Purpose Anyone?

When dissecting Common Core, I am constantly grappling with what I think I know vs. what is really truth vs. what the authors’ intend for us to do. While some ideas are clearly articulated, expanded upon, and delineated with examples, others are not. One such area is the idea of author’s purpose. If you actually search those words within the Common Core standards, it will come up blank. However, throughout the primary grades, there is a consistent reference to the author’s main purpose or reasons. I am currently examining CCSS-Literacy.RI.2.6, which states that students should be able to do the following:

Identify the main purpose of a text, including what the author wants to answer, explain, or describe.

This sounds simple enough, but my quandary lies within this – when we think about author’s purpose, we usually do not quarantine it to one genre. Generally, when broaching author’s purpose, teachers think of PIE – persuade, inform, and entertain. I also like to add in describe. However, these categories do not all work well for informational text. The terms specified in Common Core are DEA – describe, explain, or answer. Describe for expository text would be very different from describe for poetry or how an author may use a description to paint an image of scenery. The nuances within these three terms are difficult to separate. Let’s say a text was procedural, such as How to Build a Duct Tape Wallet. One could justify that the author is describing how to make the wallet. On the other hand, this procedure, while being descriptive, is also an explanation. But why did the author write this text? One could easily say to answer the question of how to make a wallet. Even in the dictionary, describe is defined as “to explain something.” So why the three different terms? Was it to be all-inclusive because in the bigger picture, students need to understanding that informational text is to inform, and DEA are three ways of teaching the reading? And what about the other reasons author’s write outside of the informational world? Why has that been left off completely?

When I searched the internet to see what other people determined, it seems the consensus is to continue making it as easy as PIE. Continue to examine narratives, poetry, and informational text for author’s purpose. However, within informational, be specific on what exactly is being taught. Perhaps we could use an organizer like the one below to think about the structure of author’s purpose:

When thinking about the purpose of Common Core, it has been made clear by the authors that there is an increased focus on critical thinking and informational text. I believe the point of the authors’ with standard RI.2.6 was to ensure that students think critically about the point of what they are reading so that they read accordingly. From my perspective, in order for students to think critically, they must also understand why author’s write any specific type of text, and through that lens, will be able to think about the organization to increase comprehension across the genres. So while author’s purpose does not make as clear of an appearance in literature, students must understand the difference between genres, and therefore understand the differences among why authors write, thereby, empowering themselves as writers to decide upon their purpose and structure their writing to that end.

Thinking about Key Details

As the first cluster of standards for both literature and informational text fall under the umbrella of key ideas and details, it is clear that they are important concepts. But what exactly are the key details students should adhere to? In literature, the elements of narratives are delineated for primary grades, along with questioning. However, aren’t the details students need to highlight relative to the task? If students are trying to unpack the characters, then perhaps the most significant details would be different from those that depict the setting. And while significant plot points should reveal elements of the character, they may not give a complete picture. This got me thinking about how to teach key details so that we understand the gist of what we read, but also have clarity in dissecting different elements of what we read. Although the standards do not mention minor details, students must also be able to distinguish between the details that represent the crux of what they are examining and the cursory details that enhance the story. Perhaps we can examine stories with a whole-part-whole approach. What are the key details that disclose the plot? What details illuminate the characters? What details paint the setting? Which details support the theme? Were these details related to the plot, characters, setting, or all? Can we pull from those key details to determine the theme? Which details are key to answering text-dependent questions? Perhaps through our process of close reading, we can read for each purpose, map out the important details for each area, and then analyze how they cross over. Perhaps then, we could all develop more clarity! Below is an idea of how to organize a class chart examining these different elements. Of course, there are still key details to think about for informational text, but I will save that for another day!

Examining Key Details

Title of Story:

Focus	Plot/Events	Setting	Characters	Theme	Questions
Key Details

Why Change?

Reading is the process of constructing meaning through the dynamic interaction among the reader’s existing knowledge, the information suggested by the written language, and the context of the reading situation. (Michigan State Board of Education, 2002)

When you reflect upon your childhood reading instruction, what stands out? Was it memorable? Exciting? Meaningful? Did you love to read and devour books? Did you know how to grapple with difficult text? Did anyone show you how to get deeper into the text? Did you spend time exploring the depth and wonders of stories? Unfortunately for me, the answer to all these questions was no. I don’t recall reading being challenging or purposeful beyond the task at hand. I remember independent reading tasks where we plowed our way through the SRA leveled text box. We started at a specific color of story, read the stories and answered the questions, and when we got enough right, then we moved on to the next color. This was of course self-corrected with an answer key, self-monitored, and self-reported. I remember getting stuck on brown, and being frustrated that I was on a level while others were passing me. I also remember eventually cheating to move on. I didn’t have the comprehension strategies to help me when things got tough, but I did have an answer key. I also remember that we did have reading groups, and I was stuck in the middle one and couldn’t get out. I always felt I belonged in the highest group, but didn’t have a way of moving.

I am sharing this story because I often hear people lament about change. “Why do we need to change education? It worked for me.” And while yes, I am technically a success story because I did stay in school and become an educator myself, I disliked school growing up. I loved my teachers, but counted down the years until I would be finished. Ironically, I have now learned that I will never be finished. Now I do love learning, but when I was a child, school was not about learning, but rather about finishing. I was not a critical thinker, and it was not demanded of me. If I regurgitated what was taught, then I was awarded good grades. I never thought about reading comprehension until I became a teacher. Reading is so internal, it is just what you do, or so I thought.

So much research has come out about reading in the past 20 years, which has often been lost in implementation in the last 10 years due to scripted lessons. Many teachers across America have been forced into following set programs in published textbooks, rather than examining the needs of the students in their classrooms. These texts, such as Open Court, give little time to differentiation, reading aloud, or access to higher level texts. Instead of student learning being the focus of each reading lesson, the script created by someone far outside the classroom dictates what should be taught. Clearly this is counterintuitive to what teaching should be. The strongest supported reading program by the government, Reading First, is another example of a highly scripted program. These types of programs were developed based on the recommendations of a highly researched based practices found in the National Reading Panel’s (NRP) Report from 2000. Scripted lessons became the result of the NRP, although many flaws have since emerged from the summary of the findings within the report (Yearian, 2011). Since implementation of Reading First in thousands of classrooms, it has been found that while phonics skills improved, comprehension did not. (Gamse et al., 2008).

With the adoption of Common Core Standards, there is a much needed refocusing back on reading comprehension. Teachers are encouraged to examine their students’ needs within school sites and develop instruction that will be most meaningful for those students. For many teachers, this will be a huge shift from the current culture and practices within their schools and districts. While you may or may not agree with how Common Core came about, and how it was written, it seems to me that some change could really do us good.

References

Gamse, B.C., Jacob, R.T, Horst, M., Boulay, B., and Unlu, F. (2008). Reading First Impact Study Final Report Executive Summary (NCEE 2009-4139). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.

Yearian, S. J. (2011). Empowerment of Teachers and Students through Innovative Literacy Practices. (Doctoral Dissertation) Retrieved from ProQuest Dissertations and Theses. (Accession Order No. AAT 3474300).

Perception and the Truth

Many credit Lee Atwater with the quote, “Perception is reality.” And when viewing your own life, does this not ring true? One would never consider a turtle to be a speedy creature, but then again, that depends on who is doing the considering.

Perspectives have much to do with experiences, schema, and interpretation. Author’s bring their own unique perspectives to the texts they write. They select what they will reveal to the reader explicitly and implicitly, how the text will be organized, and how their point of view will be carried out. Often the author’s own ideas begin as incomplete thoughts, twisting and turning through the process of writing, changing and evolving until they come out the other side into a cohesive whole. At times, the characters of novels reveal themselves to the authors through the storytelling, and take on a life of their own, and yet, the author still has command over what will be revealed through the character’s dialogue, actions, and thoughts. Despite all this control, readers develop their own interpretation based upon the evidence within the text, but also their own personal perspectives. Other experiences with texts, the world, and other people affect how they view what the author reveals. Therefore, readers apply their own connections to develop their own perspective, but must also examine the evidence within the text to understand what the author directly reveals as well as infer to gain meaning from underlying messages, ideas, and themes.

Common Core emphasizes the importance of point of view, devoting standard six for Reading Literature and Informational Text to this concept. Why is it so significant? Understanding the role of point of view allows the reader to think critically about a piece. What are the author’s motives and purposes in writing a text? What context or historical background does the author emerge from? How does this affect the portrayal of events? Readers must understand the effects of their own perceptions and the author’s point of view in order to get at the truth of what they are reading. Even then, that gets us to a deeper question – what is the truth?

Thank a Teacher!

It’s that time of year again, when everyone can smell the freedom of summer. The students begin to get antsy, and teachers stress and work intensively to make it to the end zone. I always feel like it should be an easy slide home, but it always proves to be just as hectic as the beginning of the year. Now is the time to thank teachers for their hard work. I have heard complaints before about how other jobs do not get the same type of accolades, so why should teachers? My response is as follows:

People deserve and perform better through positive recognition of their efforts and work. It’s amazing how far a few kind words and a token of gratitude can go. All people who show exemplary dedication to their work deserve this recognition. This includes mothers  and fathers (who yes, get a different day), and employees in all different fields. So why do I celebrate my son’s teachers? They are the ones who take care of him when I am not there. They give him the support he needs to grow and flourish, teach him lessons about life, and are an integral part of his experiences. A good teacher can have a profound effect on a child. With the proper guidance from both school and home, my son will develop solid foundations as he grows up. His teachers are my partners, parenting from a different perspective.

As a teacher, I know how much of myself goes into my students. It is not just about reading, math, and writing. There are daily lessons about becoming caring human beings, about demonstrating tolerance and love, and about dealing with difficulties and conflicts. Teaching is not just about improving the minds of America’s tomorrow. Tightly woven within the job is supporting impressionable young scholars’ social, emotional, and mental well-being. It is both exhausting to worry about 30+ students, and exhilarating to see their successes.

My son and I made this craft to give his teacher, but also a heartfelt personal note from me along with a gift. I wrote the poem thinking about what his teachers have done for him this year. First we traced his hands on a piece of construction paper and I added a heart. Then I cut out the hands and saved them for later. We used a sponge to paint pink and white to cover a white piece of construction paper. Then I put the cut out hands and heart on top of the page and we sponge painted with purple on top. When we were finished, we just peeled off the hands. After it dried, I glued down the poem and a picture of my son. This page went into a class book along with a page of his drawings.

The notes I get from students and parents help carry me through the rough times. They remain special even as they have moved on in their lives. I encourage you to take some time to think about your child’s teacher from this year. What has that teacher uniquely done that has made a difference for your child?

Unless…

“I speak for the trees, for the trees have no tongues.” – The Lorax by Dr. Seuss

I have been thinking about the Lorax a lot lately. It is my son’s current favorite movie, and while he enjoys the music and finds humor throughout, I find myself mulling around the inherent messages of the movie (and the book) and how it could be used in the classroom. I love the complexity of the Once-ler in the movie.  As we watch the film, my son wonders if the Once-ler is bad. In the book, that seems a little more clear cut, but the movie offers background information of the Once-ler as a dreamer, a victim of his family, and one who endures despite the odds. However, he does indeed become “bad” as he become engulfed in the greed of money. Through contrition he sees redemption. We are also offered the comparison character of Mr. O’Hare, who creates an entire city deprived of the most essential element of life, air, so that he can profit. How do we define evil? When does someone cross the line? Can someone be both good and evil? How would you characterize the Once-ler in the movie vs. the book? Why do these perspectives vary? One of the greatest goals of Common Core is to get students to think deeply and analyze from multiple perspectives. Why not use movies to support this goal? I am not saying most lessons should entail film clips, but they are an engaging way of drawing students into the world of cognition. And, while we need to consider complex texts, the use of the arts (including paintings and music) can be equally intriguing. It seems to me that the appeal of the movie could work at multiple levels.

“Which way does a tree fall? A tree falls the way it leans. Be careful which way you lean.”
– The Lorax by Dr. Seuss

“Are they sad?” This is the question my three-year old consistently asks as the animals and the Lorax mourn the loss of the tree that the Once-ler just cut down. Although he can’t articulate how he knows they are sad, older students (such as first and second graders) can. As the Once-ler hums along pulling the tufts off the tree, lying about his acts, it is clear that he feels very differently than the animals. What clues do we see and hear that tell us how the different characters feel about the first Truffula Tree being cut down? (Text-dependent question) How and why do their points of view vary? (Understanding Point of View RL 6) How does your point of view of an event affect how you behave? (Big Idea Question) In the movie, the dialogue, music, and words used to convey their thoughts reveal how each character feels. This small five-minute clip could easily be viewed several times to analyze these questions from multiple perspectives. (Close Reading)

“Unless someone like you cares a whole awful lot,
Nothing is going to get better. It’s not.” – The Lorax by Dr. Seuss

Contemplate this quote for a moment. What do you connect it to? What are your thoughts? What comes to your mind that needs change? How does this relate to our daily lives? Our current climate? How does this relate to history? Who do we know that worked to make “it” better?  The Lorax provides a lens for upper grades and beyond to delve into big ideas about change and making a difference.  What historical figures cared about transformation? How did they show that they cared? Does caring always lead to improvement? (What about those who care about negative changes?) How will you make a difference now? What issues affect your current lives that you can make better or change? (Bullying?) What are the consequences of not getting involved?

Before I exit my post for the week, I would like to leave you with one last quote to think about Common Core and –  in the spirit of The Lorax – our lives: “It’s not about what it is, it’s about what it can become.” 

Using Close Reading and Questioning

Earlier in the year I wrote about the importance of close readings and what they entailed. As close readings are an essential part of Common Core standards, teachers will need to rethink how they spend their shared reading time block. Teachers accustomed to using textbook models are comfortable with following the steps outlined in the text for a single reading of the story. Some teachers may have extended the reading a second time. Teachers familiar with comprehension strategy instruction may spend several days or a week on one story to focus on a specific comprehension strategy. Lifting the text and examining the text for evidence may be a norm. However, close reading goes beyond both of those. It certainly has elements of comprehension strategy instruction, but demands more time on text, and certainly more student time with challenging texts. Teachers may read the same text for 1-2 weeks for a variety of purposes, sometimes as a whole, other times in small parts. Teachers will need to strategically map out this time, selecting texts with depth, and focusing lessons around content that students need to understand. For example, if a third grade teacher was focusing on the comprehension strategy of questioning, with the objectives of readers ask questions about unknown words, parts, and key details, as well as readers find answer to their questions using the text, background knowledge, inferring, or outside source (with some questions being unanswered), a close reading of The Princess and the Beggar by Anne Sibley O’Brien may look like the following:

Day	Lesson	Charting/Activity	Standards Addressed
1	Read story aloud with students. Stop and pause throughout the reading.	Students write questions on post-it notes throughout the reading, including unknown words and phrases. Have students share and chart their deepest question.	RL 1, RL 4
2	Classifying questions: What type of questions do we ask? (e.g. clarifying, character motives/traits, unknown words or phrases (vocabulary), predicting etc.)	Analyze the questions from day one for how they relate. Group questions and determine categories. Have students work in collaborative groups to determine how they can categorize their questions. As a class discuss questions that didn’t fit into your categories and create any new ones that they may need.	RL 1
3-4	Chart story elements students remember from the day before. Read story aloud again. Discuss the categories from the day before. Tell them today they will examine the category for character traits/motives. As we reread the story, we will examine how the princess, the king, and the beggar think, speak, and behave. Then we will revisit those questions	BEFORE READING: Chart story elements (characters, setting, major events). Chart questions students have about the three different characters. DURING READING: Chart character traits’ motives along with the evidence from the text. Examine how those traits relate to the sequence of events. Revisit questions throughout the reading as they are answered. AFTER READING: Examine which questions were not answered. Can we answer them now? If not, why? Which questions seemed to get at the heart of our characters? Which types of questions got us deeper into understanding the characters? (For example, how and why vs. who)	RL 3
5	Examine just the poem within the story. What is the poem about? Pull the poem apart to determine meaning and infer the point/lesson of the poem. What does this poem reveal about the princess?	Have the poem written up separately from the story so you can pull it apart and discuss meaning as it unfolds and how it relates to the story as a whole. Include questions they have about the poem, and work to find the answers through pulling it apart. Examine the literal and nonliteral language within the poem.	RL 4, RL 5
6	New Words and Phrases: Examine their questions that related to vocabulary. Take words/phrases from day 1 that have not been addressed. Students should have text so they can look closely for evidence.	CHART: Write the new words/phrases, evidence or clues for determining meaning, and images to help us remember the meaning. Give students their own chart too. As the class discusses the words, they should write their thinking on their page and share out. For words without context, provide context (either sentences or pictures) for them to help support inferring for word meaning.	L4
7	Shared Inquiry: Examine a specific text-dependent question, such as, “How does pride play a role in the princess’s decisions?”	Students brainstorm their thinking first, citing text evidence for their answers. Class discussion starts with this question, but then probes beyond based on the conversation. Students have text to use for evidence. Ultimately, the class examines the data of their discussion and revisits their answers from before.	RL 1
8	Revisit Questions from Day 1: Answer and Sort	Whole Class: Examine some questions from day 1: Discuss the questions and their answers, citing evidence. Sort questions by the types of answers (Text, Background Knowledge, Infer, Outside Source/Unanswered)	RL 1
9	Answering Questions and Sorting by T, BK, I, and U/OS	Students work in collaborative groups to find the answers to the questions they sorted on day 2. Where did their answers come from? Cite evidence when answering and sort questions in the end by the categories from day 8.	RL 1
10	Recount	Students write a recount of the story using the brainstorm organizer. Students also determine the lesson of the story. Students share recount with a partner.	RL 2
11	Lesson Discussion	Examine the lessons students wrote from the day before. Organize by teams of similar thinking. Have them get into groups and develop an argument as to why that lesson matches the story. Have a class debate.	RL 2, W 1

Effective close reading should draw students deeper into the nuances of the text. Students should feel empowered and develop a greater understanding of the importance of exploring texts. Close readings should build students’ stamina and drive, and ultimately build a passion for reading, which is one of our foundational goals to begin with.

Text Structures and Features

When I was growing up, there was little thought to the type of text we were reading. I followed assignments, read the stories in the primer, and answered questions. It did not occur to me that we should read differently for different types of text. To be honest, this thought did not occur to me until I became a teacher, and more specifically, when I first taught third grade. I remember doing a STAR practice test the week before doomsday (the actual STAR test), and my students performed horribly on an informational passage. The questions seemed really difficult unless you read the passage for the structure of expository text. Once you pulled out the supporting details each paragraph detailed about the topic, the answers were clear. This required the reader to identify the type of text, understand how the text was organized, examine the relationships within and among the paragraphs, and then relate them to the questions being asked. From then on out, I made understanding genres part of my reading instruction along with learning to distinguish among them, and determining what types of organizers would help the reader unpack the text. Common Core has clearly identified the need for students to understand diverse genres and their elements. This emphasis seems very appropriate to me given my experiences with working with students. While the fact that we have two separate categories of standards to elucidate the importance of explicitly teaching types of text, today I want to look at standard 5.

Craft and Structure: College and Career Readiness Anchor Standard 5:

Analyze the structure of texts, including how specific sentences, paragraphs, and larger portions of the text (e.g., a section, chapter, scene, or stanza) relate to each other and the whole. (CCSS)

Students are expected to know how different types of texts are organized, distinguish among types of genres, and determine how the separate parts relate to the whole. When examining standard 5 for grades K-5 for literature, the types of texts mentioned include stories, poems, dramas, and prose. Traditionally, these categories were easily distinguished by stories/prose being in paragraph format, poems being written in stanzas, and dramas including a speaker before the sentence. Modern writers certainly blur these lines and can make classifying text more challenging. However, for the elementary classroom, teachers can easily select text that keeps these categories clear to build basic building blocks. The venn diagram  examines some of the basic features that distinguish poetry and narratives. Dramas are similar to narratives except that the organization is related to the speaker rather than paragraph format and that white space may be used to signify the change in characters.

Standard five for informational texts specifically examines text features and structures. Students are expected to differentiate among the different types of texts as early as kindergarten. Throughout the grade levels, students increasingly become more responsible for understanding the structure of texts, the significance of their impact on the development of the text, and the dissection of the relationships between parts, wholes, and the text progression. The set of differentiated task cards to the left support instruction and independent practice of expository text features for primary grades. These skills are essential building blocks since students in fourth and fifth grades need to be able to identify the type of text organization or structure– i.e. cause and effect, problem/solution, comparison, etc). Although some literature standards do not examine the relationship between narratives to expository text, this distinction is later made in the informational texts standards. Therefore, it is critical that students understand the features and structures that distinguish different types of texts from a basic to more complex level throughout the grades.

So how does standard 5 impact our instruction in the classroom? Students need to analyze texts from an early age, identify features that genres have in common. Primary teachers may begin the year by having students sort books as they read them aloud, then delve into the library and examine how the books can be sorted by genre. Text identification should become part of every story that is read. Perhaps instead of scaffolding the story before reading, the class can examine the text structures and features to determine what they are reading for. What type of organizer would work to keep track of our thinking about a text? What can we expect to find in the text? Thinking about comprehension strategy instruction, this relates to predictions. Rather than just predicting events, readers can predict the type of text they will be reading. Readers of all grade levels will benefit from examining texts closely to understand and determine the features and structures to improve comprehension. And, as with all vocabulary, the language of the discipline needs to be part of their every day discussions so that it becomes how they articulate their ideas.

Tiering Vocabulary

When considering the significance of language and words, it is  important to note the three-tiered analysis outlined in Appendix A of the Common Core State Standards. These tiers represent different types of words students need to grapple with, and although some are more complex than other, requiring more support, all types of words are important for students.

Tier one is everyday language that young learners develop. Although English Language Learners students will need support in this area, most native speakers naturally develop this category of words. Tier two, or general academic words, are words of precision that are found within and across texts. They are not specific to a particular area of study, but are exacting in their selection to convey a message. Teachers need to examine tier two words carefully in text, as they are often the least supported by instruction and often don’t have enough context clues to support their meaning. Tier three, or domain specific words, is particular to a field of study. Often found in expository text, they are often clearly defined and documented in a glossary. These are the technical terms students learn for a specific area of study. Students learn these words best over time when applied in multiple settings. Table 3 examines the gist of these three different categories of words. For a more in-depth analysis, Appendix A of Common Core Standards gives more examples of these types of words within context.

Synopsis of Three-Tier Leveled Words

Tier	One	Two	Three
Types of Words	Everyday Language	Vocabulary that is precise and more advanced	Language of the Discipline: Specific to a field of study
Examples	Sad, happy, angry	Devasted, elated, infuriated	Geologist, sedimentary, metamorphic

Subitizing: More Than Meets the Eye

Subitizing is a relatively new concept for me. Sadly, it is not an integrated part of the mathematics curriculum yet. Therefore, children often have little experience with subitizing. When I first learned about this concept, I thought it pertained only to kindergarten, first grade, and struggling students beyond those years. However, I have now seen that children of all ages benefit from subitizing.

What is subitizing, and why is it important? Clements and Sarama (2009) define two types of subitizing. The first, perceptual subitizing, pertains to the ability to both perceive intuitively and simultaneously the amount in small number sets. No counting is neccessary, you just know the amount when you see it. Children develop the prerequisite skills for perceptual subitization at a young age. According to Clements and Sarama, children begin naming collections of 1, 2, and 3 from ages 1-2. By age three, children can also create collections made of 1-3 objects, sometimes 4. Perceptual subitization up to a collection of 4 occurs at age four, and the recognition of sets of 5 develops at age five. To encourage the development of perceptual subitizing, parents and teachers should play snapshot games where children see an organized picture of dots, squares, and other simple geometrical shapes organized in a linear fashion for couple of seconds, then determine the number.

The second type, conceptual subitizing, relates to the ability to instantly see the parts, and join them together to make a whole. For example, given the picture of five arranged with three and two dots, a conceptual subitizer would see 3 and 2, and know that makes 5. Again, no mathematical operations may be consciously enacted, but rather, an instant recognition that the parts make that whole. As children progress, subitizing helps with the visualization of operations and mental math. Conceptual subitizing to five and ten begins at age five. By age six, children are able to conceptually subitize to 20. At this age, five and ten-frames are helpful organizers for promoting subitizing at these higher levels. Skip and counting and place value with subitization begin at age seven, and by age eight, children see multiplicative relationships, such as 5 groups of 10, and 4 groups of 3, which makes 50 and 12, so 62 dots. As you can see, children benefit from subitizing activities well into third grade and beyond. Below is a table to organize these milestones in subitizing.

Trajectory of Subitizing

Age	Type of Subitizing	Example
1-2	Precursor to subitizing: Name small collections up to 3	I see two grandmas.
3	Precursor to subitizing: Create small collections up to 3 or 4	I can count three crackers.
4	Perceptual up to 4	**** I see four stars.
5	Perceptual to 5	***   I see five stars.    **
5	Conceptual to 5	***  I see three and two **   stars. There are five stars
5	Conceptual to 10	* * * * * * * I see 3, 3, and 1, which makes 7.
6	Conceptual to 20	* * * * * * * * * * * * * I see 5, 5, and 3, so that makes 13.
7	Conceptual with place value and skip counting	I saw tens and twos, so 10, 20, 30, 32, 34.
8	Conceptual with place value and multiplication	I saw groups of tens and fours, so 5 tens makes 50, 4 fours makes 16, so 66.

All information adapted from Clements and Sarama (2009)

I encourage you to try out subitizing with your students or children. Where are they in their development? I have seen eight year olds that are conceptual with place value and multiplication, and 14-year olds who are at perceptual to 4. Experiences with numbers, both counting and visualizing, are crucial for number development, regardless of the age. Once foundations are set, subitizing can be used to teach more complex topics. I have used both subitizing and arrays to develop understanding of multiplication, algebraic properties, and division. If you are new to teaching Common Core, then my new unit on teaching multiplication using subitizing and array cards may be just for you! These cards are intended to be part of a program that also includes problem solving. You can check out my 17 page free download to see for yourself!

Clements, D.H., Sarama, J. Learning and Teaching Early Math The Learning Trajectories Approach (2009). Routledge: New York, NY.