Posted in general education, homeschool, more seeds, parents, special education

Nurturing Your Own Soul

Teacher-Friends: We Live in a Strange, Scary Time

Teacher-friends, I wanted to check in on you. How are you? Are you well? If you are struggling, I hear you.

Between the end of summer school and the beginning of the school year, my whole family came down with something horrible.

It started with a bad headache and sore throat. Then moved on to a fever. My 16-year-old had a fever for 11 days straight. With the fever came body aches, a runny nose, diarrhea, stomachaches, brain fog and extraordinary fatigue – the kind that had us sleeping for days and wondering if we were ever going to feel well. And that cough. The everywhere, anytime kind of cough that wears you out.

Two of us got COVID tested. The results were negative, but our caregivers and employers were suspicious, and required us to quarantine, anyway. I missed the first day of school, sitting at home, doing my lesson plans and worrying about my husband, who had a heart transplant in January, and had the highest fever of all of us. I moved an air mattress into our home office. My son holed up in his room (not a huge disadvantage for a teen – it’s their natural habitat). My husband would occasionally stand outside my door and look forlornly in, or bring me a cup of coffee to set on the corner of my desk before he retreated.

At this writing, I am back at work, documenting my daily symptoms. My son is still quarantining until he feels better (24 hours without a fever, so far). The one we worried about the most seemed to bounce back the quickest – thank God! I know that many people had it far worse than us, health wise. Many of you have, no doubt, had to change your work schedules to accommodate your own children’s return to school. Some people are still wondering if they will ever go back to work. Some of you may have lost loved ones, and are grieving as you get ready to return to work. There are so many things uncertain, and we teachers crave having the right answer!

The Importance of Self-Care for Caregivers

This COVID-19 / not COVID-19 thingy that we all had in my home has given me pause to consider how well (or not) I fill my own cup, being a natural cup-filler. For those of us who are also in a helping profession, filling others’ cups is part of our day-to-day existence, so much so, that we will come to school sick rather than disrupt the kids’ learning with a sub, or stay up all night to create something wonderful or catch up with household tasks after spending all the daylight hours on work-related things. Add small children, being a chauffeur for sports, or caring for an ill family member, and we have a recipe for physical and mental collapse.

Self-care is probably not something that comes naturally for many of us. I know I have developed the habit, since we closed our physical school last March, of putting a 3-hr block in my planner that says “SELF-CARE.” In that block, I put things that fill my cup, restore my energy (mental and physical) and nurture my soul and spirit.

Is your cup filled? What’s emptying it? What do you use to re-fill it?

What do you do for self-care? Click to visit my Pinterest board on Nurturing Your Soul. {Image Credit: “2015-03-25a Learning about taking care of myself — index card #self-care” by sachac is licensed under CC BY 2.0}

You Can’t Pour From an Empty Cup – So Fill It

Start today. Block your planner into 3-hr segments with a “theme” for each. Put one major task in each block – don’t pack the block full – that’s not realistic. Make sure one of the blocks says, “Self-Care.” Guard it selfishly. Fill it with things that refresh you and bring you back to your peaceful center.

During August, I focused on the following cup-filling activities:

  • Spending time with my family. We binge-watched six seasons of Vikings. Now I feel the desperate need to cover my body with Norse tattoos. Or fight with swords and giant hammers. And drink mead. Skål.
  • Doing lesson “planny” things. Those are lesson planning tasks without the pressure of HAVING to do them. I love lesson planning. I’m playing around with Google Classroom, Google Slides (I found this AWESOME filing cabinet for organizing my digital lesson plans!), and the Conferring Notebook from the Daily CAFE.
  • Cooking. I put Pandora on shuffle, and get to getting. I’m into soup and cooking with herbs from my garden these days.
  • Puttering in the garden. I don’t have a big garden. It’s more like a kitchen garden. I had salad greens, cherry tomatoes, lots of fresh herbs, and the best radishes. It was just too hot to be out there this summer. But there’s something soul-satisfying about grabbing a handful of something I grew and throwing it in what I’m cooking. It’s like kitchen magick.
  • Reading. Lately, I’ve been reading a lot about ancient ways, especially in the British Isles. I’m of Italian-Irish descent, so I love going WAY back and finding my cultural and spiritual roots. For example, did you know that we just passed out of the Coll Moon? In Gaelic, coll means “the spirit/power within.” A fitting theme for a post on self-care. I’m also…
  • Buying books. Just window shopping and making wish lists is peaceful. One book on my short list is Soul Nourishment, by Deborah Haddix.
  • Praying and meditating. I created a prayer and meditation corner in my office. I start and end my day there every day. I also have discovered the joys of washi tape and journal embellishment. For me, there’s nothing more centering than using art materials along with my writing tools, when I journal daily during meditation.
  • Writing. I write. And write. And write. I try to aim for 2000 words at a time, and do this many times a day. A full post is intimidating, but I can bang it out in small chunks.

Set a Goal for Daily Self-Care

What will you do to keep yourself in that peaceful center in September? Share your best self-care tips – sharing IS caring! And check out the link, above, to see my Pinterest board on “Finding the Peaceful Center.”

Be well,

Kim

Posted in general education, literacy, math, mind, more seeds, special education

Using the Daily 5 and Daily 3 in High School

A New Normal

I’m having flashbacks of teaching my self-contained high school last spring.

Kids on Zoom, coming to school anywhere between 7:45 am and 6:00 pm. Kids leaving to go to the store, go to the bathroom, go on the trampoline, go to sleep. Sometimes, they didn’t “leave us” to do those things (another flashback to reminding a student that he was taking the whole class with him to the bathroom – yikes).

I had great lessons prepared, and had worked out the technology kinks ahead of time. But I was exhausted by the sheer MOVEMENT of students into and out of this little window of space in front of me. At any given time, I could have two black screens, one student twirling a toilet brush like a baton (I’m not even making that up), one student with her head thrown back and mouth gaping open in a snore, two students saying, “Miss, what do I do…” or “Miss, I need help,” all while I’m trying to coax another student to NOT go to the grocery store with his mom and stay in class at least until 11:00. Oh, and don’t forget texting/emailing/calling students who have “ghosted” for the day. 

Because I work with students who have a multitude of behavioral health and academic needs, I also need to build in time to explicitly teach rules, routines and procedures that would help them build the skills they needed to be advocates for themselves and lifelong learners. Students need to learn how to wait, how to use their time wisely, how to find and submit work, how to use on-screen etiquette ~ all skills that will benefit them in post-secondary or workplace settings.

One reason I love teaching summer school is that I have a small group of students that I can experiment with for the next school year. They love being the experts in the fall, and I look like I’m an expert, too, because I had a chance to fail, refine and reimplement for 6 weeks.

Over the past summer, anticipating some form of online learning would take place, I practiced my old, elementary workshop model. The workshop model allowed students to still get individualized attention (even if that attention was a phone conversation on the importance of coming to school), while allowing kids to take a break from looking at the entire class for a period of time and practice the skill of coming and going ON A SCHEDULE. Kids appreciated the customization, fewer students fell behind on work, and the movement on the screen was more predictable.

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hybrid learning workshop
Managing student needs in a hybrid learning model can be challenging. Use a workshop model to help organize student needs ~ and create structure! {Image credit: (c) 2020, Kim Bennett. All rights reserved}

Workshop: The Daily 5 and the Daily 3

The Daily 5 is part of a learning model (the Daily CAFE) developed by Gail Boushey and Joan Moser, two sisters who also happen to be elementary educators and literacy experts. Their model uses kid-friendly language to explicitly teach students all the skills in a comprehensive literacy program, as well as the self-regulation skills that they need in all subject areas. The original model was designed for K-5 students: however, more and more secondary educators (and not just SPECIAL educators) are finding that it presents an elegant way to manage a classroom of diverse learners, give them time to work with individuals and small groups, and manage the classroom at the same time.

The Daily 3 is a similar learning model, focusing on math instruction in a workshop model.

Two paragraphs in a blog post do not do these learning models justice. I encourage you to check out their website, or even become a member (as I did this summer). Fear not if you are a high school teacher – there is a large community of secondary teachers who are members of the Daily CAFE.

What is the CAFE? How do I use the idea in a secondary setting? {Image Credit: 2013, Duncan C via Creative Commons}

Adapting the Daily CAFE Model for a Secondary Setting

First, I took the liberty of creating high school-sounding equivalents for the “5” and the “3,” leaning toward terms that my students would already recognize.

Element in the Daily 5… Becomes This in My Classroom
Read to SelfIndependent Reading
Read to Someone{Part of Conference with the Teacher OR Assessment}
Listen to ReadingChallenge Reading (with audio support)
Work on WritingWriting
Work with WordsWord Work or Vocabulary
The elements of the Daily 5 and what they look like in my classroom

The elements of the Daily 3 model, and what they become in my classroom.

Element in the Daily 3… Becomes This in My Classroom
Math by MyselfIndependent Math OR Skill Practice
Math with Someone{Part of Conference with the Teacher OR Assessment}
Writing About MathMath Applications
The elements of the Daily 3 and what they look like in my classroom

I also added Math Games, using Greg Tang Math and other resources, as a fourth element for math instruction.

In person, I’ve used partners and small research groups for literacy and numeracy work ~ I’m working on using the Zoom break-out rooms for this work. Stay tuned for updates!

Creating Instructional Groups for Workshop and Conferring

I did not change my procedures for creating instructional groups. To start the year, I will group the students using any convenient means, and assess their starting point during my first round of conferences. Because I’ve had my kids multiple years, I used roughly leveled groups, using their overall levels in reading and math, and will change my groups in a couple of weeks, based on conference data.

Planning for the Daily 5 and Daily 3 in High School

There is really no difference between planning for the Daily 5 in high school and in elementary school. The only difference might be the time you have available to use the model each day.

I am fortunate to have a self-contained classroom, and, because we have a school-wide focus on social-emotional learning, I have greater flexibility with my schedule (out of necessity). I DO, however, teach all the subject areas. I put together a schedule which divides my day into literacy/social studies (a.m.) and numeracy/science (p.m.), and thought about each class period (48 minutes) as 3, 15-minute segments: a mini-lesson, and two student tasks. Instead of letting students choose their tasks, I rotated the daily 5 and daily 3 elements through their schedule for the week, as well as my times to confer with students individually and in groups.

Here is a sample schedule of my school day:

But I Don’t Have a “Workshop-friendly” Schedule

No worries. 

If you have a set schedule by subject: Mini-lessons and groups address learning needs. Some are subject-specific (e.g., finding differentials); others cross all content areas (e.g., setting up a notebook entry). Think of your instruction as a week-long process: if you teach 5 classes a day, you have 5 mini-lessons and 10 student tasks = 15, 15-minutes blocks to fill. Plug in your conferences into the 10 student tasks, and sprinkle your mini-lessons and skills in accordingly – don’t worry if they cross into other content areas. This is where thematic teaching works well – kids (and administrators!) don’t say, “Why is this writing task in their math block?”

If you teach traditional sections: Again, think of your classes (now, they’re sections – maybe 4 sections of freshman biology and one of AP biology, or 5 sections of pre-algebra and 1 section of geometry). It might take you longer to “rotate” your students through the different elements, or you might assign one element to each day of the week. You might use the same framework for 3 sections of algebra, but a different framework for a 4th, because of the student needs. The point is, flex it however you need to – just think about your class period as 3 blocks of time: time to directly instruct, time for students to practice and apply skills, and time for you to work with specific groups of students based on need.

How do I Begin with Workshop and Groups?

Right now, on a piece of paper, I want you to think about your last group or section of students, and write the students who:

  1. Needed help reading the text
  2. Had difficulty following the directions
  3. Needed more time to copy notes from the board
  4. Were absent frequently
  5. Had para or Special Educator push-in support
  6. Were English learners
  7. Didn’t pay attention the first time you gave directions
  8. Frequently finished before the others
  9. Had more than one place to be during your class (e.g., speech services, band rehearsal)
  10. Needed a movement break

We’ve already come up with 10 “groups” for you to think about – and you don’t need all of them! My advice is to think about what you already do to support these kids, and PLAN for it, instead of reacting to it when it comes. Start small – one student, one need, one group, one section, one class period. Add more as you feel comfortable (because the kids adjust faster than we do!). Be okay with regrouping and trying something new. Invite the kids’ feedback. 

empty desks
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workshop
Starting groups for workshop can be as simple as forming a “catch up” group for students who missed school earlier in the week. Start with what you already have! {Image Credit: naosuke ii, 2004 via Creative Commons}

A Workshop Planning Tool… for You!

I created a thinking tool for you! It represents a self-contained day with four subject areas, but you can modify it to make each “rotation” a separate section or day – whatever works for you. Feel free to modify it, change the names of the elements – whatever makes it easier for you to start. 

Secondary Workshop Planner FREE
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Download a planning template for your secondary workshop classroom. Click on the image, make a copy and edit it to suit your own needs! {Image Credit: (c) Kim M. Bennett, 2020}

I’d love to hear how it turned out for you!

 

Posted in general education, homeschool, how-to, mind, social studies, special education

What’s the Big Idea? Using Big Ideas and Essential Questions in Instruction

Big ideas and essential questions
Use big ideas and essential questions in your high school history class to encourage deep thinking. {Image credit: “British Empire Map in 1886,” Forgemind Archemedia via Creative Commons}

Using Big Ideas and Essential Questions in Instruction

What’s a Big Idea? How Do Big Ideas Connect to Essential Questions?

A big idea, sometimes referred to as an enduring understanding, is an important concept or idea that students can construct as the result of a unit of study. Unlike isolated facts, big ideas can’t be merely transmitted to the learner, but must be “earned” by connecting individual pieces of learning over time. Because they reflect meaning-making on the part of the learner, big ideas are constantly being revisited and revised by the learner as they gain deeper understanding. They are often transferable from one content area to another.

For example, consider the following big idea:

Different choices can lead to different outcomes.

This big idea can be used in a US History class during a study of Congress’s decision to go to war, during a Psychology class while discussing personal responsibilities, and even in a Statistics class while learning about probability. The beauty of a big idea is that, when it is presented in multiple content areas, the understanding of the learner actually deepens.

How do teachers get learners to understand big ideas? In order to get students to think deeply and make meaning as they do, teachers guide their learning through the use of essential questions. Simply stated, a big idea is the answer to an essential question. One essential question can have many big ideas as the answer. Conversely, one big idea can answer a number of different essential questions.

Big ideas span topics and subject matter, and recur throughout our lives. {Image credit: “Jack’s War Pictures 7,” Jack Trimble, 2005 via Creative Commons 2.0}

Big Ideas vs Lesson Objectives

Lesson Objectives

“My text book includes lesson objectives – are those big ideas?”

In short, no, they are not. Here is an example of a set of learning objectives from a chapter of a US History book in my classroom:

  • Identify the European nations that sent the earliest settlers to America.
  • Describe 3 differences among European colonies.
  • Name 3 reasons settlers came to the New World.
  • Explain what the Mayflower Compact was.

Because I encourage students to think beyond Eurocentric views of history, I added the following learning objective:

  • Describe the impact of European exploration on the indigenous people of the Americas and on the rest of the world.

In a nutshell, the unit describes how the Spanish, French and English were the first European settlers of North America. They had various reasons for coming here – some similar, some different. Once here, their colonies had some similarities and some differences, one being that the English created a set of rules for their new society here, called the Mayflower Compact. The arrival of Columbus to the Americas had an effect on the indigenous people of the Western Hemisphere, as well as on the people of Europe and Africa, which lasts until this day (called the Columbian Exchange).

Big ideas can’t be merely transmitted by the teacher, but must be “earned” by the learner.

Consider the difference between these lesson objectives, and the following essential questions and big ideas:

  1. What is imperialism? Imperialism is the act of one country establishing colonies in far-away lands to increase the power and wealth of that country.
  2. What is human migration? Migration happens when large groups of people move from one area to another.
  3. Why do people migrate? People migrate for many different reasons – some similar, some different.
  4. Why do people make rules? People create rules to govern their society and their behavior.
  5. How does human migration affect the world? The movement of large groups of people has an effect on the group that migrates, the people who choose not to migrate, the people who are already in the new land, and, sometimes, the rest of the world.

Which lead to deeper understanding? Which can be used over and over again? Which give the teacher more “bang for the buck?”

Lesson objectives lead to convergent thinking, while essential questions are open-ended and lead to divergent thinking. {Image credit: “Mayflower II, Plymouth, MA,” by SJ Dunphy, 2006 via Creative Commons 2.0}

Why Focus on Big Ideas and Essential Questions?

Essential questions:

  • Are open-ended, having no “right answer;”
  • Are meant to be discussed, argued, and analyzed from multiple perspectives;
  • Encourage active meaning-making by learners;
  • Lead to higher-order thinking;
  • Raise additional important questions;
  • Have multiple entry points, so all learners can participate;
  • Naturally arise during study of a subject;
  • Can be considered multiple times, adding important new information each time.

Big ideas:

  • Represent the “essence” of the content;
  • Connect content from one lesson/unit to another and from one subject to another;
  • Increase opportunities to practice and master concepts, skills and strategies;
  • Allow the teacher to keep content grade-appropriate while allowing for learner differences.
Using big ideas and essential questions leads learners to construct their own meaning about important content. {Image Credit: “Inquiry Learning Word Cloud,” by Christopher Lister, 2015 via Creative Commons 2.0}

Using Big Ideas and Essential Questions in Instruction

Big ideas and essential questions can be used in many ways in the classroom.

  1. Use an essential question as a lesson activator. Have students write a question (“What is time? Why do we measure it?”) in their notebooks and take 5 minutes to answer the question before you begin a new unit. Alternatively, post the question on the board, give one minute for private consideration then discuss. Record student responses; compare to big ideas later.
  2. Use an essential question as a writing prompt. After we have considered an essential question (“What problems are common to everyone? What problems are not?”) a number of times in History class, I will use the question as a writing prompt, reminding students to use specific examples from their lives and class to support their answers.
  3. Post essential questions in the room as they are studied. As an “exit ticket,” ask students which essential questions they addressed in the preceding lesson.
  4. Use essential questions as assessments. I always try to include at least one essential question on each quiz. Even if the majority of the quiz is fact-based content, including an essential question lets me see the deeper understanding that students have learned from their studies, especially if the same question is at different times during the year. For example, last year, we focused on “Why do people do what they do?” throughout the school year, and the students saw it on a variety of assessments in life skills, group, social studies and English, throughout the year.
  5. Review using essential questions. Put essential questions in a box. Have students take turns pulling a question from the box and answering it aloud.
  6. Sort big ideas by essential question. Pass out big ideas learned, to date. As a review, have students match big ideas to one or more essential question.
Asking questions is an innate human characteristic. Utilize it to promote student meaning-making. {Image Credit: “Why Do Humans Q,” by Meadow Saffron, 2006, via Creative Commons 2.0}

For More Information

For more information on big ideas, essential question, and Understanding by Design, see “UbD in a Nutshell,” by Jay McTighe.

Need a jumpstart? Download “Essential Questions (and Big Ideas!) to Encourage Historical Thinking” (based on the Historical Thinking Standards of the National Center for History in Schools).

Posted in general education, homeschool, literacy, mind, more seeds, social studies, special education

Ancient History Notebooking in the High School Years

What is Notebooking?

Notebooking is more than taking notes in a notebook.

Notebooking is the routine and practice of using a notebook, in an open-ended way, to chronicle a learning journey.

While traditional notebooks are “closed” activities, with a uniform finished product, notebooking allows students to interact with the content they are studying in a customized, individualized way. Because students are free to journal about the things that intrigue them most about a topic, they spend more time on the parts of the topic that matter to them, and less time on material they already know. Thus, there is more learning, and the learning “sticks.”

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notebooking
Keeping a notebook of one’s learning is an excellent way to make new learning stick! {Image Credit: (c) 2017, Kim M. Bennett

Our Notebooking Story

I always used notebooking with my homeschooler when he was younger. The combination of drawing and writing – two of his favorite pasttimes – and the variety of page styles he could choose from made larning fun for him. We studied books, and pirates, and military helicopters, and the Ancient Egyptians, and chemistry – all through notebooking. The work he completed and the knowledge he gained as an elementary and middle school, has stuck with him all these years.

As he grew to be a junior high schooler, I doubted myself, and got trapped in the idea that the “textbook is the thing.” We fell away from notebooking for a couple of years. Maybe not as a result, but certainly at the same time, he became less enamored with his studies.

Halfway through his high school years, our teen has been revisiting his love for writing and drawing. We are going to run with that, and return to notebooking in his high school years!

Free Homeschool Resource Hub

Why Notebooking in High School?

I know that my son enjoys writing and enjoys drawing. He can do just about anything with any electronic device you hand him: make music, create amazing artwork, write a persuasive essay about why he should get his license… I want to combine all of these to allow him to learn his high school subjects in the manner that he learns best.

Debra Reed, of Productive Homeschooling, describes the benefits of notebooking at all ages, in her introductory post.

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notebooking
Notebooks are more than just “flat” pages – you can use them to store vocabulary cards and other activities – here is a middle school example where a student created popsicle stick puppets of Roman gladiators, and used an envelope to hold the pieces. {Image Credit: (c) 2014, Kim M. Bennett}

Notebooking instead of a “Report!” ~ our “Ancients of the Americas” Study

I have used notebooking pages each year as a way to help my students and homeschoolers organize their reports. You can pre-enter headings onto the sheets before copying them, if your kids need help organizing information, or leave them open-ended for students to record the information that is most interesting to them. As part of our World History class this year, my homeschooler and my high school students will choose an independent research project on one of the ancient peoples of the Americas. There are many notebooking page sets available for use for this study – follow the links to download your own.

North America

The Mound People (Mississippians)

Other North American Ancients

Central America

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notebooking
Simple pockets to hold loose items can be created in binder-style notebooks, by folding a piece of construction paper and punching holes in the margin. {Image Credit: (c) 2013, Kim M. Bennett}

The Olmecs

The Aztecs (and pre-Aztec societies)

The Zapotecs

The Mayans

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notebooking
Switching to notebooking doesn’t mean you have to ditch your organizers! They can become pages in the notebook, or can be trimmed and glued onto pages as you wish. {Image Credit: (c) 2011, Kim M. Bennett}

South America

The Moche

Other South American Ancients

For More Notebooking Help…

For more examples of how you can use notebooking with all ages, see these studies at “A Child’s Garden.”



{This blog is featured in Top 100 Special Education Blogs}

Posted in general education, mind, more seeds

What’s Your Take on Homework?

The Homework Controversy

Each year, about this time, teachers all over ponder whether or not to give homework, what kind they will send home, and what they will do with the homework when it comes back.

There are many arguments in favor of regular homework or practice in sharpening skills, and teaching responsibility. On the other hand, practitioners and experts see homework as something that doesn’t always do what we’re hoping it to do.

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homework
The research shows that homework that previews new skills and concepts, practices them and extends the learning of them is correlated with increased academic performance. {Image Credit: (c) 2017, Kim M. Bennett}

Homework: Pros and Cons

Summary of the Research

Benefits

The research above points out the following benefits of homework:

  1. practice of learned skills
  2. preparation for new skills
  3. extending the learning outside the classroom
  4. time spent on homework positively correlated with increased academic gains

The authors caution that care should be given to the amount and type of homework relative to the child’s age, as well as the amount of time that should be dedicated to homework. Some researchers state that a positive correlation does not imply causality: in other words, because the grades of students increase along with the time spent on homework doesn’t mean it’s the homework that caused it. For example, students who spend a lot of time on homework and get good grades might also be students who can read well independently, or whose homes have parents who read and can assist with homework. In these cases, it’s not the amount of homework that causes the increased grades: it’s the focus on literacy in those homes that leads to both the time on homework AND the grades.

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homework
To be effective for preview, practice and extension of classroom learning, homework should be a level that the child can complete independently. {Image Credit: (c) 2014, Kim M. Bennett}

Draw-backs

The above articles also mention several drawback of homework, as typically implemented in schools:

  1. source of stress for children and their families
  2. often exceeds child’s ability to complete independently
  3. often requires a great deal of parental teaching/re-teaching to complete
  4. when not completed, often graded in a way that punishes students who otherwise demonstrate mastery of the content (e.g., by scoring high on the exam)
  5. varies from teacher to teacher in the same program
  6. takes away from other positive home activities (e.g., meals, outdoor exercise, hobbies)
  7. takes too long
  8. involves child carrying too many materials back and forth to and from school
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homework
Homework, as a tool, needs to be balanced with other activities that are also associated with positive learning outcomes: family dinners, independent literacy activities, outdoor exercise, and “brain breaks.” {Image Credit: (c) 2009, Kim M. Bennett}

My Spin on Homework

PSA: What follows in this section is NOT a professional opinion on the value of homework. It is my own experience, as a mom and a teacher, with homework.

Homework, Through My Mom Eyes

As a mom, I have a love/hate relationship – ok, maybe a “warm regards”/hate relationship – with homework. On the one hand, I liked seeing what my children were working on in school. We would often have dinner table conversations about the topic, which all of my kids ()and we, parents!) found fun and helpful in building background knowledge. Because I am a teacher, I was able to use a variety of strategies for re-teaching, should my child have difficulty, which I could see from the homework he brought home. I could also communicate with the classroom teacher (and did, regularly) via notes I wrote directly on the homework paper.

On the other hand, I sat through arguments, tears, anger and frustration with children who were smart boys, but who did not know how to do the work they brought home. Whether he was fooling around during the lesson, pulled out for band rehearsal, absent the day it was taught, or simply didn’t understand the concept or skill, didn’t matter – he didn’t know what to do! Sometimes, I helped him. But I grew to expect that his classroom teacher would see that he didn’t know how to do something, or would at least communicate to me that he was struggling, and started to write notes to the teacher. Often, I would diagnose and TELL them what to work on: “{Honey-buns] doesn’t understand this. Could you please work with him on place value when multiplying decimals?” “This project is too big for [Baby-cakes] to plan. Can you split it up into weekly and daily assignments for him? Thank you.” It’s not that I couldn’t do these things: it’s that someone else (the teacher) was being paid to do this. AND if homework is supposed to be practice, preparation or extension of learning, then there’s no reason my child should be tormented trying to do it – it should be INDEPENDENT!

At other times, with two of my squirrelly-er boys, I would draw a line across the page and say, “He worked on this for 30 minutes and I sent him outside to play because he needed to play.” Sometimes, I would write, “We had an unexpected house guest and were gathering together as a family.” To me, research also shows the benefits, especially with young children, of outdoor activities, exercise and participation in family activities. I usually would have these two boys play FIRST, then do homework after dinner when I was right there and they got all their sillies worked out.

At still other times, I would watch my child whip through work that was far beneath him. For example, if my child is getting services for gifted and talented in math, why is he bringing home a stack of addition facts papers to work on? (As a teacher, I meet with the student, discuss how I already know he knows how to do this, then write “OMIT” and initial it, in the child’s view. If I need to, I have a parent sign it).

I don’t even want to discuss projects. I will never assign projects for home completion. I was resentful (every time) when one of these came home, financially, personally and professionally. Something that is that big and that important for a grade needs to be done in school, with the embedded skills (planning, content, editing, use of graphics, design, vetting of sources…) explicitly taught. The end.

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"Fifty Four|Three Sixty Five" by thestevenalan is licensed under CC BY-ND 2.0
If homework causes frustration, lack of proper self-care or home stress, is it really being helpful? How can we change that? {Image Credit: “Fifty Four|Three Sixty Five” by thestevenalan is licensed under CC BY-ND 2.0}

Homework, Through My Teacher Eyes

I really do believe in the power of routine, systematic practice of new skills, concepts and content. As a teacher, I believe I’ve developed a clear and calculated method of delivering this practice right in the classroom, where I can watch the process.

Back when I fell into the “homework packet” craze, I found that some kids whipped through the whole month in a day, defeating the purpose of the progressive practice, and turning in meh work, while others waited until day 29 to do 30 days of practice. Daily homework papers came in sporadically, and I was faced with developing a crazy system for docking their scores as they were later and later. NOT a good use of my time. And my seven years as a dual language teacher frustrated my families when their child received homework that the parent (who WANTED to help) couldn’t read. As a high school teacher, it takes me more time to put together the homework, than to score it, because so few come back.

My Alternatives to Homework

So, since I started teaching elementary school in the 90’s, I’ve consistently used a number of alternatives to homework that allow systematic, targeted practice of skills and concepts, embedded into the school day: daily morning writing work, binders with daily customized practice in math [done as an anchor activity], and a “cafe” or workshop model in literacy and numeracy, where part of the time students are assigned to spiral practice or other systematic review of basic literacy and numeracy skills. Consequently, I don’t send homework home, at least not the traditional type of homework, as the students have multiple opportunities for practice during the school day, when I can assess it.

Periodically, I’ve had parents who criticize my homework policy, and who do not understand the way I teach (which is not like most of my colleagues). To keep peace, I have developed other “homework” strategies: assigning family tasks: “Go for a walk with your family – explain to your parents what a quadrilateral is – write down four things that you see that are quadrilaterals.” {NOTE: this family walk idea was a big hit one year, when I taught in a dual language program – everyone could participate, and they took the babies in the strollers and had fun}; individual workbooks that I had that were on that student’s reading level, with directions to work on a page every day and return it on Monday for a grade.

Currently, I teach in an alternative high school setting. On Fridays, we send home the student’s “Friday Report,” which summarizes what we’re working on in each class, lets families know how their children are doing, shares their clinical progress toward their personal goals and the new weekly goals they’ve selected for the following week. These notes get signed and returned for a homework grade, and their return is incentivized (participation in extra school activities depends on return of the note before the following Wednesday). I reserve “homework” for routine home-school communications (forms, information about field trips, policies, etc), and communicate other information through regular family phone calls.

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homework
Consider alternative “homework assignments” that foster family conversation, creativity, and self-directed learning. {Image Credit: (c) 2010: Kim M. Bennett}

What’s Your Philosophy on Homework?

This year, I DO want to encourage students to take home, and bring back, more things (forms, information, etc.), as part of the real world is teaching that responsibility of follow-through. But I will keep this separate from skills practice, which I really want to observe with my own eyes, in real time.

Do you give homework? What will you do differently this year? Do you grade it? Share in the comments, below.


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Posted in math, mind, more seeds, special education

Writing IEP Goals and Objectives, Part 3: Standards-based Goals

Connections: Standards ~ Goals ~ Teaching

In the previous posts, we considered a math standard for Grade 6, and unwrapped it to identify key vocabulary, skills and concepts required for mastery of the standard.

6.NS.a.1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

We determined that, in order to demonstrate mastery of this standard, a student would need to

  • know and understand (as evidenced by correctly using) the terms fraction, dividend, divisor and quotient;
  • demonstrate understanding of the concepts of fraction, quotients of fractions, word problems as a representation of division problems involving fractions, and the concept of division;
  • interpret and compute quotients of fractions;
  • solve word problems involving division of fractions by fractions.

Next, we considered what obstacles to learning students might have, which would interfere with successful mastery of the standard. To do this, we thought about the kinds of questions students asked when working on work based on this standard.

Now that we’ve analyzed the standard, and anticipating where students might struggle with foundational skills, concepts, and vocabulary, it’s time to consider a student with disabilities, and determine the specific areas of support that this student might have.

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IEP Goals and objectives
Match the elements of the standard to the needs of the child to determine an appropriate standards-based goal. {Image Credit: (c) 2015: Kim M. Bennett}

Case Study: Student K, Grade 7:

Student K is a 7th grade boy in a self-contained, alternative placement. His most recent standardized math testing shows him to be near grade-level, in all areas of math. He made great academic gains over the past school year, as he worked to gain control over his own behavior.

In order to use this standard as a way to identify specific IEP goals for Student K, let’s take a look at some of our observations of him over the past year:

Study Skills:

It typically takes a great deal of time for Student K to transition between areas and begin work, especially first thing in the morning: most days, it is 30 minutes before he begins his morning work, during which time he swears at staff, walks out of the room, and sometimes shrieks in the stairwell. When he’s ready, he sits down to work, and can work independently on the task through to completion.

  • Issue #1: difficulty transitioning between activities, especially when they are in different areas
  • Issue #2: difficulty with task initiation, even when the task is within his capability

Neither of these issues are specific to this standard; in fact, they persist across all content areas and across time, making them important areas for IEP Goals.

Once Student K starts working, he works VERY slowly – on everything. His work output is very low, although he works steadily, requires little help, and produces high-quality material. His Woodcock-Johnson IV scores show a low-average IQ but extremely low processing speed. Scores on classroom assessments show him at risk due to lack of fluency (computational, math fact, reading), but the only area of fluency he actually shows deficits in is rate: his accuracy, prosody and understanding are grade-appropriate.

  • Issue #3: minimal work output due to slow processing speed

Again, while this issue isn’t specific to this standard, it will impact his learning across content areas, and bears greater emphasis in his IEP.

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IEP Goals and objectives
Poor performance in math is not always due to difficulties with math content, itself.

Mathematics:

When working, Student K appears to lack a repertoire of known mathematical procedures (e.g., long division algorithms, solving for an unknown, computing using order of operations). Once he has instruction, he learns the new procedure quickly, and can use it correctly. He tends to choose numerical models (i.e., equations) to solve math problems, and avoids visual models, even when they would be more efficient.

  • Issue #4: lack of procedural knowledge and fluency
  • Issue #5: difficulty using different modes of representing and solving the same problem

If we work under the hypothesis that Student K’s behavioral issues interfered in the past with his ability to be available for grade-level learning, it isn’t surprising that he lacks a repertoire of basic math strategies to draw upon. We can assume that this is a persistent issue with him, and worthy of an IEP Goal.

In general, Student K is fluent in his basic math facts, and can compute whole numbers and decimals accurately. His decoding and comprehension of grade-level text, including word problems, is adequate. He works independently, and learns new material quickly. We can feel that, with the proper supports, he will be well able to master grade-level content.

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IEP Goals and objectives
It helps to consider the Rule of Four when identifying areas for developing IEP Goals and Objectives in math.

The Standard and the Student

Now, let’s return to our standard, and figure out what parts of the standard he might have trouble with:

  1. Procedures for computing fractions: dividing by multiplying the reciprocal, representing the problem with a visual model
  2. Identifying and representing the problem to be solved in a real-world situation or word problem involving mathematics: restating the problem in his own words; representing the problem using numerical (equations) and visual (area) models.
  3. Starting a task on time
  4. Completing a task within the allotted time

Of these three areas, only one is specific to the standard (#1), but, since fractions represent an area where so many students have difficulty, and since grasp of fractions by 6th grade is important for later math courses, it is worth focusing more on in his IEP goals.

Our Standards-based IEP Goals

To address the specific learning barriers we mentioned above, we write the following goals (the specially-designed instruction is in italics):

  • Goal #1: Given 2 fractions with 2, 3, 4, 5 or 10 as the denominator, Student K will accurately compute the fractions, using numerical and visual models, with 75% accuracy.
  • Objective #1.1: Given 2 fractions with 2, 3, 4, 5 or 10 as the denominator, Student K will accurately divide the fractions, by multiplying the first fraction by the reciprocal of the second, with 75% accuracy.
  • Objective #1.2: Given 2 fractions with 2, 3, 4, 5 or 10 as the denominator, Student K will accurately divide the fractions, using an area model, with 75% accuracy.

We have limited the types of fractions Student K needs to use to demonstrate understanding of the standard, and have specifically named one new visual model we want him to use when computing.

  • Goal #2: After reading a word problem at the 5th grade reading level, Student K will explain the problem to be solved, and represent the problem using numerical and visual models, with 75% accuracy.
  • Objective #2.1: After reading a word problem at the 5th grade reading level, Student K will verbally restate the problem to be solved, in his own words , with 75% accuracy.
  • Objective #2.2: After reading a word problem at the 5th grade reading level, Student K will represent the problem to be solved, using an appropriate equation , with 75% accuracy.
  • Objective #2.3: After reading a word problem at the 5th grade reading level, Student K will represent the problem to be solved, using an area model , with 75% accuracy.

Again, we have controlled the level of the text to focus K’s energy on the content, have let the student explain verbally (rather than in writing), and have specified a new procedure (the area model) to add to his repertoire.

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IEP Goals and objectives
Make sure to consider multiple ways of showing what you know when determining if a student has mastered a grade-level standard.

Other Goals

We noted areas not based on this standard, but which would definitely affect Student K’s performance of this (and many other) tasks. We will also include IEP goals on transitioning appropriately from one area to another, and on starting a task within 5 minutes, and will add accommodations that Student K has a reduced number of items to finish per task, and/or extended time to complete tasks.

Summing up our Standards Work

As previously stated, you would not unwrap every standard for a grade level. However, simply choosing one standard in a problem area (use the reports from your standardized testing to help you choose), and doing this exercise will help you focus in on what your student’s most important obstacles to learning are.

Have you ever unwrapped standards?

Posted in math, mind, more seeds, special education

Writing IEP Goals and Objectives, Part 2: Identifying Obstacles to Learning

Identifying Obstacles to Learning

In the past post, we analyzed a grade-level standard to determine the skills, concepts and knowledge that all students need to gain to master the goal, as written.

For students with disabilities, this grade-level goal will be challenging to reach in a year, without specially designed instruction. Analyzing the essential components of the standard helps us determine with which parts of the standard our students will need more assistance. From this, we will come up with annual goals to help get the students where they need to, ultimately, be.

To achieve this, we need to identify, for our student, the main obstacles to the child accessing the grade-level curriculum as represented in that standard.

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Writing IEP Goals
To determine a student’s main obstacles to learning, consider the kinds of questions the student asks when doing grade-level work. {Image Credit: (c) 2019, Kim M. Bennett}

What Part of the Standard Will We Address?

Let’s reconsider the math standard we analyzed from the last post:

6.NS.a.1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

When we closely examined the standard, we determined that, in order to fully master this standard, students needed to be able to do the following:

  • know and understand (as evidenced by correctly using) the terms fraction, dividend, divisor and quotient;
  • demonstrate understanding of the concepts of fraction, quotients of fractions, word problems as a representation of division problems involving fractions, and the concept of division;
  • interpret and compute quotients of fractions;
  • solve word problems involving division of fractions by fractions.

In order to write the standards-based goal, we must first determine the portion(s) of the standard (or implied foundational parts of the standard) with which our student is struggling. I think about the questions that the student asks me, when we’re working on problems based on this standard. Below are some questions students ask, and what they might indicate. I’ve categorized them into two groups: general instruction issues and specially-designed instruction issues.

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Writing IEP Goals
Sometimes, there’s a major foundational skill that interferes with a student otherwise accessing the grade-level. {Image Credit: (c) 2018, Kim M. Bennett}

General Instruction Issues

General instruction issues are problems the student has that are parts of the grade-level standard that any student might reasonably need help with, because they represent new grade-level content. In other words, for this example, given a class of students in Grade 6, and new instruction, many of your students might not have fully mastered the skill or concept, until the end of the year, because they haven’t been taught fully yet. These would not be ideas to focus on in your IEP goals, as they should reasonably be met through general education instruction or early intervention supports:

  • “I get how to divide whole numbers, but what does it mean to divide a fraction?” (the student has difficulty understanding division as it applies to numbers that are not whole numbers)
  • “I know what it’s asking me – but how do I divide fractions by fractions?” (the student doesn’t know a procedure to use to solve the problem)
  • “How do I set that up?” (the student does not know how to represent the word problem using visual models or an equation)
  • “I read it, but I don’t get it. What am I supposed to do?” (the student has difficulty understanding the word problem as a problem that can be solved using mathematics)
Difficulty with using multiple means of representing mathematical ideas is a common area for student difficulties in mathematics. {Image Credit: (c) 2018, Kim M. Bennett}

Specially-designed Instruction Issues

Close examination of the grade-level standard, and the student’s performance in class, will often indicate underlying difficulties the student has which make accessing the grade-level curriculum standard difficult. Since our goal as special educators is to develop customized instruction to help the student access the grade-level curriculum, these are the areas where we should focus our IEP goals and objectives, as they represent current obstacles to the student mastering the standard, as written:

Vocabulary Issues

  • “What does this word say?” (the student has difficulty reading key content vocabulary)
  • “What does this word mean?” (the student has difficulty with the meaning of key content vocabulary)

Reading Comprehension Issues

  • “What does this word problem say? What does it mean?” (the student has difficulty reading and comprehending mathematical word problems as a genre of literature)

Fact Fluency Issues

  • What’s 8 divided by 4?” (the student lacks fluency in basic math facts)

Computational Fluency Issues

  • “I did what you said, but the answer is wrong… why?” (the student lacks accuracy in computation)
  • “How do I divide this?” (the student has difficulty with the idea of division as making equal shares of a whole)

Other Issues

  • “What is a fraction? What does a fraction really mean?” (the student has difficulty with the concept of fractions as relative parts of a whole)
  • “What does THIS fraction mean?” (the student has difficulty interpreting fractional notation – he may understand “1/4” when represented using concrete objects, but has difficulty when presented with the symbolic representation)
  • “How do I say this [fraction]?” (the student has difficulty reading numbers expressed in fractional notation – this is similar to the previous)
Fractions represent a common conceptual challenge to many students, with and without disabilities. {Image Credit: (c) 2014, Kim M. Bennett}

Identifying a Focus for SDI

Of course, you don’t complete this process for every grade-level standard. And you don’t write an IEP goal for every area that a student has difficulty. However, even if you did this activity with one grade-level standard, chances are that you will see patterns of challenges for a particular student. For example, I have one student who would struggle with this standard, simply because he cannot decode the text. If you read the problem to him, and allow him to represent the problem with a drawing or concrete objects, he can accurately complete the grade-level task. You wouldn’t want to give him an elementary task, simply because the reading level is easier for him – that’s not respectful of his math ability.

He also struggles with basic multiplication facts. So, for him, focusing on “work-arounds” for the text-based portion of the standard, and providing accommodations for the math fact fluency issues, would be helpful no matter what math standard he was working on. Make sense?

Always consider embedded literacy skills as areas of difficulty with many math students. {Image Credit: (c) 2014, Kim M. Bennett}

Writing that Standards-based Goal

In the last post, we unwrapped the grade-level standard, to identify key vocabulary, skills and concepts embedded in the standard. In this post, we reviewed where our student would struggle with the standard, using his questions as a guideline for diagnosing his obstacles to accessing the grade-level curriculum. Then we identified obstacles that would likely pop up in multiple areas of his curriculum, to prioritize what we set for goals for him.

In the next post, we will use what we know about the grade-level curriculum and our student’s needs, and write IEP goals that will enable him to better access his grade-level curriculum.

Posted in how-to, more seeds, special education

Writing IEP Goals and Objectives, Part 1: Understanding Grade-Level Standards

Why this Review?

I work as a special educator in an alternative setting, so the students on my caseload come from many different districts, and from many different special education teachers, all of whom had very different training when it came to writing IEP goals and objectives. So my kids’ IEPs look like, well, many different people wrote them!

Additionally, many of my kids come to me after being newly identified with a behavioral need. However, once they get to me, and they become more stable, their underlying or concomitant academic issues become apparent. So I need to now add academic goals to their IEPs. That probably happens to you, too.

Additionally, in a smaller district, such as mine, we don’t have a cadre of speech and language pathologists, psychologists, nurses or other individuals, so I sometimes have to use all of my special ed skills to come up with appropriate goals and objectives on, say, making healthy choices for a student with diabetes, or using specific language in conversation, for a child who uses the word “thingy” all the time.

IEP Direct has built-in pull-down menus, and you can Google all types of banks for IEP goals and objectives. But, have you ever had a student with IEP goals/objectives that seem like they were selected for someone else? It’s easy to just scan and click. But it makes our jobs so much easier if we choose the right goals and objectives in the first place.

Standards, Goals and Objectives: Review of Terms

Standards

In layman’s terms, the standard (whether Common Core Standard, National Curriculum Standards for Social Studies, or Components of Social, Emotional and Intellectual Habits) is the grade-level expectation for all students, by the end of that school year, as stated in the standard.

In other words, the standard lets us know what we should expect a student in that grade to know, understand and do, as a result of the general education curriculum.

Example #1: Math, Grade 6 {Common Core Standards}

6.NS.a.1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

Example #2: Social-Emotional Learning , Early Elementary Grades {Illinois Learning Standards}

3A.1a.  Consider ethical, safety, and societal factors in making decisions - Explain why unprovoked acts that hurt others are wrong.  

Example #3: Instrumental Activities of Daily Living, Grades K-12

Make a list of all the chores you need to do. Check each chore off as it is completed.   

If a student has a disability of some sort, he comes with a document called an Individualized Educational Plan (IEP), that says what his Planning and Placement Team (PPT) wants him to be able to know, understand and do, after one year of general education and specially designed instruction. These are his annual goals, which will be something different from the grade-level standard – otherwise, he wouldn’t need the goal.

Along with each goal are one to several objectives. These present the details of what the PPT wants the student to achieve, after a year of instruction. Sometimes, the annual goal will remain the same, and new objectives will layer in, especially if the goal is broad (e.g., “Katie will learn and use two new strategies for note-taking and demonstrate them successfully in all content areas”).

Often, the specially-designed instruction will be incorporated into the IEP goals and/or objectives, making it clear how the PPT wants any educator to work with that student to help him reach his annual goal.

In order to write standards-based goals and objectives, it helps to fully understand the scope of the standard, as written.

https://search.creativecommons.org/photos/16d7a2f6-d844-41b7-8982-adf23f628e30
Grade Level Standards
fractions
Fractions,” by Tim Green via Creative Commons License 2.0

Unwrapping the Standard

The results of our periodic testing might tell us that a particular student needs to work on computing with fractions, specifically, dividing fractions by fractions. But this result is only based on the fact that it was items such as these that the student missed on the assessment. To use these results to write a goal and its associated objectives, we first need to understand all the components of the standard, as it applies to students in a given grade-level.

We can “unpack” the standard into its composite facts and vocabulary (what the student needs to know), embedded concepts (what she needs to understand), and the associated skills required (what she needs to be able to do). Some curriculum materials refer to these as KUDs. These are the performance standards for all students by the end of the given academic year.

Let’s use the Grade 6 math standard, listed above:

6.NS.a.1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

What the Student Needs to Know (Facts and Vocabulary)

For 6th graders, the critical vocabulary from this standard that we would want them to know and understand include quotient, and fraction.Other vocabulary we might include would include dividend and divisor, as they are related to the word quotient. We would want students to recognize, define and be able to use these terms. We would assume that students already know the vocabulary addition, subtraction, multiplication and division, but we might list them as review terms, along with the word operation.

What the Student Needs to Understand (Concepts)

To find the concepts in the standard, we underline the nouns and noun phrases, like so:

  • quotients (of fractions)
  • word problems (involving division of fractions)
  • division (of fractions by fractions)

What’s the difference between what students need to know and what they need to understand? Aren’t these the same words?

Not exactly. For example, students might be familiar with an array, or base ten blocks, and use them as visual models to solve problems – in other words, they understand the concept of a visual model, but they don’t necessarily have to know the term, visual model. You can teach it to them (I usually do), but it’s not a requirement of the standard that the student know the term. On the other hand, we would expect, by grade 6, that a student would know and use the words fraction and quotient.

To put it a different way, the standard requires 6th graders to understand what a quotient is (the answer you get when you divide a number by another number; an equal share), that word problems are verbal representations of problems that can be solved with mathematics (in this case, division of fractions), and that division means breaking up an area or set of objects into equal shares. This goes beyond explaining what a word means to understanding a bigger mathematical idea.

Also worth noting is that the actual standard is the portion of the text BEFORE the “e.g.” – “Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.” The part after the “e.g..” constitutes one way in which the child can show what she knows.

The way I was taught was there are many possible ways to do something. However, if you’re NOT doing the part after “e.g.” in a standard, you better start! Someone very smart thought this was an appropriate strategy for your grade. In this case, if you aren’t using visual models to represent fractions and computation of fractions with your sixth graders, this standard says that is a grade-appropriate way for them to learn – not just through numerical algorithms. Also, if these are recommended ways to teach the standard to all children, then we know that students with disabilities will need something different. This would NOT be the specialized instruction.

Sometimes, the grade-level standards gives suggested strategies for teaching the standard to your students.

What the Students Needs to Be Able to Do (Skills)

Phew! That was a lot. But it was important. Often, especially in math, we teach the way we learned. In my case, it was, “Ours is not to reason why – just invert and multiply.” While we will show this numerical algorithm to the students, we need to make sure they understand WHY it works, through other means.

So, what do we expect kids to DO? For the skills, we will circle the verbs and verb phrases:

  • intepret (quotients of fractions)
  • compute (quotients of fractions)
  • solve (word problems involving division of fractions by fractions)

Implied in this standard is the following skill:

  • divide (fractions by fractions)

Suggested Strategies

As we previously saw, many standards include some suggested strategies for teaching the standard, usually separated from the standard by parentheses or the abbreviation “e.g.”

  • use visual models to represent word problems (involving division of fractions by fractions)
  • use equations to represent word problems (involving division of fractions by fractions)

Anyone familiar with the Rule of Four can see that the standard is recommending three of the four modes of representing mathematical problems (geometrical/graphical, words/verbal, and numerical/symbolic). Not included here is patterns/algebraic representation.

The Rule of Four in mathematics describes the four ways that all students should be able to represent mathematical problems. Download the poster here. {Image Credit: (c) 2019, San Francisco United School District Department of Mathematics)

Note that the standard does not tell the educator what visual model to use to teach the standard. Here’s where the special educator might use a second method to support students with disabilities.

What’s the Bottom Line?

So, to recap, I’ve unwrapped my grade-level standard, and found that, in order to master the essential components of THIS standard, my 6th students need to do the the following:

  • solve, compute and explain problems involving division of fractions by other fractions [I got these skills from underlining verbs and verb phrases in the standard]…
  • … explaining the ideas of division, fractions, quotients [I got these concepts from circling nouns and noun phrases in the standard] … by
  • … using verbal [writing, speaking], symbolic [equations] and graphical [visual model] representations [I got these suggested strategies by looking for them after the abbreviation, “e.g.”] … while
  • correctly defining and using the terms fraction, quotient, divisor and dividend [I got these terms by listing words from the standard that the students would have to understand in print and use in their speaking and writing]

There will likely be other standards in the same lesson, but this is all that is required to master this particular one.

In my next post, we’ll talk about how to use our analysis of the grade-level standard, and the needs of a student, to write appropriate standards-based goals.