Nonlinguistic Representations to Create Meaning
To back up slightly, last week’s blog posting shared that knowledge is stored in two forms: linguistic form (as language) and nonlinguistic form (as mental images and physical sensations). The more that we can teach our students to use both types of representations, the better they are able to reflect on and recall knowledge. When we branch out from linguistic form and ask our students to use nonlinguistic representation as well, the effects on student achievement are significant (Pitler et.al, 2007).
Midcontinent Research for Education and Learning (McREL) makes the following five recommendations for classroom practice using nonlinguistic representation:
 Use graphic organizers to represent knowledge.
 Have students create physical models of the knowledge.
 Have students generate mental pictures of the knowledge they are learning.
 Use pictures or pictographs to represent knowledge.
 Have students engage in kinesthetic activities representing the knowledge.
According to Marzano’s original metaanalysis (1998), using graphic representations had one of the highest impacts on student achievement, with an average effect size of 1.24, the equivalent of a gain of as many as 39 percentile points. As you begin a unit or a lesson, provide your students with a matrix or another graphic way to organize the information they are about to encounter. Students’ attempts to complete the structure as a prelearning activity can prime their brains and create anticipation. The following anticipation guide is an example of how we can help to structure students’ initial thinking about All Quiet on the Western Front before they begin the novel.
Themes in the Book  My Opinion  My Group’s Opinion  The Author’s Opinion  Additional Comments 
Nature is indifferent to mankind’s pain and decisions.  
“To no man does the earth mean so much as the soldier.”  
Cruel trainers make the most useful trainers for soldiers about to go to war.  
War forces people to reject the traditional values and civilized behavior.  
“This book is to be neither an accusation nor a confession, and least of all an adventure.”  
“Every soldier believes in Chance.”  
Friendships endure all. 
Similarly, the row headings in the analysis matrix below show students what to look for as they read an article on the components of blood—and the cell contents show how one student might complete it after having read the assigned material.
Questions to Ask  Red Cells  White Cells  Plasma  Platelets 
Purpose?  
Amount?  
Size and Shape?  
Nucleus?  
Where Formed? 
Analysis matrices are also great for helping students to develop patterns of understanding. The completed matrix below is designed to help students apply the pronouns. The fillintheblank organizer at the bottom is designed to help students apply the understanding that subjunctive pronouns always perform the action of the verb, and the objective pronouns always receive the action of the verb.
Analysis Matrix and Application: Personal Pronouns  
Personal Pronouns  Subjunctive  Objective  Possessive  Reflexive  
Singular  1^{st}  I  Me  MyMine  Myself 
2^{nd}  You  You  Your(s)  Yourself  
3^{rd}  HeSheIt  HimHerIt  HisHersIts  HimselfHerselfItself  
Plural  1^{st}  We  Us  Our(s)  Ourselves 
2^{nd}  You  You  Your(s)  Yourselves  
3^{rd}  They  Them  Their(s)  Themselves 
1^{st} person singular: __ hit the ball. The ball hit ___. The ball is ______. ____ looked in the mirror ball and saw __________.2^{nd} person singular: __ hit the ball. The ball hit ___. The ball is ______. ____ looked in the mirror ball and saw __________.3^{rd} person singular (masculine): __ hit the ball. The ball hit ___. The ball is ______. ____ looked in the mirror ball and saw __________.
Etc. 
As you may remember, during our staff development last year, Heather Mullins and Donna Murray shared many examples of multipurpose graphic organizers. This might be a good time to revisit some of the strategies from last year’s training or to contact Heather or Donna for a refresher.
You may want to check out Donna’s delicious links for graphic organizers. She has tagged 38 different sites that provide a variety of organizers for classroom use. http://delicious.com/murraygirl/graphicorganizers
SummarizationLingusitic and Nonlinguistic
A summarization pyramid is a versatile tool that comes in many formats, has many sizes, and can be used with many prompts. It’s easy to adapt the basic foundation of this technique to your curriculum and your students’ needs.
Basic Sequence
Construct a pyramid of lines on a sheet of paper. When first playing with this format, begin with eight lines, as shown below.
Summarization Pyramid 
___________ ___________________ __________________________ ____________________________________ _____________________________________________ _____________________________________________________ _____________________________________________________________ ____________________________________________________________________

For each line, choose prompts that yield oneword or short answers for the shorter lines and longer responses for longer lines. If you have a large pyramid and a prompt that requires a lengthy response, consider asking students to use more than one line of the pyramid for their response. Consider these prompts and add your own as you experiment with this strategy:
• A synonym for the topic
• An analogy between the topic and a sport
• One question the topic sparks in you
• Three attributes or facts about the topic
• Three words that best describe the topic
• A news headline that would capture the essence of the topic
• One or two other topics related to this topic
• Causes of the topic
• Effects of the topic
• Reasons we study the topic
• Arguments for the topic
• Ingredients of the topic
• Personal opinion of the topic
• Demonstration of the topic in action
• The larger category from this topic comes
• A formula or sequence associated with this topic
• Insight gained from studying the topic
• Tools for using the topic
• Three moments in the history of the topic
• One thing that we used to think about the topic that we’ve discovered to be incorrect
• Samples of the topic
• People who use the topic
• What the topic will be like in 25 years
This list could go on forever. As you decide on prompts and pyramid sizes, challenge yourself to choose experiences that will allow the students to interact with the topic in several ways. Your goal is to have your students learn something from more than one angle in order to promote retention of the concept or skill.
Variations and Extended Applications
Consider asking your students to create a visual related to the topic as they respond to your prompts. For example, use clouds with various forms of precipitation to express information about the water cycle, a ziggurat to express information about Mesopotamia, or a bar graph or pie chart to express information about graphing data.
Research on the “dualcoding” theory of retaining knowledge suggests that knowledge is stored in two formsa linguistic form and an imagery form. The linguistic mode is semantic in nature. The imagery mode, in contrast, is expressed as mental pictures or even physical sensations, such as smell, taste, touch, kinesthetic association, and sound (Richardson, 1983). The imagery mode of representation is referred to as nonlinguistic representation. The more that we ask our students to use both systems of representation—linguistic and nonlinguistic—the better they are able to think about and recall knowledge.
References
Marzano, R. J., Pickering, D. J., & Pollock, J. E. (2001). Classroom instruction that works: Researchbased strategies for increasing student achievement. Alexandria, VA: Association for Supervision and Curriculum Development.
Wormeli, R. (2004). Summarization in any subject: 50 techniques to improve student learning. Alexandria, VA: Association For Supervision and Curriculum Development.
Planning for Student Processing Time
Several of you are using advance organizers as a way to provide instructional scaffolding for our students. Instructional scaffolding is a way of offering students templates, direct instruction, and other tools that can help them experience success. The idea is to provide support until our students can “fly solo.”
Providing students with a fillintheblank style advance organizer is a great scaffolding strategy that also serves as a summarization device. See the example below:
Advance Organizer: Dividing Mixed Numbers

Working independently, fill in the blanks below.When dividing mixed numbers, we must first turn each mixed number into a ______________________.
Once done, we change the operation from division to ________________________________________. Now, we multiply the first fraction by the__________________ of the second fraction. If our final answer is topheavy or an ________________ fraction, then we rewrite it as a _____________________________, and we reduce it to ___________________ terms. 
Try this method, and see how it works for your students. Write your own summarization of the material that you’re presenting. Then review what you’ve written and make a second draft, replacing key words and phrases with blank lines.
Either during or after the learning process, ask students to complete these fillintheblank organizers by writing the correct terms. If appropriate and if time allows, they might share their responses with a class mate and agree on the best answers. As students discuss their responses, they will engage in evaluation of their own responses as well as the responses of their peers. Furthermore, if answers differ, students will justify their responses as they converse.
Even though you will have a specific idea of what word or phrase goes in each blank, you will be surprised at how our students can show us that the blank can be interpreted differently and how something else can fit logically into the space. When we are open to allowing students to explain their logic and reasoning for selecting a term or concept, we see that our students have a lot to teach us too!
Advance organizers are a great means of formative assessment. Teachers can quickly discern what students understand as well as where clarification is needed. The use of questions, cues, and advance organizers has an average effect size of 0.59 and can result in a 22 percentile gain in student achievement (Marzano, Pickering, & Pollock, 2001).
Share One; Get One is another quick processing technique that works as a “brain dump” to break lectures and other extended learning experiences into smaller chunks. These miniprocessing activities can be done at any time during the lesson.
Present the lesson’s concepts as you normally would. When it’s time to take a break and have students process what has been presented, ask them to fold their paper or draw a grid of nine squares, big enough to cover at least half a sheet of notebook paper. In any three squares of the matrix, ask students to record three different concepts, facts, or skills they recall from the presentation. Now, ask students to move around the room asking classmates to fill in the remaining squares with concepts, facts, and skills that they haven’t recorded on their matrix. Each classmate can add only one idea to another classmate’s matrix, but students can add ideas to as many matrices as time allows. The task is complete when six different classmates have filled all remaining six squares with different concepts, facts, or skills. Then students return to their seats.
Ask your students to make a coherent summary of the presentation using the information recorded in their matrices. Have your students put the concepts, facts, and skills in logical order and to rewrite the points from each square in sentence form. This manipulation of content and skills into a particular format is very effective because it forces students to interact with the material, not just record it. It also allows the students an opportunity to interact with the learning environment and to get out of their seats.
References
Marzano, R. J., Pickering, D. J., & Pollock, J. E. (2001). Classroom instruction that works: Researchbased strategies for increasing student achievement. Alexandria, VA: Association for Supervision and Curriculum Development.
Wormeli, R. (2004). Summarization in any subject: 50 techniques to improve student learning. Alexandria, VA: Association For Supervision and Curriculum Development.
Summarization Techniques that Work
As we continue to make adjustments to our instruction based on the results of the 6week benchmarks, pacing guides, and formative assessments, retention is a common area of concern. Putting strategies in place to assist students with comprehension and retention of lesson concepts will decrease student and teacher frustration.
Consider poor old Aunt Sally. She’s constantly making mistakes in the mathematical order of operations. You will have to excuse her if you already understand when to perform each order of operation: parentheses, exponents, multiplication, division, addition, and subtraction.
“Please Excuse My Dear Aunt Sally” is an extension of PEMDAS, the classic acronym for the order of mathematical operations. This mnemonic device assists students daily in understanding what to do and in what order. When you think about it, PEMDAS is also a summarization strategy. Creating acronyms for concepts, cycles, protocols, sequences, and systems is a great way to allow students to summarize and retain information.
One way to begin is by asking students to list the essential attributes of something that you have been teaching. For example, say that you have been focusing on how to write good introductions to essays. In response to your prompt, students might generate a list that includes the following:
• Hook the reader with an interesting attention getter that provides background information to set the stage for your thesis.
• Add your thesis statement.
• Provide an organizational hint to serve as a preview for the content of the essay.
• Use a clincher to transition from the introduction to the first body paragraph.
Then, ask your students to examine each attribute and identify a single term to serve as a key word for remembering that attribute. This group activity involves discussing and deciding on key words, providing yet another opportunity for summarization. Key words for remembering how to write good essay introductions might be attention getter (AG), thesis (T), organizational hint (OH), and clincher (C).
Now it’s simply a matter of sequencing the letters in an order that makes sense. If the attributes are things that do not need to be in a specific sequence, then all the students have to do is move the letters around until something coherent and meaningful emerges. If the sequence is set, such as the steps in a math problem, the process of how a bill goes through Congress, or the metamorphosis of mealworms, the order of the letters is nonnegotiable, and creating a memorable acronym can be a bit more challenging, but it is certainly a worthwhile task.
This technique can also work as a preassessment activity. You might ask your students to create an initial list of attributes as a whole class activity. Then, have the students revise the lists on their own (another opportunity for summarizing). As mnemonic devices, acronyms can be even more powerful when created by students themselves. Consider asking each student to design his or her own acronyms for something to be studied, and then vote on the top three. The voting criteria might include clarity, accuracy, and how easily the acronym can be remembered.
Summarization is not only a technique proven to improve student achievement, but it is also a method of formative assessment that can help you assess where your students are and help them selfassess. By implementing various summarization strategies, we can help provide students with yet another exposure to higherorder thinking activities.
References
Marzano, R. J., Pickering, D. J., & Pollock, J. E. (2001). Classroom instruction that works: Researchbased strategies for increasing student achievement. Alexandria, VA: Association for Supervision and Curriculum Development.
Westerberg, T. R. (2009). Becoming a great high school: 6 strategies and 1 attitude that make a difference. Alexandria, VA: Association for Supervision and Curriculum Development.
Wormeli, R. (2004). Summarization in any subject: 50 techniques to improve student learning. Alexandria, VA: Association For Supervision and Curriculum Development.
Formative Assessment… Now what?
Over the past two weeks I have had the pleasure of meeting with most EOC teachers to discuss the results of the 6week benchmark tests and how the results will drive their instruction for the next 6 weeks. It is exciting to see that we are beginning to reframe our questions as we strive to achieve 17 of 17 targets and meet AYP.
We are moving away from asking, “What labels do students have? to asking, “What are their interests and needs?” We are not looking at just what deficits students have, but we are also looking at what strengths our students bring to their classrooms. We are moving beyond thinking solely about questions such as, “How do we remediate?” We are starting to focus on how we can maximize access to the richest possible curriculum and instruction.
We are no longer simply asking, “How do we motivate?” but we are beginning to explore what it would it take to tap the motivation already within our learners. We are moving to the point that all of us are asking, “What circumstances maximize the student’s full possibilities?”
By asking these questions, we are moving from the blame frame to exploration of potential for all kids. In her article “Deciding to Teach Them All,” Tomlinson (2003) outlines principles for fostering equity and excellence in academically diverse learners. I thought that this might be a quick reference for exploring ways to reach and teach all of our students now that we have the data about student performance for the first six weeks of school.
Good curriculum comes first. The teacher’s first job is always to ensure a coherent, important, inviting, and thoughtful curriculum. All tasks should respect each learner.
Every student deserves work that is focused on the essential knowledge, understanding, and skills targeted for the lesson. Every student should be required to think at a high level and should find his or her work interesting and powerful.
When in doubt, teach up! Good instruction stretches learners. The best tasks are those that students find a little too difficult to complete comfortably. Be sure there’s a support system in place to facilitate the student’s success at a level that he or she doubted was attainable.
Use flexible grouping. Find ways and time for the class to work as a whole, for students to demonstrate competence alone, and for students to work with varied groups of peers. Using only one or two types of groups causes students to see themselves and one another in more limited ways, keeps the teacher from “auditioning” students in varied contexts, and limits potentially rich exchanges in the classroom.
Become an assessment junkie. Everything that a student says and does is a potential source of assessment data. Assessment should be an ongoing process, conducted in flexible but distinct stages, and it should maximize opportunities for each student to open the widest possible window on his or her learning.
Grade to reflect growth. The most we can ask of any person—and the least we ought to ask—is to be and become their best. The teacher’s job is to guide and support the learner in this endeavor. Grading should, in part, reflect a learner’s growth.
References
Tomlinson, C. A. (2003). Deciding to teach them all. Educational Leadership, 61(2), 611.
Formative Assessment and Benchmark Testing
As I continue to meet with teachers regarding results of benchmark testing, I am reminded that sometimes we just need to take time to reflect on why we do what we do. As a school and a district, we are challenged to decrease the achievement gap between white students and students of color by 25%. Research shows that high quality formative assessment does have a powerful impact on student learning. Black and Wiliam (1998) report that studies of formative assessment show an effect size on standardized tests of between 0.4 and 0.7, an effect larger than most known educational interventions. Effect size is a measure of the impact of an intervention or strategy on student outcomes.
.
.
.
Data from formative assessment/benchmark tests provide us with a better understanding of gaps between learning goals and students’ current knowledge. The feedback you provide to students following a formative assessment/benchmark test helps them become aware of their specific learning gaps. The clear and specific feedback you provide guides students through actions necessary to achieve the learning goal (Ramaprasad, 1983; Sadler, 1989).
The most helpful type of feedback on tests and homework provides specific comments about errors and specific suggestions for improvement (BangertDrowns, Kulick, & Morgan, 1991; Elawar & Corno, 1985). When we encourage students to focus their attention thoughtfully on the task rather than on simply getting the right answer, we move them toward mastery learning, not just performance on a particular assessment on a specific date.
.
.
.
Specific feedback is particularly helpful to lower achieving students because it emphasizes that students can improve as a result of effort. Formative assessment helps support the expectation that all students can learn at high levels and counteracts the cycle in which students attribute their poor performance to lack of ability (Ames, 1992; Vispoel & Austin, 1995). When students become discouraged, they are unwilling to invest in further learning; formative assessment coupled with specific feedback provides a second chance for students to relearn and master previously taught concepts.
.
.
.
.
Admittedly, feedback generally originates from a teacher. However, some of you are allowing students to play an important role in the formative assessment process through selfevaluation. Two experimental research studies have shown that students who understand the learning objectives and assessment criteria and have opportunities to reflect on their work demonstrate greater improvement than those who do not (Fontana & Fernandes, 1994; Frederikson & White, 1997). Furthermore, students with learning disabilities who are taught to use selfmonitoring strategies related to their understanding of reading and writing tasks also show performance gains (McCurdy & Shapiro, 1992; Sawyer, Graham, & Harris, 1992).
.
.
.
During our last session on The Power of Formative Assessment, I found it interesting that our students struggle with selfassessment, as evidenced by the posting regarding using Stoplight strategy. When students indicated that they positively knew the answer to a specific question and coded it green only to discover that they were wrong, we must reevaluate why students harbor these misconceptions. This posting tells us that we must teach our students how to selfassess and guide them through that process as a procedure promote mastery learning.
As we continue to learn about formative assessment, whether through our benchmarks or our daily assessments, our goal is to make necessary adjustments in our instructional practices to improve student achievement.
References
Ames, C. (1992). Classrooms: Goals, structures, and student motivation. Journal of Educational Psychology, 84 (3): 261271.
BangertDrowns, R.L., Kulick, J.A., and Morgan, M.T. (1991). The instructional effect of feedback in testlike events. Review of Educational Research, 61 (2): 213238.
Black, P. and Wiliam, D. (1998b). Inside the black box: Raising standards through classroom assessment. Phi Delta Kappan, 80 (2): 139148. (Available online: http://www.pdkintl.org/kappan/kbla9810.htm.)
Elawar, M.C., and Corno, L. (1985). A factorial experiment in teachers’ written feedback on student homework: Changing teacher behaviour a little rather than a lot. Journal of Educational Psychology, 77 (2): 162173.
Fontana, D., and Fernandes, M. (1994). Improvements in mathematics performance as a consequence of selfassessment in Portuguese primary school pupils. British Journal of Educational Psychology, 64 (3): 407417.
Frederiksen, J.R., and White, B.J. (1997). Reflective assessment of students’ research within an inquirybased middle school science curriculum. Paper presented at the annual meeting of the American Educational Research Association, Chicago, IL.
McCurdy, B.L., and Shapiro, E.S. (1992). A comparison of teacher monitoring, peer monitoring, and selfmonitoring with curriculumbased measurement in reading among students with learning disabilities. Journal of Special Education, 26 (2): 162180.
Ramaprasad, A. (1983). On the definition of feedback. Behavioral Science, 28 (1): 413.
Sadler, D.R. (1989). Formative assessment and the design of instructional systems. Instructional Science, 18 (2): 119144.
The concept of formative assessment. Boston, Carol. (n.d.). Retrieved October 18, 2009, from http://pareonline.net/getvn.asp?v=8&n=9
The Value of Formative Assessment  FairTest. (n.d.). Retrieved October 18, 2009, from http://www.fairtest.org/valueformativeassessmentpdf
Vispoel, W.P., and Austin, J.R. (1995). Success and failure in junior high school: A critical incident approach to understanding students’ attributional beliefs. American Educational Research Journal, 32 (2): 377412.
Pacing and Summarization
As you continue to explore ways in which you can help students process and retain content, it is important to examine your professional practice in terms of pacing. As you know, pacing involves the speed with which you move through chunks of information. If you are lecturing for more than fifteen minutes at a time before asking the students to summarize, the brain reaches its saturation point, and mastery learning does not occur. We must ask our students to summarize en route to mastery.
As a professional, you determine when to use summarization strategies — at the beginning, the middle, or the end of a lesson. Whether a student is asked to read a passage from a text, watch a video clip, participate in a debate, create artwork, or participate in a review game, summarization techniques will enable you to help students improve both their comprehension and retention of lesson concepts.
321 is an example of a summarization strategy that you can use to adjust your pacing. This technique is versatile and relatively quick. You can use it for any situation in oral, artistic, or written forms. For the written version, ask your students to write the numerals 3, 2, and 1 down the left side of a half sheet of paper. Then post or announce prompts for each number, asking the students to write three of something, two of something, and one of something.
For example, you might ask students to write:
3 — things that they learned from the lesson
2 — areas that they are still confused
1 — way they might apply what they learned to another area
The specific prompts will vary with the lesson content and your instructional goals, but you may want to think about making the “one item” task more challenging than the “three item” task.
More Examples:
3: Identify three characteristics of Renaissance art that are different from those of art in the Middle Ages.
2: List two important scientific debates that occurred during the Renaissance.
1: Provide one good reason that “rebirth” is an appropriate term to describe the Renaissance.
3: List three applications of slope, yintercept knowledge in the professional world.
2: Identify two skills that someone must have to determine slope and yintercept from a set of points on a plane.
1: If (x¹, y1¹) are the coordinates of a point W in a plane, and (x², and y²) are the coordinates of a different point Y, then the slope of WY is what?
3: Identify at least three differences between acids and bases.
2: List two uses of acids and two uses of bases.
1: State one reason knowledge of acids and bases is important to citizens in our community.
The 3, 2, 1 strategy can also be expressed artistically or verbally. For those versions, follow the same sequence but change the medium by which students express themselves. Consider allowing your students to choose their mode of expression to summarize lesson content.
If you have used this strategy or made modifications to this strategy, please feel free to share your experiences.
Check out this link for more summarizing strategies.
References
Wormeli, R. (2004). Summarization In Any Subject: 50 Techniques To Improve Student Learning. Alexandria, VA: Association For Supervision & Curriculum Development.