculum.

Most simply put, curriculum is a list of things students should know and be able to do. We call the list a list of standards because we hope that all students will be able to know and do these things when they leave school. Then we create benchmarks, clarifying what those standards “look like” at various grade levels.

I often hear teachers and other school leaders saying that they want to find a curriculum that teaches to the standards. What they’re really saying is this: They are looking for the “magic bullet” educational materials that will help student test scores improve.

I haven’t used textbooks in over ten years. What I learned from my Australian colleagues is this: Teachers can look at a list of standards and figure out the best way to teach to those standards.

So here are some questions: Are schools underestimating teachers? Are schools assuming that teachers cannot teach to standards unless they have the “right” materials?

Clarification 2: Standards are different than Standardization

If we understand curriculum as a list of standards describing what students should know and be able to do, we can differentiate between curriculum and instruction.

Curriculum is built on standards. Instruction may or may not be standardized.

The progression of assumptions goes something like this (my reaction in italics):

  1. We need to teach to the common core (standards). True.
  2. The district has purchased materials that align with the standards. Okay.
  3. If we all teach this curriculum (a misuse of the term), then [the company's] research suggests that students will test better. Here is training on how you should all use these materials… Hold the phone!!!!!

We have crossed a line at #3. We assume that, to hit standards, instruction must be standardized according to commercially-created materials.

My next question: Once companies have convinced us that they have the “right” materials, are we requiring all teachers to use those materials in the same way?

Clarification 3: If we agree that instructional standardization is unnecessary, we can maintain creativity and passion in a standards-based classroom.

But we need to make a few paradigm shifts.

Specifically,

  1. Look at the standards before we look textbooks or think of “thematic” activities. The unit on Spiders is no longer a list of activities. It is a list of standards first (classification, expository writing, research, health and safety), then activities.
  2. Use team meeting time to plan. Work together to compile activities and resources that will teach to the standards. Use textbooks and other materials as resources. Trust yourself to create new activities that teach to standards more authentically than pre-packaged materials.
  3. Maintain checklists of standards and keep track of students that have and have not met specific standards. Project-based learning is then tweaked to include the following instructions: Somewhere in your project, you need to show me that you understand the difference between insects and spiders. You need to tell me whether or not your spider is dangerous and how you can tell. When I come and talk to you, I will ask which books and websites you have been reading and how they helped you.

Clarification 4: There are some things that are just wrong.

Wrong: Awards and sanctions for schools, teachers, and students based on test scores. Household rewards and sanctions do not get kids to bed on time, nor is bedtime a single standard by which we judge parenting (thank heavens!). Let’s pay attention to the scores, but realize that tests will never tell us the full extent of student knowledge.

Wrong: Hours and hours of standardized testing. I’ve created assessments where students learn through the process of demonstrating, synthesizing, and evaluating their knowledge and skills. Students learn nothing when they fill in bubbles. A few hours per year is okay. Weeks? Wrong.

Wrong: Teaching all students the same way. The little Steve Jobses and Mark Zuckerbergs in your classroom (who probably test well), will withdraw or start programming social media when they should be underlining the topic sentence.

There are more wrong things, but those are the biggies.

Conclusion: Education is not doomed, unless we confuse standards with standardization.

As Yong Zhao Trim said, American education was “doomed” in the 1960s when the Russians beat us to space. American education was “doomed” according to the 1980s publication “A Nation At Risk.” NCLB was created because schools were failing.

Yes, we have work to do in education. But, we have innovative teachers who care about student passions and are capable of creating lessons that teach to standards. Accomplished teachers know their students and how they learn.

Let’s teach to the standards, but teach them in ways that are individualized, differentiated, and personalized.

My last question: What if we change the assumptions?

If the new assumptions are as follows…

  • Teachers can teach to standards with or without specific, commercial materials.
  • No one set of materials (commercially-created or otherwise) will help teachers teach all standards to all students.
  • Standards can be taught and tracked in the midst of innovative, project-based classrooms.
  • We fight government initiatives that are truly wrong while resolving to show the world that students learn through individualized, differentiated, and personalized instruction.

…how would schools look different?

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Teaching Oral Reading Fluency to Older Students

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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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Top 10 Lessons Learned the First Year Overseas

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A few weeks ago, International School Services tweeted the question What did you learn in your first year of International School teaching?

1. Human Resources personnel and principals are your best friends.
After receiving the official job offer, I must have emailed Human Resources once per week. Should I bring x? Does the school have y? What rare tropical diseases might I encounter? Japanese Encephalitis exists outside of Japan???

Visa paperwork can be overwhelming: health checks, copies of transcripts and diplomas, proof of vaccinations. If you have pets, plan on a separate set of procedures.

2. International Schools have a culture of their own.
I signed to join a group who met monthly to discuss critical issues related to education. One of our first topics for discussion was Third Culture Kids (TCKs). I learned that many of my students have never lived in their passport countries. Also, they do not regularly interact with host country children. The students develop a culture of their own.

I’ve since realized that overseas faculties are much the same. Teachers in more politically unstable countries live on compounds and rely on each other for socialization and general sanity. Faculties in large cities tend to get out and mingle with other expats – many of whom are not teachers. Some schools tend to attract younger folks in search of adventure. I landed at a school with a rich history that could be learned from colleagues who had been at the school more than 20 years.

3. Different cultures give teachers varying amounts of respect.
Although I left the USA before the infamous passage of No Child Left Behind, I heard and read plenty of criticism about the state of education in America. I taught in a district without music or PE teachers. Colleagues in other districts were put on paper rations and were required to dust and mop their classrooms. The school district had many active, wonderful parents. Also, the school district held restraining orders against parents who had threatened staff and students.

My first parent night overseas: At least one parent of every student showed up. Dressed up. Took notes. Parents frequently brought gifts. If I called a parent about a discipline issue, the issue never arose again.

4. Expat parents expect a LOT.
While parents gave me a huge amount of respect, they kept me on my toes. “Average” and “Meeting Expectations” were unacceptable grades for many. They wanted to know what else could be done to ensure that their 10-year-old entered an Ivy League university. For some, standardized test scores below the 95th percentile were reason for an extra parent-teacher conference. Perhaps that is not true in all schools, but it was true in mine.

5. Absentee parentism is as prevalent in rich schools as in poor schools – but it looks different.
The main reasons parents had such high expectations for their children was that the parents expected a lot of themselves. Many of my students’ parents were bilingual and traveled throughout Asia overseeing factories, starting joint venture companies, attending regional CEO meetings, and more.

The kids missed their parents. They eagerly awaited parents’ return home. Some felt abandoned because, even when parents were home, they were on regular conference calls.

In the end, many students spent less time with their parents than did students in my former USA public school. Kids of divorced parents typically saw Dad on Wednesdays and every other weekend. The international students were never sure when Dad (and sometimes Mom) would be home again.

6. One of the most valuable forms of professional development is working with teachers who are natives of other countries.
When I hear of Common Core Standards, I recall the first year I taught with an Australian teacher. While I was struggling to figure student grades by rubrics and percentages, I watched her create checklists of things students needed to know. She ticked the boxes when students had mastered standards. Although I didn’t know it at the time, it was called Standards-based education.

Standards-based marking made sense. List what students must know and do, mark progress, and make a special mark when students go above and beyond the standard.

7. You long for the smells of home.
Christmas 2001. I had been in Asia since August. The weather was no longer oppressively hot – it felt like Spring.

One afternoon I opened the classroom door and stopped. Pine smell. Could it be??? I must have looked like a basset hound sniffing the trail. The scent got stronger as I climbed to the third floor, the fourth floor, and around to the office. There stood a Douglas Fir, imported from my home state of Oregon.

I ate my lunch beside the tree every day until the Christmas break. Most of my life, I had taken the smell of pine for granted. Now the scent took me home to my family.

8. There are spices other than salt and pepper.
I lived a meat-and-potatoes childhood. One of the first weeks of school, my colleagues invited me to dinner at an Indian restaurant.

I couldn’t make any sense of the menu but, since all the dishes were served family-style, I let others do the ordering.

I took a bite. My eyes watered. I grabbed beer, gulping it down and praying for my tongue would forgive me. A colleague turned to me and chuckled. He said, Yes, Janet, there are spices other than salt and pepper.

Indian and Thai are now favorites – but they shocked the palette (and the intestines) the first few times.

9. Labels meet different things to different people.
I quickly stopped using the words conservative and liberal. In Australia, the Liberal party is like more like the US Republican party and the Labour is more “Democrat”. I was in a group of South Africans, Dutch, Germans, and Americans. One American was a self-proclaimed conservative. Another in the party turned and said to him, “Oh, so you’re racist.” Whoa.

I’m happy to talk about my feelings on an issue, but I’ve learned to not try and capture the opinions under an umbrella label. Political and religious labels do not translate well across the various forms of English.

10. Life really isn’t fair.
Yesterday I wrote a post for Expat Sisterhood about how my understanding of “woman-hood” has changed since moving overseas.

Early in my first year, I joined a Family Bike Trip into the Pearl River District of Mainland China. I saw Asian poverty for the first time. We passed through rural villages with no plumbing.

We needed a nurse for the Family Bike Trip. One of the families brought along their domestic helper. Their helper had been an Emergency Room nurse in the Philippines. She made more money as a domestic helper (approximately US$400 per month) than she did as a nurse in her home country. She left her two children to work in Hong Kong so that her children could go to High School.

The first summer, I taught English to English teachers in another part of China. As I got to know them, I realized the hardships they face when they are educated, they want to earn more money, but they must apply and wait up to 20 years to move from the village to a city.

I went with a team to deliver scholarships to students in China. These A-students had been accepted into High School but could not attend because the family was unable to pay the required US$150 for annual tuition. We helped 30 young people. Millions are in similar circumstances.

I guess it’s fair to say the learning curve is pretty steep the first year. What did you learn?

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