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

Vocabulary and Multiple Meanings…Not So Uncommon

The Common Core Standards have a renewed focus on vocabulary development across the grade levels. While this is not a new concept, there is certainly more clarity and dissection in approaching the variety in the type of words students should learn, as well as the skills students should develop to become proficient at their grade level. Certainly one of the prevailing  themes within the Language Acquisition and Use standard 4 for grades K-5 is that students should be able to determine the meaning of unknown and multiple meaning words. Clearly this should reflect an increase in the complexity of language students encounter as texts become more complex, but students of all levels should be grappling with these concepts.

The College and Career Readiness (CCR) Standard 4 for Language is as follows:

Determine or clarify the meaning of unknown and multiple-meaning words and phrases by using context clues, analyzing meaningful word parts, and consulting general and specialized reference materials, as appropriate.

CCR 4 examines the role of the reader in actively making meaning while reading. Readers need a variety of skills to support them in attaining this standard, such as knowledge of multiple meanings, affixes, context clues, and how to use resources. Students must become attuned to when they don’t know the meaning of words, and actively apply strategies to determine meaning.  Therefore, teachers must teach the strategy of inferring for word meaning across the grade levels, focusing both on using clues both within the word and within the context to gain insight into meaning.

It is evident that for this standard, students will need to grapple with complex text that allows them to explore the nuances of language beyond the literal.  For example, the word “interesting” can mean a variety of messages as the word alone does not necessarily convey the writer’s or speaker’s intention. It could mean fascinating, it could mean boring, it could mean different. Without further explanation, the word by itself is nondescript. If someone tells a story and the listener nods his head, rubs his chin, and replies, “Interesting,” the word could mean something worth contemplating. If the speaker comments on a how a meal was prepared as, “The meal was…interesting,” he or she may be communicating that it was different, but not necessarily tasty. The pause within the sentence sets a tone, as well as the word choice of interesting. If the meal was delicious, then interesting wouldn’t be an appropriate choice. It is possible the meal was not good at all, but the speaker was looking for a descriptive word that would not be offensive. (This would especially be true if the context included that the chef or host of the meal was someone of respect.) Sometimes the absence of stronger word choice sends a message as well as the selection of powerful words. Therefore, readers must examine words that are selected (and at times, omitted) for their basic meaning, but also analyze the context and tone to determine the essence of the message behind the words.Students need to engage with multiple meanings during reading, but it is also helpful to examine common words students know that have multiple meanings and focus the classroom discussion on how words get their meaning. Sometimes we take for granted that a concept as simple as a “word” can really be quite a loaded discussion. What is a word? Why do we have words? How do words gain their meaning? We have a tendency to talk about words all the time, but not really examine the very essence of its meaning and purpose. Perhaps this can help students refocus their attention on the marvel of words and how finding new words is like opening a treasure chest.

In order to help support teachers, I have created this set of differentiated task cards that focus on the guided or independent practice of multiple meanings. New words give children (and adults!) better access to clear communication, and clarity in expressing ideas. When students understand new vocabulary, and engage with it in meaningful ways, they become empowered. I have often seen kids try out their new words on family and friends, and wear them with a sense of pride. Even my three year old son likes to bring up new words, and through repeated rereading, is able to tell me the meaning of words such as ajar and eider. I hope that as you explore new language with your students, they become entrenched in the excitement and power of vocabulary, as I do with my  son.

The Big Changes with Common Core Standards

I realized that in my posts I have jumped into some of my findings within the standards without stepping back and discussing some of the broader changes brought by the Common Core Standards. I suppose these are the elements that are well documented and discussed frequently at any of the Common Core Support websites. However, I will address them here as well in case you haven’t had the time or energy to research out these changes.

The New York State Department of Education (www.engageny.org) cites five specific instructional shifts in literacy related to the primary grades. The first is the balancing of literature and informational text. By third grade, students should be engaging with 50% of each type of text. Secondly, when reading, students should be focusing on text-dependent questions, which require text-based answers. While skills such as main idea are still relevant, teachers should focus on questions that get deeper into the structure and craft of a particular story.  Third of all, writing should shift from personal response and narrative to writing from sources. Rather than convey feelings, students should write arguments that are deeply grounded with evidence to inform their audience. A fourth critical aspect of Common Core is text selection, demanding that teachers evaluate the quality of text so that they increase with complexity and have enough depth for students to perform close reading. The last significant shift focuses on the importance of students developing academic vocabulary at all ages. This focus on specificity of language should also help support students in accessing complex text.

The Student Achievement Partners (www.achievethecore.org) classify the instructional shifts with Common Core by three major changes, which embody those reported by New York. Essentially, students build their schema through content-rich literature and informational texts, focus both reading and writing on evidence from text, and build complexity in reading through types of text and by developing vocabulary.

While at first glance, these change may not seem sweeping, in actuality they are. The Common Core Standards really do embody what good comprehension strategy instruction has always entailed – lifting the text, examining the text from multiple perspectives, and sharing and discussing ideas. However, new guidelines on what students should be examining are inherent within these standards, and the idea of slowing down is in greater depth. Greater emphasis is place on informational text than in the past, and although vocabulary has always been deemed important, Common Core makes a resounding statement about how we must do much better for all our students by making all grade levels accountable and pulling apart the types of vocabulary students must develop. In addition, Common Core demands critical thinking rather than intuition.  “What’s your evidence?” should be a frequent question that demands textual proof. I’m not going to lie – when you teach your students to question, debate, and produce hard evidence, they may begin to question things they once accepted as “just because”…

Splitting Hairs Part 2: Language of Common Core

Last week I examined the progression of central messages, lessons, morals, and themes in the second standard for reading literature. This week, I want to take a look at that same standard, but examine the the use of the following terms: retell, recount, and summary.

In kindergarten and first grade, students are to retell stories. In second and third grade, students are to recount stories, and in fourth and fifth grade, students are to summarize stories. Both retells and summaries are common formats in our educational system, but what is a recount? Let’s examine each one to determine how the three terms build in complexity.

According to Kissner (2006) retelling is when a student orally tells what is remembered about a text. Generally the retell is related to events. The retell is somewhat casual in its format and relies mostly on what the reader remembers. A summary is a more formal account of the text, can be both written and spoken, and must include the main ideas within the text and key events and details. Often a format for developing a summary includes a topic sentence with the title and author of the story, followed by a verb, and then is finished with the main idea. The rest of the summary includes other important main ideas throughout the text, or key details.

So, what is a recount? The term recount is more easily found in English and Australian publications. Recounts in those countries are a type of written account of a story that is in chronological order, includes the 5 W’s (who, what, why, where, and when), and has a concluding sentence. The format can be described as the orientation (introduction), series of events, and the re-orientation (conclusion). In short, a retell gives the experience of the story, a recount is a shortened experience of a story, and a summary is an explanation of the main ideas within a story.

In order to help support teachers in grappling with a recount, I have developed a brainstorm that follows the format as outline in Targeting Texts by Sue Stubbs. I have also included a retell checklist to support teachers in analyzing oral retells.

Through the process of unpacking the standards, I have found that language that I had previously taken for granted also needed unpacking. As we explore Common Core and its implications in our classroom, we must look with a new lens to make sure that we can find clarity in what we are teaching so that we really do benefit our students.

References

Kissner, E. (2006). Summarizing, Paraphrasing, and Retelling Skills for Better Reading, Writing, and Test Taking. Heineman: Portsworth, NH.

Stubbs, S. (2000). Targeting Text. Blake Education: Sydney, NSW.

Splitting Hairs: Language of Common Core

Upon setting out to unpack ELA Reading standard 2, I found the language, which seemed so normal at a glance, to be unclear. The more I dug into the nuances of the words within the standards, the less consistency I found. When examining the terms of recount, central idea, central message, lesson, moral, and theme, I found conflicting ideas, and ultimately, had to make my own assertions. I must thank two of my sisters for helping me think through this one, as they both have literature backgrounds. I would love to hear your thinking on the topic.

The second College and Career Readiness Anchor Standard (CCR) standard for reading reads as follows:

Determine central ideas or themes of a text and analyze their development; summarize the key supporting details and ideas.

This overarching standard, which is to represent how students should think about both narratives and expository text, uses the terms central ideas or themes.

Within the grade levels, the language progression within Reading Literature Standard 2 is as follows:

   1st Grade           2nd Grade                   3rd Grade       4th Grade   5th Grade
central message  central message,       central message       theme             theme
or lesson              lesson, or moral          lesson, or moral

Common Core was developed with both an increasing of complexity of concepts throughout the grade levels, as well as a mirroring of concepts between literature and informational text standards. The CCR standards are meant to envelope diverse types of text. Therefore, when the CCR standard uses the term “central idea,” I believe this refers to the main idea, which is the gist of what the author is saying. In narratives, the main idea could be thought of who, did what, and how or why that was important. In expository, the main idea is the topic. The central idea/main idea is bound by the text. On the other hand, the grade level specific terms transcend the text. At first glance, these words seem like the same ideas, however, since the standards were created to increase as we progress through the grade levels (as seen below), then there must be nuances in their application.

Let’s examine each term individually, and then examine how they are related:

Theme

According to Griffith (2011), the theme expresses ideas about the real world outside of the text. Symbols, patterns, and problematic situations within narratives are some clues that help readers determine the theme. The theme is not the subject of the story, but rather, the commentary about that subject. While Griffith states that the theme must be a developed sentence, others believe the theme may be expressed in a word or phrase. Kirsner and Mandell (1994) examine themes as words, phrases, and sentences that depict human emotion, conflict, and experiences such as jealousy, loss of innocence, disillusionment of adulthood, and the beauty of love. Themes can be implicitly or explicitly stated, and stories may have multiple themes (Barone, 2011).

Central Message/Lesson

Students begin looking for the central message or lesson in first grade, which indicates that it is a concept that is less complex than theme. When we think of a central message or lesson, we can formulate our lesson around the question, “What can we learn from this story?” or “What does this story teach us?” These questions are simpler than theme, and while they do require a level of analysis by drawing conclusions and synthesizing the text, it does not require the reader to examine the text in the same depth as theme. There can be overlap between lessons and themes, but in general, themes go beyond lessons. (Barone, 2011)

Morals

The moral of a story is related to the lesson. Morals deal with issues of ethics or general truths. Often morals are found in fables, although they can also be found in other tales as well. At times the moral is explicitly stated at the end of a fable. This is called the maxim.

Morals are mentioned in the third grade standards, which makes sense as fables are also introduced at this grade level. This is more about a progression of explicitly expanding the types of narratives students read as they progress through the grade levels.

Tying it all Together

Based upon the individual analysis of terms, these are my conclusions:

The Central idea is the same as main idea. The central message is a lesson, which could be the theme. A moral is a specific type of lesson, most often found in fables. The theme is less concrete than lessons. To find the theme, readers must draw conclusions and infer based on a variety of evidence as found through recurring events, patterns, symbols, and underlying conflicts. The theme goes beyond a lesson, although there can be overlaps. Figure 3 is one visual interpretation of how these concepts can be viewed.

Therefore, in the story Cookies from Frog and Toad Together, the central or main idea could be Frog and Toad keep moving their cookies out of sight to show willpower, but they keep finding the cookies hard to resist. Within that story, they keep hiding the cookies from their sight, and keep finding that does not help because they always have access to the cookies. They learn (lesson or central message) that temptations are hard to resist, or that willpower takes more than putting something out of sight. The theme is based on recurring patterns. If we look at the collection of Frog and Toad stories, there is a focus on friendship. What does this story particularly say about friendship? Although Frog keeps helping Toad (and himself) by hiding the cookies and then ultimately feeding the birds, Toad ends up going back home to make more treats. Therefore, a theme at its most basic level could be friendship, or could be expanded to although we can help our friends, they ultimately must help themselves. As you can see, the concepts may align or cross over between what is bound within the text and what transcends the text.

References

Barone, D. M. (2011) Children’s Literature in the Classroom: Engaging Lifelong Readers. The Guildford Press. New York, NY.

Griffith, K. (2011). Writing Essays About Literature A Guide and Style Sheet. Eighth Edition. Wadsworth Cengage Learning: Boston, MA.

Kirsner, L. G., & Mandell, S. R. (1994). Fiction: Reading, Reacting, Writing. Harcourt Brace & Co: Fort Worth, TX.

Lobel, A. (1999). Frog and Toad Together. New York: HarperFestival

Closing in on Close Reading

The headlining College and Career Readiness anchor standard has far more depth than may be ascertained upon the first read, which is exactly its point! CCR Standard 1 reads as follows:

Read closely to determine what the text says explicitly and to make logical inferences from it; cite specific textual evidence when writing or speaking to support conclusions drawn from the text. (Common Core ELA Standards)

Calkins, Ehrenworth, and Lehman (2012) refer to this as the literal comprehension standard, emphasizing Common Core’s heavy concentration on students understanding and focusing on the meaning of the text. Although students will clearly need to delve deeper beyond the literal details as supported by grade level standards, Common Core purports that it is essential that all students have a stronghold on literal details and basic inferences first and foremost. Rather than the reader spiraling through his or her perspectives and the connections, the text should be the primary focus.

As we delve into this standard, you may notice that it begins with two seemingly innocuous words: read closely. Although teachers have supported this idea for many years, Common Core is actually referring to a more specific concept called close reading. Close reading is not a new term, having been used in both middle and high school in the past, but its focus in primary grades is a new application. This type of reading requires effective, deliberate teaching and strategy instruction. It is not enough to just tell students to look closer. They need quality text of appropriate complexity that is worth the reading, and specific ideas on how they can examine the text.

What does a close read look like? Below are three different definitions that embody similar ideas:

Rereading for the purpose of recognizing details and nuances of text that may go unnoticed during a cursory first read so that new understandings and insights may reveal themselves (Burkins and Yaris, 2013).

A careful and purposeful reading and rereading of text; an intensive analysis of a text. Reading to uncover layers of meaning that leads to deep comprehension. A focus on what the text says, how it says it, and what it means.

Close reading may include text-based questions and discussion with attention to vocabulary and word choice, context, tone, argument, and imagery (Tyson, 2013).

 Careful and purposeful rereading of a text (Fisher, 2013).

I like to think of close reading as scuba diving. When we speed through text and get the general meaning, we are swimming along the surface. Previous comprehension instruction where we paused throughout the story to discuss elements is like snorkeling. You can see beyond the surface, and depending on the clarity of the water (or your thinking) you can look into the story. But with close reading, you get to hang out for awhile and explore the wonders and nuances within texts. You have the air (or reading tools) necessary to immerse yourself completely and examine the deep structures of a text and connect your background knowledge to expand your schema.

These deep structures are the focus of Common Core, and include text organization, author’s purpose, connections among ideas, and synthesizing ideas. Readers must pay close attention to the word choice used within a text, and how the specificity of words is used to advance concepts, along with its key details, arguments, and inferences. Through close reading, students develop a deeper understanding of what the text is truly saying, and while their own ideas and schema will also affect their ideas, text analysis will really drive their thinking. Close reading entails examining complex, short passages that students and teachers can analyze from multiple perspectives through rereading. Rather than spending much time on frontloading, or activation of background knowledge, teachers and students should discuss their connections as they arise through the need to make sense of the text. Teachers should have previewed the text in advanced, and be prepared to examine the text with students using text-dependent questions. These questions include key details, general understandings, vocabulary and text structure, inferences, author’s purpose and point of view, arguments and intercontextual connections. All of these components of close reading can be found in Table 1. Close reading should not replace all types of reading, but is an essential part of the reading instruction. (Fisher & Frey 2012)

Table 1: Components of Close Reading

Deep Structures to Analyze	Modes of Teaching Accompanying Close Reading	Key Features of Close Reading	Types of Text-Dependent Questions
Text OrganizationAuthor’s Purpose Making Connections Synthesizing Inferring Key Details Arguments	Interactive Read AloudsThink Alouds Shared Reading Guided Reading (leveled texts) Collaborative Reading Independent Reading Writing	Short PassagesComplex Texts Limited Frontloading Repeated Readings Text-Dependent Questions Annotation	General Understandings Key Details Vocabulary & Text Structure Author’s Purpose & Point of View Inferences Opinions, Arguments, and Intertextual Connections

Through these close readings, students will develop the rest of the skills within CCR 1. Specifically, students will develop literal and inferential understanding of the text and be able to support their ideas with evidence from the text. Each grade level develops specific skills that students should master within this frame, but teachers must keep this bigger picture in mind when teaching students about questioning and key details.(Fisher & Frey 2012)

References

Burkins, J., Yaris, K. (Jan. 22, 2013). Defining Close Reading. Burkins and Yaris: Think tank for the 21st century Retrieved on Feb. 13, 2013. From http://www.burkinsandyaris.com/defining-close-reading/

Calkins, L., Ehrenworth, M., Lehman, C. (2012) Pathways to the Common Core. Heinemann, Portsmouth, NH.

Common Core State Standards. (2010). Common Core State Standards for English Language Arts and Literacy in History/Social Sciences, Science, and Technical Subjects. Retrieved May 14, 2012, from http://www.corestandards.org.

Fisher, D. (n.d.). Close Reading and the CCSS, Part 1. Common Core State Standards Toolbox. Retrieved on Jan. 25, 2013. From http://www.mhecommoncoretoolbox.com/close-reading-and-the-ccss-part-1.html

Fisher, D., & Frey, N. (2012). Close Reading in Elementary Schools. Reading Teacher. Vol. 66.3

Tyson, K. (2013). 25 Great Ways to Prepare for Common Core. Learning Unlimited LLC. Retrieved on February 2013. From http://www.learningunlimitedllc.com/25-ways-to-prepare-for-the-common-core/

Graphic courtesy of Mycutegraphics.com

ELA Common Core Resources

In my quest to unpack Common Core and to develop a deeper understanding of how to teach with the new standards, I have spent many hours researching the nuances within the CCS document, and I am still in the early phases. Common Core focuses on outcomes, but not the teaching process (with the  exception of close reading). While resources to support teachers are just beginning to emerge, there are a few great websites and blogs that are already in place. Below are a few that I have stumbled across:

New York State Department of Education 

http://schools.nyc.gov/Academics/CommonCoreLibrary/default.htm

New York has provided many free resources in relation to Common Core, including sample units, support videos, and descriptions of instructional shifts mandated by the new standards.

Achieve the Core http://www.achievethecore.org

This website maps out specific lessons for doing a close read with your students at a variety of grade levels, examines how to develop text-dependent questions, and a list of websites supporting Common Core.

The Reading and Writing Project http://readingandwritingproject.com

This website is led by Lucy Calkins and provides insights on perspectives about Common Core and  resources for teachers, including checklists and text lists.

Burkins & Yaris Blog http://www.burkinsandyaris.com

These two educators, one being a published author and another being a literacy coach, provide insightful thoughts in their exploration of common core.

Read Tennessee http://www.readtennessee.org

This website unpacks reading standards for grades K-3. They go into depth of concepts, ideas, and skills that support the standards, as well as look at the language of the discipline.

North Carolina http://www.ncpublicschools.org/acre/standards/common-core-tools

North Carolina has set about unpacking all the standards for both reading and math. This is a much more superficial examination compared to Tennessee, but may be a good starting point.

Whether you have begun examining the Common Core State Standards or not, you will need to in the near future. It is a daunting task. I hope that they sites may be a support to you in your learning journey.

Discourse and Debate

As a teacher, I have spent many years developing my understanding of children in the 7-9 year old range. Now that I have my own child, I find it infinitely fascinating to watch him grow from the ground up. I suppose that was the great interest of Piaget, and in watching my son, I realize he is a unique individual with unique experiences like all children. However, watching him make mathematical sense of our world is both delightful and entertaining at times. He was a late bloomer when it comes to speaking. It wasn’t until shortly after age two that he began really expressing himself verbally, and that we could gain some insight into how he processed his world. We had spent much time counting, especially the 13 stairsteps in our house. Counting to 13 seem to come easily to him, learning three numbers at a time. What was especially interesting was when he first began speaking in 2-3 word phrases and he noticed that both of his grandmas were in the kitchen with him. He looked back and forth out them, and said with delight, “Two gras!” Since then, he has shown how he explores our world mathematically by choosing to count different objects and people. Although he may not really understand the concepts, it is fascinating to hear him use mathematical terms in his daily conversation. He has expressed numbers such as 20 1/2, 100, and 1000, and looked at objects and said, “I’m trying to find how many inches,” as he demonstrates his own form of measuring. His learning is certainly not linear, and he is absorbing far more than what I intentionally work on with him.

So how does this relate to my topic? It is through conversation that I gain insights into my son’t thinking. As a toddler, these discussions are rather short, however, questioning still plays a role. How many do you see? Which is more? How much do you want? The importance of dialogue does not change as children get older. Unfortunately, we don’t have the leisure of much one-on-one time with a classroom full of students, and it is easy to fall into the pattern of teacher talking and students “listening.” However, learning is not a passive role, and without discourse, we don’t really know what students are thinking. Conversations play a central role to eliciting student misconceptions, conjectures, and big ideas. Conversations can allow for us to probe student thinking, scratch away the surface, and develop enduring understanding. Conversations will tell us more than any test alone.

So how do we give students more time to talk? Put them in the driver’s seat. Instead of leading the lesson, pose problem situations that students can grapple with and debate. Be the facilitator, rather than the leader of the classroom conversation. And when kids really don’t agree, then organize a debate. Students love this opportunity to defend their thinking, and it forces them to analyze the nuances of the problem to develop a greater understanding. It is also memorable, which has a lasting effect.

Other tools for giving students more talk time include pair-share thinking frequently throughout a lesson, conferring with students one-on-one, in pairs, or small groups during independent work time, and strategic student share outs. When students are ready to support each other in their learning, I put them in collaborative groups to discuss their strategies and efficiency with concepts. I call these small group  activities “Math Chats.” They are differentiated cards that groups of 3-4 work with to discuss their thinking behind a concept. Students are encouraged to offer different perspectives and analyze how their strategies make the problem friendlier.

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.