Anticipation Guides

*Note: This post is a work in progress.

Students need to listen, speak, read, and write about mathematics as well as archive their learning process.  Teachers need windows into their students’ minds, to see their thinking. 

Using Numbers I have created Anticipation Guides for students to assess their own understandings of mathematics content (before and after learning experiences).  

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With the integration of apps such as Explain Everything or SeeSaw, learners can annotate their thinking with text, language, and images/sketches.  Through the process of design, delivery, and reflection, students and teachers will have the opportunity to access their current level of understanding in relation to the developmental progression of learning mathematics.  

The button below provides access to Elementary, Middle School, and High School appropriate templates.

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The buttons below provide access to grade-specific Anticipation Guides in iCloud.

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#NoOfficeDay

Inspired by Matt Arend’s No Office Day plan to devote about one day per month out of his office and into the classrooms with learners, I spent my first No Office Day today, the first day of school.

My Why

I choose to intentionally schedule time out of my office and onto campuses in order to connect (and re-connect) with educators and learners.  I choose to not lose touch with the daily responsibilities, challenges, and celebrations that come with being a teacher.  I choose to recognize the impacts that my daily decisions make on teaching and learning.  I choose to know why I serve children and adults in my district through my role as Math Director.

My Day

As liaison to Wilson Elementary, my day began there with the awesome opportunity to welcome parents and students to the campus on this, the first day of school!  I offered to take family photos and opened car doors before the school day began.

Then, I headed to Cottonwood Creek Elementary.  A fifth grade educator had reached out to me and invite me to his classroom the first week of school for a visit.  I wouldn’t miss it!  Invitations from educators like this take priority on my calendar.

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Then, I headed to Coppell High School for the very same reason – an invitation from an educator that I would not miss for the world.

I had the opportunity to read responses that Algebra II learners contributed to the prompt: What are the qualities that you look for in a teacher?  The most common response I noted: kindness.  This will come full circle later in the day.

The next two stops were Wilson (again) and Cottonwood Creek (again) to deliver lunches to the campus administrators and counselors.  This wonderful tradition provides us one opportunity to show these campus leaders how much we appreciate them.

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Next, I headed to Richard J. Lee Elementary and did not make it past the media center where Blue House learners were exploring with Legos.  They invited me in and I had a lengthy conversation about how their day had gone (not great but wonderful!) and how much they love the Blue House!  This was a highlight of the day, for sure!

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My No Office Day ended back at Wilson with dismissal.  This is when I asked kindergartener after kindergartener about his/her day.  Every one of them mentioned how his/her teacher was nice, or kind, or smiled.  From 5 years old to 17 years old, that is what is important: kindness.  And, back to dismissal – Of course I would brave the Texas heat and sun to open car doors and wave parents through the car rider line.  I wish I could do more.

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I am looking forward to my next No Office Day and I am so very thankful for Matt Arend for opening my eyes to this valuable way to invest in my teachers and students.  I am not sure when or how often I will be able to spend a day in this way, but I know when I do, it will be worth every minute!

Building a Campus Mission

I was extended the opportunity to lead my liaison campus, Wilson Elementary, through a process to develop their campus Mission.  The voice of each staff member was welcomed and the outcome included a statement that captured their purpose, their why.

First, we focused the work on the existing Wilson Elementary Educator Creed.  This common language sets the tone for the campus by announcing the responsibilities, expectations, and motivation for the educators.  Those educators who were present at Wilson when the Creed was written shared stories of the development process as well as the impact it makes on their classrooms with the new hires.

I am a Wilson Ranger Educator.
I have great expectations for my learners and myself.
I accept the challenge to be the best I can be.
It is my responsibility to create a learning environment
conducive to optimum academic, social, and emotional growth.
I provide a model of decorum and respect
that guides my learners as well as honors them.
I cherish every learner.
I change the world one learner at a time.
I am a Wilson Ranger Educator.

Then, we used an Affinity Map to collect ideas to use to build the Mission.  The educators were given 3 minutes to brainstorm thoughts – one per sticky note.

Looking for common topics, the educators then collected ideas and grouped them with those at their table group.

As a whole campus, the educators gathered in groups, one representative per common theme, and wrote them on sentence strips.

The sentence strips were collected and organized with a pocket chart.  The Mission was arranged (and re-arranged) until it captured their fundamental purpose.

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Finally, the table groups indicated their support in a non-verbal way with plastic cups.  Green: We are good to go.  Red: We have a question or concern.

After some editing, the final Mission reads:

At Wilson Elementary, we provide a safe environment where each learner is loved, valued, and accepted.  We embrace and address the needs of the whole child, encourage academic, social and emotional growth, and develop character to the highest level.  We promote wonder and build a community of empowered, curious minds.  We inspire lifelong learners who positively impact the world.


This process was efficient and effective in developing the campus Mission.  I modeled classroom facilitation strategies and emphasized the necessity to use this Mission as a lens through which to consider all children.  I am looking forward to seeing this Mission in action at Wilson!

 

 

 

What Your Students are Thinking

How do you know that your students are thinking?  How do you know what EACH ONE of your students is thinking?  I encourage the valuable implementation of mathematical discourse communities to model problem solving, promote higher depth of knowledge and the necessity for justification of mathematical arguments, promote the use of accurate academic vocabulary coupled with growth of language for English Language Learners, allow students to build their confidence in mathematics, and provide opportunity to formatively assess students throughout.  This formative assessment is what your students are thinking.

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mathematical discourse community (MDC) includes productive mathematics discussions, centered around common problem situations in which the environment is safe enough for all students to contribute in multiple means.  MDCs are accessible for all learners, including those exhibiting gaps in prerequisite knowledge or academic vocabulary.

Though the benefits are great, building a mathematical discourse community in a classroom is a challenging feat for educators.  Quality should trump quantity and conceptual understanding is a goal worth seeking.

Lynn Liao Hodge and Ashley Walther describe 4 initial practices to build a foundation of productive discourse in mathematics classrooms in their article Building a Discourse Community: Initial Practices:

  • Use a more open task
  • Support think, pair, and revoice/compare
  • Offer three ways to participate
  • Define a contribution

In my work to design and support curriculum for PK-12 mathematics, I recognize the need for a balance between scalability and fidelity.  That is, what structures I put into place in my curriculum that can be utilized horizontally (throughout the school year) and vertically (throughout the courses) by educators, and in doing so, can be done well – accurately, efficiently, and effectively.  I choose to implement a few structures in order to support teachers to do them well.  3-Act Tasks, Notice and Wonder, and Which One Doesn’t Belong? are three such structures I work to embed in my curriculum.

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Hodge and Walther refer to open tasks as those with embedded student choice, multiple paths to solve, the necessity to justify solutions, all within a real-world scenario.  Related to this, I strive to embed inquiry-based learning experiences, in the structure of 3-Act Tasks.  I focus on 3-Act Tasks as a means for clarity, consistency, and opportunity for professional learning related to the implementation in the classroom.

When not deep within a 3-Act Task, it is important to continue to support the discourse community in the mathematics classroom.  I argue Notice and Wonder and Which One Doesn’t Belong? are two structures that continue this work to allow conversation, comparison and justification by students about mathematics concepts.

When teachers use the Notice and Wonder structure, it causes them to pause.  It also pushes the ownership of the knowledge to the students.  The conversation begins when a prompt of some sort is shared with the students.  This prompt may be an image, an object, a graph, a situation, or any other representation that leads to interpretation.  The simple question, “What do you notice?” is open enough to encourage contributions.   Based on the work of Hodge and Walther, it is advised to encourage participation by more than a single student through think, pair, revoice/compare.  I challenge you to avoid choral responses as a go-to with Notice and Wonder.  This excludes nearly all students in the room, allows students to hide behind their classmates, and narrows the scope of the conversation.  To move beyond verbal-only contributions, I challenge you to support sketches, gestures, and other non-spoken notices and wonderings.  Then, when the conversation lends itself to transition to the wonderings, the question, “What do you wonder?” is used.  Read more about Notice and Wonder here.

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When teachers use the Which One Doesn’t Belong (WODB) structure, it also causes them to pause.  Wait time is a valuable commodity in the mathematics classroom!  WODB also pushes the ownership of the knowledge to the students.  Similar to Notice and Wonder, a prompt is used, but this time it includes multiple items of some sort.  This prompt is usually a set of images, but does not have to be.  Any set of images, objects, graphs, situations, or other representations that lead to interpretation can be used for WODB.  The simple question, “Which one doesn’t belong?” is open enough to encourage contributions – with justification.   Seek participation by many students (ALL) through think, pair, revoice/compare.  I challenge you to avoid choral responses as a go-to with Which One Doesn’t Belong?.   Hodge and Walther say to offer three ways to participate.  What three ways will you support in your classroom?  What tools will you encourage your students to use to communicate about mathematics?  Sketches, gestures, and other non-spoken ways to identify and justify Which One Doesn’t Belong? builds the mathematical discourse community in your classroom.  Need a place to start with Which One Doesn’t Belong?  Try this or this.

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Focusing on the means to contribute, I encourage reflection on our English Language Proficiency Standards.  That is, opportunities for students to listen, speak, read, and write about mathematics during the learning process as well as while they are demonstrating their understanding.  These four modalities should not be seen as a checklist, because listening is not hearing, speaking is not repeating, reading is not looking, and writing is not copying.  I bring you back to the initial questions on this post:

How do you know that your students are thinking?

How do you know what EACH ONE of your students is thinking?

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Balanced Mathematics

As the leader of mathematics curriculum and instruction in my district, it is imperative that I clearly articulate the vision for teaching and learning mathematics and support it with a guaranteed, viable curriculum that includes practical, actionable items for the classroom.  As I work to complete a new curriculum rooted in the beliefs outlined in the Visioning Document and in response to the results of a recent, deficit model audit, I recognize the need for a succinct balanced mathematics plan.  This model of lesson design, instruction, assessment, and learner support will be evidenced throughout curriculum documents and professional learning opportunities for educators and campus administrators.  Successful implementation will include district-wide common understanding of the purpose and implementation of the balanced mathematics model.

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Within a balanced mathematics program, classroom structure supports intentional, responsive lesson design and facilitation of learning experiences in order to guide all students to success in mathematics.  

The components of the CISD Balanced Mathematics Plan include:

  • Conceptual Understanding: Learners understand mathematical ideas, make connections to other topics, and are able to transfer thinking to new situations in order to solve problems. Conceptual understanding builds to procedural fluency.
  • Inquiry:  Formulated by educators and learners, compelling questions are developed and subsequently guide inquiries into concepts and problems related to specific learning outcomes. (Supporting English Language Learners: Inquiry)
  • Fluency:  Procedural fluency is demonstrated by students as they carry out procedures flexibly, accurately, efficiently, and appropriately.  Fluency in the mathematics classroom is built on a foundation of conceptual understanding, strategic reasoning, and problem solving.  Mental math and estimation are aspects of fluency developed within balanced mathematics. (link to NCTM position statement)
  • Discourse:  Mathematical Discourse Communities are fostered to support students to make and test conjectures, question, and extend concepts in a welcoming classroom environment with student-created norms aimed for conceptual understanding.  (Link to article, Supporting English Language Learners: Academic Talk)
  • Intervention & Acceleration: In order to respond to the academic needs of all learners, mathematics content is intentionally designed and delivered in small group instruction with progress monitoring toward specified goals. (Supporting English Language Learners: Student Ownership of Learning)
  • Evidence of Learning: Learners demonstrate conceptual understanding or skill development through multiple modalities.  This evidence is created for learners to track their own progress and for educators to formatively monitor learner progress throughout the content.  In addition, the accumulation of evidence of learning builds toward a learner’s portfolio in a summative manner.

Components of this Balanced Mathematics Plan are evidenced in curriculum documents.

  • Conceptual Understanding: Curricular resources are organized into the Concrete/Pictorial-Representational-Abstract learning continuum.  This sequence of instruction builds a thorough understanding of mathematical concepts as learners progress developmentally, building upon prerequisite knowledge and extending to subsequent ideas.  Conceptual understanding is built through low-floor, high ceiling learning experiences.  That is, the content is accessible to all learners, including those who may demonstrate gaps in procedural skills, as the problem may be solved accurately through less efficient methods.  These less efficient methods would be used by a learner who has not yet attained procedural fluency in that given process.  High ceiling tasks allow for extensions for learners ready to make connections deeper in the content or beyond the scope of the course.  These tasks do not limit thinking with one-step, simplified processes.
  • Inquiry: Whole group or small group learning experiences following the 3-Act Task format. (link to post by Dan Meyer, link to post by Mary Kemper) The structure of 3-Act Mathematical Tasks provide built-in opportunities for learners to build background knowledge, connect to prior learning experiences, access the mathematics without the barrier of language, and extend thinking, as appropriate.
  • Fluency: Station-based or other individual learning experiences intentionally designed and accessed by learners to reinforce or extend conceptual fluency within the zone of proximal development.  Learners archive evidence of work and are held accountable for their fluency growth.  Specific practice to attain fluency should be intentionally designed, based on the current level of understanding of the learner and the next developmentally appropriate goal.
  • Discourse: Prompts such as What do you notice? and What do you wonder? as well as Which one Doesn’t Belong? are used to promote academic discourse and specific talk moves such as I agree with ___ because ___ are used to promote accountable talk related to the concepts within the unit of study.  Structures such as Number Talks provide opportunities for mathematical discourse by all learners during a whole group or small group experience.
  • Intervention & Acceleration: All students set SMART goals related to concepts as appropriately aligned within the developmental progression of mathematics.  For those learners identified as At-Risk, this small group instruction as guided mathematics fits within the CISD Mathematics RtI Program.  For those learners not identified as At-Risk, setting goals, receiving guided mathematics instruction related to the goal, and monitoring progress toward the goal, supports growth as well toward acceleration.
  • Evidence of Learning: Learners create evidence of understanding as aligned to the CISD Mathematics Transfer Goals as they display, explain, justify, and communicate mathematical ideas and arguments using multiple representations, including symbols, diagrams, graphs, and language as appropriate with precise mathematical language.  Learners use technology, as appropriate, to demonstrate understanding using verbal and visual articulation with annotation apps (such as See Saw or Explain Everything).

The components of the CISD Balanced Mathematics Plan are implemented in a synchronous manner.  Inquiry-based experiences include opportunities for mathematical discourse and result in evidence of learning, for example.  A mutually exclusive mathematics plan would not maximize the potential to balance the intentional, responsive design and facilitation of learning experiences to guide all learners to success in mathematics.

 

3-Act Task: Counting Coins

This 3-Act Task involves skip counting by twos, fives, and tens in order to determine the value of a collection of coins.

Act One

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What did you notice?  What do you wonder?

What questions come to your mind?

What is a reasonable estimate?

Act Two

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What information do you need to know in order to answer the question?

Act Three

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What was the solution?

How does your solution compare to your estimate?

Three Acts Recording Sheet

Less is More: Interpretation of Graphs

Inspired by recent conversation through blogs and on Twitter, I have been exploring analysis of visual images by removing barriers.  The barriers to interpret graphs include the details of numbers and labels.  These specific details are what makes the graphs precise and impact the interpretation, so this gradual reveal allows learners to access the graph as a whole at the appropriate time, not all at once.  In addition, the numbers and labels are intentionally revealed so attention is focused on those as the discussion promotes.  The structure of notice and wonder supports learners to interpret the graphs without being confined by the details of the graph.  That is, by allowing learners to consider the graph first, the learners are allowed to construct meaning in anticipation of transfer to new and unique situations.

The order of gradual reveal includes: the graph of the data with trend lines (that does not show specific points), the graph of the data with specific points, then the graph of the data with labels, the data in the chart.

The example below is related to Stock Market data.   The concepts behind the Stock Market are abstract to young children.  By removing the details on the graph to allow them to focus without clutter makes the math accessible, even to abstract ideas.  This promotes inquiry and fosters the mathematical discourse community.  The meaning making in this structure is the value that cannot be overlooked.  Guiding learners to make connections and interpret representations and abstract images supports them as they look to transfer this understanding.

Step 1: Graph with Trend Lines

What do you notice?  What do you wonder?

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Step 2: Graph with Specific Points

What do you notice?  What do you wonder?

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Step 3: Graph with Labels

What do you notice?  What do you wonder?

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What do you notice?  What do you wonder?

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The barriers removed in this structure allow learners to access the mathematical content.  I continue to explore removing barriers in curriculum and instruction including:

  • removing the barrier of language
  • removing the barrier of disengagement
  • removing the barrier of limits
  • removing the barrier of time
  • removing the barrier of prerequisite knowledge

We must design for the margins.  For whom is the curriculum designed if not for all?

 

 

 

 

 

Why 3-Act Tasks are Powerful for English Language Learners

As I continue to study accessibility in education, specifically Universal Design for Learning, structure and strategies for supporting learners served through Special Education and Gifted and Talented Education, and our English Language Learner population, I have come to the (obvious) conclusion that curriculum development and design involves a complicated, intricate web of planning long before the first words are added to a blank canvas of direction for educators.  It comes down to scalability.  What format/structure/strategies should be embedded in the curriculum (that may be applied horizontally and vertically throughout) so that the resources are seen with clarity and may be supported through efficient and effective professional learning?

Before I can move forward, I need a plan.  This is a huge opportunity and I want to make the most of it.

Recently, my perspective on curriculum development and design has been impacted by a Ted Talk by Todd Rose and various articles and information related to Universal Design for Learning.

  • Todd Rose: The Myth of Average (TEDx): Mr. Rose shares the story of the U.S. Air Force design of the cockpit  for the average pilot and makes a connection to an education system’s design for an average student.  He challenges us to to wonder: Does there exist an average student?  If not, then if we design for the average student, we design for nobody.  We must recognize that students vary in each dimension and we must respond accordingly.  As Mr. Rose says – Ban the average. Design to the edges.
  • Universal Design for Learning: By planning from the beginning for curriculum to be accessible to as many learners as possible, the need to retro-fit lessons and materials are minimized.  (Hunt & Andreasen, 2011).

Enter: The 3-Act Task.

First, a little background on the format of 3-Act Tasks (more info here):

  • Act One: The learners are provided with an image, video, or other piece of information that introduces a conflict.  This conflict may be that the learners disagree with their classmates, or with themselves.  That is, what they see may be contrary to what they believe, mathematically.  Key: Use as little text as possible, because once you tell the learners something, you cannot untell them.
  • Act Two: The learners determine what tools are needed to resolve the conflict or problem.  They must either request these tools or develop these themselves.  Key: Provide as little as possible, because once you give the learners something, you cannot ungive them.
  • Act Three: The learners resolve the conflict.  This is when the solution is determined and compared to the initial idea for reasonableness.  A reflection occurs to foster metacognition and add to the learners’ toolboxes to use in future problem solving.

Now, for the connection to our English Language Learners:

According to Beyond Good Teaching: Advancing Mathematics Education for ELLsthere are five Guiding Principles for Teaching Mathematics to English Language Learners.  I argue the inquiry model of 3-Act Tasks in mathematics (done well) support these guiding principles.

1.  Challenging Mathematical Tasks

All learners, ELLs included, need to experience mathematical tasks at a high level of cognitive demand.  This article (link) articulates the four levels of Depth of Knowledge according to Norman Webb.  The levels are neither developmental (this means even our youngest learners can experience strategic and extended thinking) nor sequential (learners need not experience level 1 before tackling level 2, etc.).

One of my favorite 3-Act Tasks is Volcano.  Challenging, indeed!  There are multiple entry points to solve this problem.  That is, the learners may successfully solve the problem in various means – not only by using a single algorithm.  They may draw a picture, look for a pattern, make a table of data, or use abstract formulas to solve.  Because the task contradicts the obvious method of solving (2-dimensional measurement rather than 1-dimensional), I argue this is a level 3 DOK task.  And thus, engaging!

2.  Linguistically Sensitive Social Environment

Such a learning environment fosters extensive educator-supported interactions in all forms among the learners and the educator (this includes between the leaners themselves).  This atmosphere is safe, allowing for opportunities for learners to ask questions and seek knowledge related to language.  Careful attention is paid to providing a low-stress classroom.

During the Volcano task, the town name “Tarata” and the abbreviations for hour and minute should be clarified to avoid barriers that may occur.  Though the language of this task is very minimal, even the three aforementioned terms could cause a stressful environment for ELLs to manage and therefore may be unable to engage optimally in this learning experience.  The educator should kindly check in with ELLs and provide a safe environment for them to ask questions, either to other learners or to the educator.

3.  Support for Learning English While Learning Mathematics

A Mathematics Discourse Community (MDC) supports all learners’ communication about mathematics.  This includes reading, writing, speaking, listening – all about the mathematics of the task.  Mathematical discourse builds the language while learning the mathematics concepts.

Technology integration while experiencing the Volcano task provides an opportunity to capture the process of problem solving.  Using a voice recorder app such as Voice Record Pro allows learners (specifically ELLs) to capture the metacognition involved in the problem solving process.  Note taking apps such as Notes or Notability allow learners to capture images within notes and have an embedded microphone feature to include verbal reflection as well.  Once learners have engaged in the MDC and practiced articulating the mathematics of the task in a safe environment, they may use technology tools to capture their language.

4.  Mathematical Tools and Modeling as Resources

Within Act Two of the inquiry experience, learners recognize the necessity for specific tools to support the problem solving process.  These tools may include measurement tools, images, or diagrams as scaffolds for the task.

In the Volcano task, handouts include maps with city names and additional video footage of the situation.  Additional models may include recreations of volcanic eruptions (as concrete representations) and connections to concepts of area, distance, and other measures.  Educators and learners may create/reference anchor charts as tools as well.

5.  Cultural and Linguistic Differences as Intellectual Resources

As members of a learning community, the cultural and linguistic differences among the class are valuable resources, seen as a commodity to be used to collaboratively solve problems and feed into the MDC.

Related to the Volcano task, the MDC within the classroom should foster input from all learners, supporting the collective insight of the members.  Strategies such as a Socratic Seminar build learners’ discussion and listening skills and provide opportunities to contribute to the MDC.


3-Act Tasks are more than engaging, high quality math problems.  Their structure, with intentional implementation of MDCs and technology integration, supports the Guiding Principles for Teaching Mathematics to English Language Learners.  Done well, 3-Act Tasks support implementation of the English Language Proficiency Standards and open the doors of problem solving to all learners.  All Learners.

Then, those learners who have positively, successfully tackled inquiry experiences continue to build background knowledge and a positive perspective on mathematics learning.  And, we know the value of mindset.

 

Hunt, Jessica and Janet Andreasen. 2011. “Making the Most of Universal Design for Learning.” Mathematics Teaching in the Middle School. 17: 167-72.

Anticipation Guides

As I continue to study ways to move local and state mathematics teaching and learning forward, I am focused on accessibility (content and language) for all students.  This study has brought me to the English Language Proficiency Standards (ELPS) and Sheltered Instruction strategies.  Using these lenses as I continue to guide teachers and campus/district instructional leaders to transform their practices (with the Visioning Document as the North Star), I recognize the overlap is unavoidable: redefine practices with intentionally designed, responsive teaching practices and meet the needs of each learner – taking them from where they are to next steps in their learning journey.

This post is about one tool to support learners, especially English Language Learners: Anticipation Guides.

An Anticipation Guide is a comprehension tool used before a learning experience to activate learners’ prior knowledge.  It may also be used to link new learning to prior learning.

Anticipation Guides are intentionally created lists of questions or statements about a specific topic of study.  Students are provided the document in which to read and reflect in the form of a checklist. Typical checklists for Anticipation Guides are True/False and Agree/Disagree.

Numbers, by Apple, is a productivity app that allows you to create spreadsheets with templates, including a checklist.  Numbers supports collaboration (currently in Beta form) through iCloud, allows for integration with PC users, and is compatible with Microsoft Excel.

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In 4th Grade Mathematics, students study angles in a new way.  In this grade level, students measure angles with protractors and consider angles in triangles in order to classify the geometric shapes.  The Anticipation Guide example below, created using Numbers, includes this 4th Grade Mathematics content.  Notice the boxes in the Agree/Disagree columns provided for learners to respond to before and after the learning experience.

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Downloadable files linked below:

The images below show examples of before (left) and after (right) completion of the Anticipation Guide.  Notice the checklist selections made before the learning experience are not changed or erased as a result of new learning.  This provides the student and educator evidence of learning when comparing the selections with those made after the learning experience.

Example documents linked below:

Anticipation Guides are among Sheltered Instruction Strategies for English Language Learners as they may allow educators to intentionally build background and comprehensible input for students.