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About Jean Soyke

Jean Soyke is a certified elementary educator with specialties in math and curriculum development. She taught in both public and private schools before homeschooling her four children, grades K-12.

How Do You Use Math-U-See? [Lesson Plan]

This blog post presents one family’s lesson plan for working through a Math-U-See lesson in a week.

While Math-U-See is a mastery-based math program, it does follow a predictable pattern; this allows it to easily fit into the rhythm of many of our customer’s weeks.

This blog post presents one family’s lesson plan for working through a Math-U-See lesson in a week; you can tweak to fit your individual family’s schedule and student’s pacing.

Amanda Capps is a homeschooling mom who has used Math-U-See for several years with her own children. Her ideas are outlined below and reflect the flexibility a family can have using Math-U-See. Read on to learn what a typical week looks like for her family.

An Average Math-U-See Lesson Plan


Monday is concept day! This is when we learn the new concepts presented in the lesson. First, my student and I watch the DVD lesson together; then, depending on the student’s age and level, either my student or I read through the written lesson in the Instruction Manual. We then work with the new concept using the example problems, making sure we’re following the Build, Write, Say process.

If you’re new to Math-U-See or need a math refresher, it is important that you watch the DVD and read the Instruction Manual before working with your student.


If the student hasn’t already completed Lesson Practice A, that’s the first assignment. Then the student can continue working on Lesson Practice B. You will want to provide as much support as needed but encourage as much independence as possible. The completion of the B page is generally the fork in the road. If the student is able to complete the B page independently and with confidence, it’s time to check for mastery.

This is very important! My student gets to be the teacher and teach me the concept. I always make sure they build, write, and say it for me. Only after the student can teach back the concepts with confidence and accuracy and can solve problems without using the manipulatives will I move on.


If the student did not demonstrate mastery, you should plan on continuing your week with Lesson Practice C and additional practice problems until they are able to work independently.

If I am noticing that they have struggled, are making significant errors when I check their work, or do not teach back with confidence, then I might go ahead and utilize the online worksheet generator, reviewing the DVD and sample problems again as needed.

However, if the student is able to teach back the concept, you can spend these two days on the Systematic Review pages for the lesson. The Systematic Review pages are essential. It’s important that your student work through at least one to apply new concepts in the context of previously learned material and to keep skills sharp.


If your student has mastered the lesson concepts, it’s time to bring the week to a close. You can administer the lesson test if you would like a record of your student’s achievement; you can also continue with the Application and Enrichment/Honors page to extend learning. Then it’s time to celebrate with your student on a job well done!

We’re presenting Amanda’s ideas as guidelines to get you started. Again, it cannot be stressed enough that Math-U-See is not a “cookie-cutter” program but one that is meant to be adapted to ensure that your child attains mastery. However you choose to modify these guidelines when you are planning your homeschool instruction for the week, keep your eye on your student, not on the calendar. Let your schedule work for you as you use Math-U-See and you will help your student achieve mastery and become a confident problem solver who enjoys math.

Fractions Are Critical for Success in Higher Math

What is it about learning fractions that is so powerful? This blog post will show you why you need to make sure your student really masters fractions.

ANN ARBOR, Mich.—What part of math success comes from knowing fractions? More than you might think, according to a new study that analyzed long-term data on more than 4,000 children from both the United States and the United Kingdom.

Published in the current issue of the peer-reviewed journal Psychological Science, the study found that understanding fractions and division at age 10 predicted algebra and overall math achievement in high school, even after statistically controlling for a wide range of factors.

This quote is the first part of an article that appeared in June of 2012 and caused quite a stir in the educational community. Basically, this study (as well as several others) seems to indicate that a student’s ability to understand and work with fractions predicts how well he will do in higher levels of math.

The Importance of Learning Fractions

If you’ve worked with a student in upper-level math (or if you can remember back to your own schooling), you might immediately be able to see some areas in which fractions are used in higher math. For example, in algebra, the slope of a line is expressed in fractional form, and students work with fractions that have variables in the numerator and/or denominator (rational expressions). In geometry, students work with trigonometric ratios (sine, cosine, tangent, etc.) and similar figures, which also require the ability to work with fractions. Even in their science classes, such as chemistry and physics, students need to be able to use their knowledge of fractions to convert units of measure. If for no other reason, students need to know how to work with fractions so that they can apply this knowledge to tasks they need to perform in higher-level math.

Benefits of Mastering Fractions

There are more benefits to mastering fraction concepts, however, than just their application to future math tasks. Think about the math that a student learns before focusing on fractions — the material that is covered in Math-U-See Primer through Delta. At these levels, students focus primarily on the basic operations of addition, subtraction, multiplication, and division. While conceptual understanding is still needed to master these operations (for example, why you move over the second line when multiplying by a two-digit number), the reality is that it is possible for students to “get by” if they simply memorize the steps or rules for performing those operations. When dealing with fractions, however, simple memorization is not enough to truly master the concepts. It is much easier to add 12 + 35 mentally than it is to add 2/3 + 3/5. The study of fractions forces students to begin working more fluently with numbers and think more abstractly than they have before. Students who becomes competent with fractions develops fundamental mathematical reasoning skills that they then can apply to even more abstract concepts in the higher levels of math; in other words, students who have worked to master fractions have “primed their brains” for advanced mathematical knowledge.

This leads to the final reason why mastering fractions is so critical to success in higher math. Students whose brains are developed in this manner become more fluent mathematical thinkers. They find that they are able to understand math problems better and that they solve more of them correctly and efficiently. This builds their confidence so that they are able to approach new concepts with less stress (which interferes with learning), and they become more willing to attempt challenging activities.

So what can you do to make sure your student is competent with fractions? Fractions are the primary focus of the Epsilon level of the Math-U-See program. If your student has not yet reached Epsilon, make the commitment to ensure your student masters the material in that course. Take your time going through Epsilon and do the manipulatives activities, which are designed to build understanding. If your student is beyond Epsilon, you might want to consider going back and using the course material to strengthen your student’s foundation in these concepts. As we state in the beginning of every Math-U-See Instructor’s Manual, “Our goal is to help produce confident problem solvers who enjoy the study of math.” We want to make sure your student is one of them!

Spelling You See at Your Child’s Pace

One of the beauties of using Spelling You See is the ability to move at a child’s individual pace.

One of the beauties of using Spelling You See is the ability to move at a child’s individual pace.

If a student is taking a little more time to understand a concept, you can simply slow down and offer more practice; if he demonstrates understanding, you can move ahead. Some subject areas, such as math and grammar, are easy to adjust, but some, like spelling, are a little harder. How can you tell if a child has “mastered” spelling and is ready to move on? Specifically, how can you adjust the Spelling You See curriculum to fit your child’s individual pace?

If you read my previous blog post on spelling mastery, you’ll understand that this is a skill that develops over a long period of time, so it isn’t easy to assess after a single lesson or even a single level. However, as your child works through Spelling You See, there will be some clues that your child either needs to slow down or move a little more quickly. This blog post will look at these clues in the different levels and offer suggestions for ways to address them.

Listen and Write

In Listen and Write, children learn to associate letters and sounds by writing words with short vowels from dictation. Letter boxes are given to help them with this task. The level moves carefully through the following steps:

• Writing a three-letter word with all letters provided (Lessons 1-3)
• Writing a three-letter word with vowel provided (Lessons 4-5)
• Writing a three-letter word with vowel space shaded (Lessons 6-7)
• Writing three-letter words with no assistance (Lessons 8-15)
• Writing four-letter words with initial blends and diphthongs (Lessons 16-25)
• Writing four-letter words with ending blends and diphthongs (Lessons 26-29)
• Writing four-letter words with no assistance (Lessons 30-31)
• Writing five-letter words with medial vowel shaded (Lessons 32-34)
• Writing five-letter words with no assistance (Lessons 35-36)

Because so many skills are covered at this level, it’s important to stop after each lesson to assess how well your student is doing. Is your student struggling to complete the task, or does he need a lot of assistance? The answer is NOT to make the work sessions longer—10 minutes is the max! Instead, if the student is struggling near the beginning of the book, you should probably put it aside for a month or two and then try again. If he’s further along in the program, you can download additional letter box pages from your online resources and use the words from the General Dictation List for more practice sessions before moving on. Can your student spell nearly every word quickly and without error? You may want to consider skipping the remaining pages in that lesson and moving on to the next. The important thing is to make sure your student feels confident and demonstrates no anxiety before moving on to the next lesson.

Jack and Jill

The first half of Jack and Jill reviews and solidifies the skills presented in Listen and Write while adding the new skills of reading, copywork, and chunking. Watch your student carefully as she goes through the first few lessons. If you are near the beginning of the book and your child did not complete all of Listen and Write, you may need to go back to that book to build foundational skills. If you did complete Listen and Write previously, you will need to determine the specific skill that is causing difficulty. If it’s copywork, remember to keep the time relaxed and limited to 10 minutes, even if your student can only copy a few words. Remember to celebrate success! If the issue is letter box dictation, you can download additional letter box pages from your online resources and use the words from the General Dictation List for more practice sessions before moving on. Whatever you decide, do NOT make your child’s work sessions longer—10 minutes is the max!

Students who struggle in the second half of the course generally have difficulty transitioning to passage dictation. Again, it’s important to limit these sessions to 10 minutes, celebrating what the child is able to accomplish during that time. Be sure to watch the demonstration video on passage dictation (available in your online resources) to see how Dr. Holinga conducts these sessions. Also, be sure to take time for the No Rule Day activities—they will help keep spelling fun and minimize stress.

On the other hand, if your student can spell nearly every word quickly and without error, you may want to consider skipping the remaining pages in that lesson and move on to the next. Once again, the goal is for the child to feel comfortable and confident as he continues through the level.

Wild Tales through Modern Milestones

As you work through these levels, it is very important that you follow the program as it is designed. Generally students struggle or lose interest simply because well-meaning parents make significant alterations, such as skipping one or more of the core activities, adding in phonics rules, requiring the student to complete each dictation, focusing on errors, or using the book for handwriting instruction. If you have any questions about how the program is meant to be used, please contact a Customer Service representative for assistance.

Given the fact that growth does tend to come in spurts, you will also want to assess your student’s progress at the end of every lesson. Was he able to chunk the passages accurately, without error or assistance? Was the first dictation practically flawless? Then it might be possible to move a little more quickly through the level. Try the A and B pages of the next lesson, and if your student does well, skip the C page. Then try the first dictation without assistance; if the student completes it confidently with few errors, skip the second dictation and move to the next lesson. Once again, use your student’s confidence as a guide in deciding whether you should move more quickly through the level.

Spelling You See is a carefully crafted, research-based program designed to help students learn to spell confidently and accurately. While it is meant to be followed exactly, there is room to adjust the pacing to meet the needs of your individual student. While spelling mastery doesn’t happen overnight, as you continue to use Spelling You See, you will eventually see your child become a clear and confident communicator.

The Five Core Activities in Spelling You See

Spelling You See is built on five core activities designed to increase your child’s experience with words; learn how each activity ties together.

We’ve seen it many times—the quizzical look on a parent’s face when she looks at the Spelling You See program for the first time. Next come the questions, usually prefaced by “If this is a spelling program…”

“Why are there passages to read?”
“Why do I have to read aloud?”
“Why does my child have to write so much?”

I totally understand where the questions are coming from.

Language arts instruction is often confusing because of all the subskills involved; reading, spelling, handwriting, composition, grammar. Some parents choose a separate curriculum for each area, and some go with a more integrated approach. After many years of homeschooling experience and professional research, I can say one thing with confidence: while you may choose to use different materials for reading, spelling, grammar, etc., children learn language in an integrated way. They learn words, and the more familiar they are with words, the more successful they will be in all aspects of their language study. To put it another way, “The more deeply and thoroughly a student knows a word, the more likely he or she is to recognize it, define it, and use it appropriately in speech and writing.” (Source)

For this reason, the Spelling You See program is built on five core activities designed to increase your child’s experience with words. This blog post will discuss these activities briefly and explain how each one contributes to spelling success.

5 Core Activities


While reading and spelling are different processes, they are also complementary, working together to build a student’s proficiency with language. In the lowest levels of Spelling You See, students use their knowledge of phonics to write words and then read them back, developing fluidity as they move from one skill to the other. In the other levels of the program, students are given short, interesting passages to read, copy, and write from dictation. These passages provide a meaningful context for the words the student will be learning to spell, showing him how they are used in “real life,” instead of presenting them in isolated lists. In Spelling You See, care is taken to make sure the process of reading does not interfere with the student’s focus on spelling. Passages are deliberately written at lower reading levels, and, even then, parents are strongly encouraged to read new passages aloud to students so that they don’t have worry about figuring out words. While you might be tempted to skip the reading portion of a Spelling You See lesson, it’s important to remember that incorporating this core activity helps build language proficiency.


Listening is another core activity in the Spelling You See program that is often overlooked. For the youngest students in the Phonetic stage of spelling development, much time is spent listening to individual sounds and learning to connect those sounds with letters. In subsequent levels, passages are read aloud so that students hear the correct pronunciations of words and make connections between sounds and letter patterns. Dictation activities in Spelling You See help students practice the skill of transferring sounds that they hear into correctly written words—which is, after all, the fundamental definition of spelling.


It may seem meaningless to have students simply copy words, but there is actually great value in this core activity. A 2006 study by Virginia Berninger found that students who wrote words by hand, as opposed to using a keyboard, showed greater brain activity in the areas associated with reading, writing, and working memory—the areas needed to process words. In addition, the physical act of writing stimulates muscle memory, thereby helping students transfer spelling to long-term memory. It’s important to note that correct letter formation should NOT be emphasized during copywork sessions in Spelling You See; that is the goal of handwriting practice, which should be conducted at another time.

Learn more about copywork here <<


The term chunking refers to a technique unique to Spelling You See in which students mark recurring letter patterns with assigned colors. This core activity, which appears in the second half of Jack and Jill and beyond, teaches students to pay attention to the individual letters that make up a word, which enhances visual memory of the correct spelling. Parents should understand that chunking should never be associated with phonics “rules”; phonics instruction helps students decode (read) words but is generally unhelpful and even confusing when a student is trying to encode (spell) a word.


Dictation is to spelling as a flight simulator is to piloting an aircraft; it’s a controlled way of practicing a skill before launching into real-time, unassisted application. In Spelling You See, the passage the student has been working on all week is read back, one word at a time, and the student writes each word as it is given. During the dictation session, students are given as much assistance as they need; however, in Americana and beyond there is a second dictation, which students are expected to complete independently. As students become more confident spelling words that are familiar to them, their proficiency in spelling gradually increases and becomes incorporated in the writing they do in other subjects and in everyday life.

Learn more about dictation here <<

While each of the five core activities of Spelling You See have value in themselves, when combined they create a powerful mechanism to help students learn to spell correctly. As their skill in spelling improves, their written work communicates ideas more clearly, which in turn increases their confidence. We invite you to explore this exciting program and see what it can do for your student.

What Does Spelling Mastery Look Like?

Spelling mastery is subtle and takes time to develop, but it is an important skill for your child to grow in.

There’s a story going around our office that Steve Demme originally wanted to call Math-U-See “Piece of Cake Math.” Whether this is true or not, I think the story reflects one of the foundational principles behind Demme Learning products. We want students to become learners who are confident in their knowledge and abilities. We want them to be able to tackle appropriate learning tasks with success and efficiency. We want them to get to the point that the subject really does become a “piece of cake.” In other words, we want our students to attain mastery.

What exactly do we mean by “mastery” when it comes to learning? Think about something that is a “piece of cake” for you, maybe something like driving a car. How can you tell that you have mastered this skill? First, you don’t need any assistance to perform the task; you don’t need anyone to supervise, and you don’t need to consult a manual. You also don’t need to think through the steps (“turn the key, put the gearshift into reverse…”) but are able to perform the task automatically. Also, if you have mastered the skill of driving one type of vehicle (a sedan, for example), you are generally able to drive another type (minivan, SUV, or even a truck) with little difficulty. While drivers may have differing levels of experience or confidence, we can say they have mastered the skill of driving a car if they meet these criteria.

Now consider this idea of mastery as it relates to spelling. Someone who is a “good speller” doesn’t rely on a dictionary or spell check. Not only is he or she able to retrieve correct spellings automatically, but this person also uses correct spelling in all contexts, whether it be writing a formal report or emailing a friend. There’s probably also something you may notice about good spellers: they tend to be good with language in general. Research has shown that strong spellers are often avid readers with large vocabularies. One set of researchers explained the phenomenon this way: “the more deeply and thoroughly a student knows a word, the more likely he or she is to recognize it, spell it, define it, and use it appropriately in speech and writing.” (Source)

The conclusion that we can draw from this research is that mastery in spelling doesn’t come from memorizing lists of words or phonics rules. Instead, spelling proficiency comes from being exposed to words and interacting with them repeatedly in a variety of ways, which is the instructional approach used in Spelling You See. First, students see words in short, interesting passages so that reading and vocabulary skills can be applied. Next, students practice writing the words in context and analyze word structure through “chunking” activities. The dictation exercises at the end of the week help students develop the skill of retrieving correct spelling from memory. Commonly used words appear over and over again throughout the lessons, enabling the student to develop competence and confidence in their ability to spell them correctly.

So how will you know when a student has achieved spelling mastery? It’s similar to learning to drive a car: mastery doesn’t happen overnight, and it can be demonstrated in a variety of ways. You can see spelling mastery when your child is working in another subject and says, “I know that word! It was in my Spelling You See book!” It happens when your child asks for help less and starts spelling more words correctly in his everyday writing. It happens when your child points out a misspelling on a sign. Some parents have even reported improvement in reading and an increased interest in words in general. Spelling mastery is subtle and takes time to develop, but once you see your child growing in this important skill, you will know that he is further along on the path to becoming a lifelong learner.

Are Spelling and Reading Manipulatives Effective?

Other than helping to keep hands occupied and minds engaged, is there actual value to using “manipulatives” to teach spelling and reading?

Other than helping to keep hands occupied and minds engaged, is there actual value to using manipulatives to teach spelling and reading?

Let’s face it – it can be hard to make a language arts curriculum interesting. Sometimes the reading passages can capture a child’s attention, and colorful graphics may help, but the actual work of learning letters, sounds, punctuation rules, parts of speech, spelling patterns, etc., can be downright tedious. It’s no wonder that parents can be drawn to programs that include letter tiles, magnetic letters, or foam letters (especially in pretty colors).

There has been some research that supports using letter tiles or magnetic letters to develop reading skill, especially for students with language-based learning issues. Being able to break a word easily into its component letters can help children with word analysis and decoding. However, it’s important to remember that learning to read and learning to spell are two very different processes. If letter tiles help students with reading, do they also work for spelling?

Actually, researchers have found that the best way to make spelling “stick” is to have the child write the words by hand. More recent studies, using advancing technology to study the brain, have supported these findings.

A 2012 study compared three groups of students: those who traced a letter, those who wrote it freehand, and those who typed it on a computer. Those who wrote the letter by hand showed increased activity in the areas of the brain that are activated by adults as they read and write.

Another researcher found that the brains of students who wrote by hand showed greater activity in the areas associated with reading, writing, and working memory.

It is becoming increasingly evident that writing by hand stimulates important areas of the brain that help students improve language skill, especially in the area of spelling.

Language Arts Manipulatives

All of this makes sense when considering the processes involved in handwriting, as opposed to using letter tiles or magnetic letters. When working with the manipulatives, the student must execute these tasks:

1) Think about the sound being made.
2) Decide which letter needs to be written. (visual memory)
3) Choose the letter from a total group of letters. (visual discrimination)
4) Place the letter in the correct order. (visual sequencing)

Writing by Hand

Note that, with letter tiles and magnetic letters, the hand follows the exact same motion for every letter. This is significantly different from the process of writing by hand:

1) Think about the sound being made.
2) Decide which letter needs to be written. (visual memory)
3) Think about how the letter is formed. (kinesthetic memory)
4) Engage the proper hand motions. (kinesthetic sequencing)

Writing by hand helps students take greater advantage of more areas of the brain, which is why it’s a core component of Spelling You See. We invite you to investigate this unique research-based program that is easy to use and fun for students.

Image source: Munchkin Inc.

Should Your Preschooler Use Math-U-See Blocks?

You can prepare your preschooler for Math-U-See by providing her with purposeful activity and play in advance.

You can prepare your preschooler for Math-U-See by providing her with purposeful activity and play in advance.

Perhaps it’s happened in your house. It’s time for Math-U-See, and your older children are getting out their workbooks and manipulatives. In the meantime, your preschooler, drawn to the colorful blocks, asks, “Can I use the blocks, too?” Your child isn’t ready for Primer yet, so you really don’t have anything planned. Is it all right to let your child just play with the blocks, or are there meaningful activities you can do to help your child prepare for Primer?

Manipulatives Research

Quite a bit of research has been done in the area of using manipulatives for math instruction. From this research, there are two important principles that parents using Math-U-See should keep in mind.

First, manipulatives work best when students view them as “tools”, like a ruler or compass, rather than toys.

Second, manipulatives do not teach math in and of themselves; it is only when a student uses them under the guidance of an instructor that he comes to understand their meaning and their use as representations of mathematical concepts. (Source)

Therefore, if you’re going to be using Math-U-See with your current preschooler, it’s probably better for you to guide your child through purposeful activity, helping them get the most out of their play.

Manipulatives Activities

So what would this “purposeful activity” look like? If a child isn’t ready for Primer, you don’t want activities that involve actual numbers or counting; instead, you should aim for developing pre-number concepts and familiarity with the blocks as learning tools. The activities you choose can address any of these four areas:

Identifying Block Colors

The association between the color of each block, the length of the block, and the number that the block represents will all be fundamental concepts in the Primer level of Math-U-See. You can begin developing this understanding by completing the following activities (in order of increasing difficulty):

• Play “Simon Says”, giving specific directions using the colors of the blocks (ex., “Put a pink block on your knee”).
• Have your child trace around each block and color the rectangle correctly.
• Give your child a paper with block tracings. Have him use the blocks to determine which color each should be and fill in the rectangle. [Download a free printable for this activity]
Trace Math-U-See blocks in this fun activity.

• See if your child can color in the block tracings correctly, without using the blocks as a reference.
• Have your child close his eyes. Give him two blocks to feel and tell their colors (ex., pink and brown). Can he guess which block is which just by feeling them?

These activities will help your child become familiar with the block colors before associating them with actual numbers in Primer.

Exploring Relationships Between the Blocks

These activities develop an intuitive sense of number relationships, which will be important when your child uses the blocks in Primer to model concepts such as greater than and less than.

• Use a paper of block tracings. After your child has correctly identified the color of one block, see if she can identify other tracings that are the same size and will be the same color. Have her use the blocks to check her guess.
• Have your child put the blocks in order of length, both forward and backward.
• Put the blocks in order and then play “What’s Missing?” Have your child cover her eyes while you take a block away from the order. Can she tell which color is missing?
• Play “Match Me.” Lay down a block and have your child find groups of blocks that are just as long as the original block. (For added difficulty, lay down two or three blocks end to end and have your child find matching combinations.)
• Play “Cover the Block”. Have your child take a red hundred-block and cover it with smaller blocks. There should be no gaps and no blocks extending over the side. Talk about the different ways that a row can be filled (ex., two light blues, a brown and two greens, etc.).

Creating Patterns

Once the child learns to associate the blocks with numbers in Primer, he will be able to extend his understanding of patterns to those numbers.

• Put the blocks in order of length. Remove every other block and have your child say the color pattern (ex., dark green, pink, light blue, tan, light green).
• Have your child make other repeating patterns with the blocks (ex., yellow, pink, yellow, pink).
• Play “Copy My Pattern.” Have your child make a pattern, and you copy it with your blocks. Take turns.

Sorting the Blocks

These activities help children learn how to organize information and think logically—both important skills to support mathematical reasoning.

• Simply have your child dump out the blocks and put them back into the right compartments of the plastic tray.
• Ask your child to group the blocks in different ways (long/short blocks, light/dark colors, etc.). Encourage him to come up with his own groupings. Begin with two groups and then move to three, if your child is able.

Note that none of these activities actually have the child count or refer to numbers. Instead, you are using the blocks to develop cognitive skills that lay a foundation for the Math-U-See program. These activities have the added benefit of making math fun, which will build confidence and encourage understanding. Meaningful activities with the Math-U-See integer blocks are a wonderful way to start your preschooler on the path to lifelong learning!

Going Deep in Math

Encouraging our children to “go deep” in math can increase motivation, help them learn how to think and reason, and yes, even make math fun!

Encouraging our children to "go deep" in math can increase motivation, help them learn how to think and reason, and yes, can even make math fun!

“Why do I need to learn this?”

“Math is SO boring!”

“I hate math!”

Have you ever heard any of these from your children (or perhaps even thought them yourself)? Why does math seem to come so easily for some people, while for others it just doesn’t “take”? Research suggests that the depth at which concepts are taught has much to do with a student’s competence, confidence, and general attitude toward math. What does it mean to “go deep” in math?

In the late 1990s, Norman Webb, an educational researcher, proposed the Depth of Knowledge (DOK) model of learning. Webb divided learning tasks into four levels of complexity: recall and reproduction, skills and concepts, strategic thinking, and extended thinking. Let’s take a simple mathematical concept (multiplying by 9) and see how it might appear in all four levels of cognitive depth.

Recall and Reproduction

At this level, a student simply retrieves information from memory. With the multiplication facts for 9, for example, your student should be able to recite them randomly, at any time or place. The problem with rote learning, however, is that it doesn’t offer any context to make it meaningful or interesting. This is why students need to move to deeper levels in math.

Skills and Concepts

Students now apply the facts that they’ve learned to familiar tasks. Most math programs offer simple word problems to challenge students at this level, such as the following:

CDs are on sale for $9 each. How much will it cost to buy 5 of them?

First, the student needs to analyze the situation to determine that multiplication is required; then he must select the correct fact (9 × 5) to find the answer. Now students see a reason for math, but this may not be enough to stimulate interest or develop critical thinking skills.

Related post: Help! I Need to Solve a Word Problem!

Strategic Thinking

At this cognitive level, students use reasoning and planning to tackle a learning task. This sample problem for the 9 facts shows how a student at this level can apply deeper thinking.

The number 3,806,784 is multiplied by 9. In the product, what digit is in the ones place? Explain your answer.

A student at a lower cognitive level would most likely need to perform the actual calculation to arrive at the answer. At this level, however, a student would draw on his factual knowledge (9 × 4 = 36) and deduce that, since 36 has a 6 in the units place, the product of 3,806,784 and 9 will also have a 6 in the units place. In his explanation, the student is required to reason aloud, thus developing important critical thinking skills.

Extended Thinking

This is the deepest cognitive level and can also be the most fun! Student-designed projects generally fall into this category because they require pulling together multiple ideas and skills into an experiment, survey, model, or investigation. To utilize the multiplication facts for 9, for example, a student might be asked to plan a party for 9 people and present a detailed list of the costs, using newspaper ads or websites to find prices. (For an extra challenge, the student could be given a spending limit.) This task obviously draws on the 9 facts but also incorporates many other skills, both mathematical (adding) and practical (finding the best price).

Looking at these examples, you may be able to see how rich mathematical learning can be. You are probably wondering, though, “What does this mean for me as a parent?” I’d like to suggest three possible applications:

1. Determine the depth of learning that is best for a particular task. Not all mathematical learning needs to involve complicated problems or projects. In fact, it’s generally best to keep the activities varied to maintain interest.

2. Determine how well you are able to coach your child in “going deep.” You may have never been given the opportunity to think past the second level yourself, and, even then, you may have struggled. Being aware of your own abilities will help you with the next item.

3. Choose the math program that offers the best support. If you function well at the deeper levels in math, you can supplement any curriculum by planning instruction and learning activities similar to the ones presented as examples. If you are not comfortable thinking this way, you may want to seek out programs that include the types of problems and activities that encourage deeper thinking.

As parents, we want to ensure that our children acquire basic math skills and are able to apply them in advanced study and everyday life.

How to Embrace the Chaos of Homeschooling

If you can learn to look beyond the chaos, your family can survive homeschooling and realize the sweet return on your investment.

If you can learn to look beyond the chaos, your family can survive homeschooling and realize the sweet return on your investment.

Go to any homeschooling website and you’ll probably find it—a photograph of a homeschooling family, parent and child smiling sweetly at each other, lost in the love of learning. If you’re a new mother with an infant sleeping peacefully nearby, you might immediately start superimposing the faces of you and your little angel onto the image as you dream of the future. If you’re a veteran homeschooler, however, you might find yourself trying to remember the last time your family looked even remotely like that. No matter where you are in the homeschooling journey, from just thinking about it to being deep in the trenches, it’s important to remember that homeschooling rarely resembles the photos on the websites. Homeschooling often involves mess: messy living spaces, messy schedules, and messy relationships.

I grew up as the oldest of seven children in a house with 2½ bedrooms and one bath. My father was a construction worker, and my mother stayed at home. With a tight budget, my mother hung onto everything, which made our little home feel even smaller. When I became an adult, I was determined that I was never going to have kids, and I was never going to have a home that was cluttered and chaotic. Of course, God knew better. I ended up having four children of my own, living in a city where private school was out of our price range and public school was out of the question. As we transitioned from day care into the brave new world of homeschooling, I suddenly realized that my children would now be around pretty much 24/7, which meant that they would rarely be out of the house long enough for me to make it presentable. It took more than a few tears, conflicts, and adjustments before I came to terms with mess of the homeschooling lifestyle. Here are the three biggest lessons that I learned as I worked through the process:

Focus on What’s Important

Perhaps you’ve seen this last stanza from Ruth Hulburt Hamilton’s famous poem, “Song for a Fifth Child”:

Oh, cleaning and scrubbing will wait till tomorrow,
But children grow up, as I’ve learned to my sorrow.
So quiet down, cobwebs. Dust, go to sleep.
I’m rocking my baby. Babies don’t keep.

The idea behind this poem is the same as the one behind our house rule: “People before things, and principles before property.” In our case, it might very well mean leaving a pile of unsorted laundry to read a story, trekking into the woods for some “real life” science, or rescheduling the school day to take a meal to a sick neighbor. The satisfaction of knowing you have done something purposeful and meaningful, perhaps even with eternal value, will help you realize that any mess or chaos left in the wake was well worth it.

Set Reasonable Expectations

At first I was going to entitle this section, “Lower your expectations,” but then I realized that the expectations you set will be based on what you deem to be important. For example, if teaching your child to be careful and conscientious is important, you will set a high expectation for any assignment that is turned in. However, having a spotless bathroom on a daily basis may be an expectation that needs to be lowered. As an example, it was important for me that my children have experience with all kinds of art, including paint and clay, but those activities could only be done on Friday afternoons and only within established parameters (such as covering the area with newspaper and wearing smocks). I knew that our sessions would be messy (and they were), but having realistic expectations for both myself and my children helped make it manageable.

Cultivate a Positive Attitude

There we were—watching the rain as it continued to fall for yet another day. So much for our fun vacation! It seemed like all I was doing was trying to keep the kids from going stir-crazy, the camper relatively mud-free, and myself from the brink of despair. I had taken a moment to tend to the baby when suddenly I heard squeals of laughter from outside the camper. I looked out to see my husband and children in their bathing suits, sliding and swimming in the mud and having the time of their lives. This was a deciding moment. I could continue off the cliff and fall headlong into the self-pity, anger, and frustration, or I could choose to enjoy the sight of my family determined to have fun despite the weather. I am thankful now to say that I chose the latter. Choosing to look on the sunny side—even to see the humor in the situation—can be a wonderful way to “weather” the mess and the chaos of life.

There is no way around it; life is messy, and homeschooling is life up close and personal. It is my hope that it won’t take you as long as it took me to accept this fact. Focus on what’s important, set reasonable expectations, cultivate a positive attitude, and embrace this wonderful mess called homeschooling.

When Should You Teach Latin and Greek Roots?

Does Spelling You See teach Greek or Latin roots? Can it be applied to spelling? We answer these questions and more in this blog post.

Does Spelling You See teach Greek or Latin roots? Can it be applied to spelling? We answer these questions and more in this blog post.

If you’ve been teaching for any length of time, you’ve probably seen it—the “deer in the headlights” look when a child encounters a new word in a reading selection. Your first instinct is probably to suggest, “Sound it out,” which might be helpful for a word like graze or fleet; however, this strategy isn’t as helpful for an older student faced with a word like spectator or chronicle. Once students begin to encounter longer words, they need to acquire strategies other than “sounding out” to gain meaning from those words. These strategies often involve learning how to break words into parts, including Greek and Latin roots (such as the Latin root spect– in spectator and the Greek word chronos in chronicle). Studying these roots can help students not only learn to read new words but also how to spell them.

Root Study and Spelling You See

If root study is so helpful in learning how to spell, why doesn’t Spelling You See use this strategy in its program? The answer to this question comes from an understanding of the five stages of spelling development. During the majority of the elementary years, students are in the Skill Development stage of spelling. This is the stage in which vocabulary expands dramatically and incorporates more and more words that are not spelled phonetically. The only way that students are able to use the correct spellings of these words consistently is if the words are stored in visual memory. Spelling You See uses research-based strategies to help students accomplish this goal, which includes presenting commonly-used words in the context of an interesting passage.

Consider this example from Americana, a book from the curriculum at the Skill Development stage:

Katharine Bates took a train ride across the country. She saw many beautiful sights. In Colorado she went to the top of Pikes Peak. She was over a mile above the city below. She could see so far that the distant mountains looked purple. The beautiful view gave her great joy. Back in her hotel, she put her thoughts into a poem. It became the song “America, the Beautiful.” (Lesson 28)

You will notice that there are many commonly-used words in this passage that students at this level need to be able to spell, such as country, beautiful, mountain, purple, view, and thought. However, while the words country and distant do have Latin origins, there are no words with clear Latin or Greek roots that can be used as an aid to spelling. The reality is that Greek and Latin roots tend to appear in words at higher vocabulary levels and not in the text that most elementary students are expected to read. Therefore, teaching roots at this level is generally not helpful; students should be focusing instead on mastering the spellings of words they frequently read and write in their everyday experience.

Once students have mastered these spellings, it’s a natural progression to the Word Extension stage, which is covered in Spelling You See’s Modern Milestones. Here students study longer words, first identifying words they have already learned how to spell, either as a base word or as part of a compound word. Then they learn to identify and spell common prefixes and suffixes and how to add them correctly to base words to spell new words. It is only after students become comfortable adding to words they already know are they able to progress to adding to roots, which are not words in themselves. This task is accomplished in the Derivational Constancy stage of spelling, which most students cover in a traditional vocabulary program focusing on Greek and Latin roots and/or in their other studies, which will include more words containing these roots.

Applying Root Study

Some of you may ask, “What if my student is already learning Latin (or Greek)? Can’t we just apply it to spelling?” Before answering this question, I need to stress the difference between language acquisition and language study. If your goal is to have your student read, write, and speak Latin or Greek as he does English, you are focusing on language acquisition. When anyone is acquiring a new language, it generally takes several years to establish fluency. If your student has learned a classical language to this level of competence, it is perfectly appropriate (and even beneficial) to point out the similarities between the two languages as an aid to both reading and spelling. However, it is a different matter if your student is studying Greek or Latin vocabulary and grammar as an academic exercise (“book study”). In this case, it is better to wait to make the connection to English spelling until your student reaches the Derivational Constancy stage and has already mastered the spellings of basic words and the principles for adding affixes correctly.

Does learning Greek and Latin roots help a student with spelling in English? Absolutely! The key is to teach the roots in the correct developmental stage of spelling, after the student has mastered the prerequisite spelling skills. Teaching according to developmental level, as the Spelling You See program does, enables students to become competent spellers who are able to express themselves clearly and confidently in their written work.