Happy Tuesday. Today I'm linking up with Stephanie from "Forever in 5th Grade" for this months peek into my Resource Room.  This month I have been helping with PARCC testing. It's also the time of year when I start reflecting back on the past 9 months and beginning thinking about next year.


I know for me this year, striking a balance between the art and science of teaching was not as balanced as I would have liked. I think I bent more towards the art and a little less than the science. Using data binders students kept track of their goals and data. This helped move them more than a year. These are a must for next year.
I have things I want to trash to like rotations. But I want to add more co-teaching and student driven embedded data collection--students collecting their own IEP data and taking more ownership of their growth.



If you have not tried Seesaw--I would.  I came across Seesaw and was impressed with the idea that it is student and time friendly. I only have my groups for about 30 minutes. This means I either need to do it when I have 2 minutes or they need to do the uploading and creating within that 30 minutes. I love the app options that can be uploaded into the platform. My hope is this is REALLY student friendly and will become a place students can create and show off their app-smashing.

Students are proficient in using Seesaw as part of their workflow and it has been a great and easy place for them to put their work to share, self-assess, and track their own progress. A must for next year. Seesaw makes data collection in Special Education and RTI easy to do. (Which we all need. Right?)

CHAMPS. A behavior management system I added this year. I love this as I set a visual expectation for each task like "Group Instruction" or "Test." Students are aware of what the expectations are before I start talking. A must keep!



I love putting things in pictures. Pictures move faster to the brain than words. This one has become our Problem Solving Rubric which shows not tells students what is needed to score a 3 on the rubric. Problem Solving is one skill I want students' to take back to the classroom. When I do rubrics I do them with each group's input. The picture helps remind them what it needs to look like. I need to add more like this--not sure for what but this needs to happen.


If you remember I had a couple of groups early in the year almost to grade level and started reading rotations with them. Well with 30 minutes, this was not successful. As they were 2nd and 3rd graders, they didn't have tons of independence to maintain work on their own part of this idea. I ended up moving them back to guided reading and changing their schedule to have them spend more time in the classroom. 

This year has been filled up ups and downs. Ideas I want to keep and ideas that need to be trashed. I need to find more ways to embed data collection of IEP goals and RTI needs. What do you want to trash? What do you want to keep? Share them.

Students, even the best ones, can become frustrated and demotivated when they feel like they’re struggling or not getting the recognition that other students are. Make sure that all students get a chance to play to their strengths and feel included and valued. It can make a world of difference in their motivation.

Some days motivating students feels like the only thing I get done and other days it works itself. What are you favorite ways to keep students motivated?

Number sense begins very early and must be a focus of primary math. This is the solid foundation in math that all kids need.

A sense of numbers is critical for primary students to develop math problem solving skills.
The National Council of Teachers of Mathematics increasingly calls for districts to give more attention to building this skill, and studies have found that number sense accounts for 66% of the variance in first grade math achievement.  The council have also addressed five critical areas that are characteristic of students who have good number sense:

• Number Meaning
• Relationships Between Numbers
• Number Magnitude
• Operations Involving Numbers
• Referents for Numbers/Quantities (referents are words or phrases that denote what something stands for)

WHAT IS NUMBER SENSE IN CHILDREN?

Having a sense of how numbers work is a very broad topic that covers all numerical thinking. At its core, it is making sense of math concepts and mathematical reasoning.

Operationally, it is counting skills, having number knowledge, using estimation, and the ability to use problem solving strategies.

Knowing the why of how numbers work is of utmost importance, and children should not be shown the how until they understand the "why."   Techniques such as using ten frames and using concrete models to show place value concepts are daily necessities for young children.

Inquiry-based approaches (such as math dice games) to teaching children mathematics should be utilized as primary teaching methods in the early grades.

This is not to say that explicit teaching of sense of numbers skills is not essential, especially for those students from low socio-economic status.  We absolutely need to do this.

It is saying that teachers should provide multiple opportunities for students to experience numbers and make connections before putting the pencil to paper.

Carefully consider your objectives and the type of learners in your room when choosing a math game to include. NCTM also suggests you consider:

• the type of mathematical practices involved in each game (there should be more than one)
• how feedback will be given
• does the game encourage competition, collaboration and communication?
• the types of strategies students will have to use to solve a puzzle or to win

Seven ways teachers can directly impact a developing sense of number.

1. Link school math to real-world experiences
Present students with situations that relate to both inside and outside classroom experiences. Students need to recognize that numbers are useful for solving problems.

2. Model different computing methods
Focus on what methods make sense for different situations. There is no one right way to compute. We need our students to be flexible thinkers.

3. Mental Math
Real life requires mental computation. Students need to be able to move numbers around in their heads and discuss their strategies.

4. Discuss Strategies
Students must be able to explain their reasoning. This not only will give you insight into how they think, but also will help the children to cement their own ideas and reevaluate them.

5. Estimate
This should be embedded in problem solving. This is not referring to textbook rounding. Real life estimation is about making sense of a problem and using anchor numbers to base reasoning on.

6. Question Students About Reasoning Strategies
All the time, not just when they make a mistake. Constantly probing sends several important messages: your ideas are valued, math is about reasoning, and there are always alternative ways to look at a problem.

7. Measuring Activities
When teaching children mathematics, measuring activities should be front and center. Make students verify estimates through doing.

You have your first teaching job, what did you think about? If you’re like most people, you thought about making a difference in children’s lives, about helping them learn, making them think, “touching the future.” You didn’t think about IEPs, disinterested parents, students with behavior problems, or the isolation of being alone in a classroom with thirty students.

You weren’t wrong before you started teaching. Hang onto that idealism. But you may be finding out now that making it a reality is harder than you thought. Hopefully, these ideas will out you out.  The first thing I always do before jumping in head first or tackling a difficult situation I always remember to breathe. A deep yoga breath.

Unfortunately, many of us in the education profession are guilty of exacerbating the difficulties faced by new teachers. Handbooks and websites for beginning teachers often try to reassure you that teaching is simple or straightforward, offering quick solutions for simple problems — if you have this kind of “troublemaker,” deal with him this way; try this handy checklist to “get organized.”

So now what?

Ask your team mate. They will help you find the resources, support, ideas, and advice you need to make your classroom the rewarding, positive learning environment you want it to be.

Keep this in mind

Teaching is hard.

Like anything worth doing, good teaching takes work and experience. You can’t expect to walk into a classroom for the first time and immediately connect with every student, make everything clear to everyone and teach every child everything he or she needs to know. What you can do, though, is learn from the experience of successful teachers. Ask questions. Visit others. Ask for help!

You can’t go it alone. (And you don’t have to.)

Are you feeling isolated? Lonely? Many teachers believe that they can — or should — go it alone in the classroom. But you can’t, and you don’t have to. Our resources will help you take advantage of mentoring, learn to communicate more effectively with parents, colleagues, and administrators, and build the support network you need to grow as a teacher (and survive as a human being).

Every classroom is different.

Just as every student is unique, every teacher is unique, too — and every class and classroom is unique. There are no “one size fits all” solutions in teaching, and we don’t try to provide them. Instead, these articles give you the perspectives of real teachers who have faced problems like yours and overcome them. You’ll see how different teachers have used their own talents and teaching styles to be successful in a variety of environments.

Classroom management means solving problems before they occur.

Running your classroom is about more than just discipline. Experienced teachers know that effective classroom management begins before you ever meet your students and carries through every aspect of teaching. It’s about preventing problems, not just cleaning them up after they occur. Instead of looking at student behavior in isolation, our resources for new teachers consider it in the context of classroom design, curriculum, and instructional strategies. It's never perfect and always changes depending on your students. Get to know your students.

Remember to breathe and ask questions. The Colorado Tribe is giving away five meet up bags and five subscriptions to planbook.com. There will be five winners! The photo shows you what's in the meet up bags! Wow!!

Have a great week!










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I think one of the more challenging parts of being a special education teacher, is finding time to talk (really talk) with classroom teachers. This year has only been made more difficult by have close to 40 students on my case load--that I see during a day.  I thinking sharing with teachers about their students are doing towards IEP goals is very important, it also gives me time to share with teachers specific ticks and tips that have worked since the last time I met with them.



 "Learning at the Primary Pond" has created a 1 page communication log for each student but I use it for all the students in the teachers class and put it in her box weekly. This way the teacher knows what kind for progress has been made toward IEP goals. This is also great to keeping everyone on the team in the loop with what the student is doing well and what they need to work on. Perfect
for progress report time or IEP writing time.




 Google is a girls best friend. Google is an over worked special education teachers best friend. The thing I like about google is that I can share my data with teachers before meeting with them. I have found that this makes our time together more focused and easier to create short term game plans. Edgalaxy has highlighted 12 different ways to use google to collaborate with teachers--my favorite being the forms which I can then turn in to graphs. I love my pictures at meetings-this does it for me.









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Today, I'm linking up with With Love from Texas for this blog hop on my teaching beliefs.

The funny thing about looking for a new position, is listening to others beliefs about their students, program, and building--it focused my own beliefs about the students I work with.

I believe in my students--they can do anything.  I think this is why  love doing student data folders. It is the singularly most important thing that I do with them each year. They take at SMART goal and create their goal and then charge for it. Are the goals always reasonable-no but the important fact is the ownership of their learning.

Others always find it weird to party of other little things like making a goal or finishing a book. These are the things that make my day.





I think one of the hardest things the do in small group is getting them to take risk. They now the other members and sharing is hard but setting up the group rules and not judging them for speaking up and sharing. They in turn get to the point where they understand it's OK to talk and share.



In sum way this Dr. Who quote tells all about my teaching.










Until next time,




Be sure to hop by Rissa's Teaching in the Heart of Florida to learn about her beliefs for her students.

Its funny to think about going Back to School. I'm hoping to have a new position in the school district that I grew up in. But everyone in Parker is getting ready to go back.



My room is in storage. Well everything I own is in storage. Last year I moved, got half way to buying a house and then lost my FTE, so everything is still in storage:(.  I keep all my students in binders--the IEPs, contact notes from parents, teachers, and outside therapists. I also create student data binders, so they can keep track of their own data. I have found it to be very powerful with motivation.

One thing that I do add to my student binders is specific materials that they are working on mastering that are tied directly to their IEP goals. One in particular students always struggle with is reading non-sense words without segmenting. I created it so students could go from segmenting to reading the whole word with each word on the ring. Plus, I love how I have been able to move students basic reading skills with this product.




For the first time last year I used GoogleDocs to create all my collaborating documents with classroom teachers. It was one less thing I had to keep track of and everyone could add information to. I kept SMART goals, progress monitoring notes, and who was taking care of what. No losing anything.

Because the size of my caseload, I put all IEP dates on my calendar--meeting, call parents about set up date and time, testing dates. Anything and everything that has to do with meeting compliance I have there for the whole year. Missing dates should NEVER happen. This is my may to make sure that it doesn't.
I drive my team mates crazy with how organized I happen to be. But I try very hard to leave school at school. My life is so much better when I don't bring it home-besides I anything I bring home says in my bag.

I put everything in binders both my students and my lesson plans. Plus, I do everything on everything online.




 What I wouldn't do for more time--there never is enough time to move students. I would wish that by the end of the year students find themselves and realize that they have a voice and they can use it!









I love my timer. I always use it. Be it for warm ups or for the whole group time. Its the only way I can find to stay on time  Teachers hate it when students come back late.

Yes, lesson planning take time. (I use planbook.com. I plan on my laptop and keep my iPad on my teaching table. I can print it out when asked to I need too. Its not free but for 12 dollars I can set it up to meet the needs of those in the groups.)I find that the more time I put into a lesson plan and really think it through from beginning to end the more bang for my buck I get each day. I try to sketch out the whole week even if it changes I know where the group is going. Knowing the group or student scope and sequence and where they are headed each week is time well spent.

Since moving to a small district there are fewer questions from teachers when they are working with students who are learning English as a second language. Though it is a beginning, have students in a group or a classroom talking is important--it builds social language skills first but it also helps build academic language. (Academic language takes students longer to wrap their heads around.) I find these ideas a step. One that is important for all students.

Oral Language Acquisition and Learning to Read and Write?

How powerful is this relationship?

Implications

• A low-anxiety environment: This includes a setting where students feel nurtured and supported by their teacher and peers, and in turn, they feel safe to take risks without the fear of being laughed at or made fun of.
• Repeated practice: This is just like what it sounds! Students need repeated practice hearing and using a new language. They need multiple opportunities to comprehend and express their ideas in a new language. Like with anything new that we learn, practice helps us get better.
• Comprehensible input: This means finding different ways to make what is being said comprehensible and easier to understand. Things to consider with comprehensible input might include using speech that is appropriate for students' language proficiency, providing a clear, step-by-step explanation of tasks, and using a variety of techniques to support their understanding.
• Drama: This is a sense of excitement and engagement, can be found in activities like Reader's Theater, dramatic play, puppetry, narrating wordless picture books, etc. All of these activities also have the other three factors embedded within them. These activities assist in the development of oral language in addition to introducing students to oral reading and rich literacy experiences and responses in a classroom setting.

Connections to ESL Students

Stage	The Student	The Teacher
Preproduction	Minimal comprehension. Does not verbalize. Nods "Yes" and "No." Draws and points.	Show me … Circle the … Where is …? Who has …?
Early Production	Limited comprehension One/two-word responses. Uses key words/familiar phrases. Uses present-tense verbs.	Yes/no questions Either/or questions Who …? What …? How many …?
Speech Emergence	Has good comprehension. Can produce simple sentences. Grammar/pronunciation errors. Misunderstands jokes	Why …? How …? Explain
Intermediate Fluency	Has excellent comprehension. Makes few grammatical errors.	What would happen if …? Why do you think …? Questions requiring more than a sentence response
Advanced Fluency	The student has a near-native level of speech	Decide if … Retell …

Concrete - Representational - Abstract:  Sequence of Instruction

The purpose of teaching through a concrete-to-representational-to-abstract sequence of instruction is to ensure students truly have a thorough understanding of the math concepts/skills they are learning. When students who have math learning problems are allowed to first develop a concrete understanding of the math concept/skill, then they are much more likely to perform that math skill and truly understand math concepts at the abstract level.

What is it?

• Each math concept/skill is first modeled with concrete materials (e.g. chips, unifix cubes, base ten blocks, beans and bean sticks, pattern blocks).
• Students are provided many opportunities to practice and demonstrate mastery using concrete materials
• The math concept/skill is next modeled at the representational (semi-concrete) level which involves drawing pictures that represent the concrete objects previously used (e.g. tallies, dots, circles, stamps that imprint pictures for counting)
• Students are provided many opportunities to practice and demonstrate mastery by drawing solutions
• The math concept/skill is finally modeled at the abstract level (using only numbers and mathematical symbols)
• Students are provided many opportunities to practice and demonstrate mastery at the abstract level before moving to a new math concept/skill.

As a teacher moves through a concrete-to-representational-to-abstract sequence of instruction, the abstract numbers and/or symbols should be used in conjunction with the concrete materials and representational drawings (promotes association of abstract symbols with concrete & representational understanding)

What are the critical elements of this strategy?

• Use appropriate concrete objects to teach particular math concept/skill (see Concrete Level of Understanding/Understanding Manipulatives-Examples of manipulatives by math concept area). Teach concrete understanding first.
• Use appropriate drawing techniques or appropriate picture representations of concrete objects (see Representational Level of Understanding/Examples of drawing solutions by math concept area). Teach representational understanding second.
• Use appropriate strategies for assisting students to move to the abstract level of understanding for a particular math concept/skill (see Abstract Level of Understanding/Potential barriers to abstract understanding for students who have learning problems and how to manage these barriers).

How do I implement the strategy?

When initially teaching a math concept/skill, describe & model it using concrete objects (concrete level of understanding).

• Provide students many practice opportunities using concrete objects.
• When students demonstrate mastery of skill by using concrete objects, describe & model how to perform the skill by drawing or with pictures that represent concrete objects (representational level of understanding).
• Provide many practice opportunities where students draw their solutions or use pictures to problem-solve.
• When students demonstrate mastery drawing solutions, describe and model how to perform the skill using only numbers and math symbols (abstract level of understanding).
• Provide many opportunities for students to practice performing the skill using only numbers and symbols.

After students master performing the skill at the abstract level of understanding, ensure students maintain their skill level by providing periodic practice opportunities for the math skills.

How Does This Instructional Strategy Positively Impact Students Who Have Learning Problems?

• Helps passive learner to make meaningful connections
• Teaches conceptual understanding by connecting concrete understanding to abstract math process
• By linking learning experiences from concrete-to-representational-to-abstract levels of understanding, the teacher provides a graduated framework for students to make meaningful connections.
• Blends conceptual and procedural understanding in structured way

Concrete

What is it?

The concrete level of understanding is the most basic level of mathematical understanding. It is also the most crucial level for developing conceptual understanding of math concepts/skills. Concrete learning occurs when students have ample opportunities to manipulate concrete objects to problem-solve. For students who have math learning problems, explicit teacher modeling of the use of specific concrete objects to solve specific math problems is needed.

Understanding manipulatives (concrete objects)

To use math manipulatives effectively, it is important that you understand several basic characteristics of different types of math manipulatives and how these specific characteristics impact students who have learning problems. As you read about the different types of manipulatives, click on the numbers beside each description to view pictures of these different types of manipulatives.

General types of math manipulatives:

Discrete - those materials that can be counted (e.g. cookies, children, counting blocks, toy cars, etc.).

Continuous - materials that are not used for counting but are used for measurement (e.g. ruler, measuring cup, weight scale, trundle wheel). See example - 1
Suggestions for using Discrete & Continuous materials with students who have learning problems:

Students who have learning problems need to have abundant experiences using discrete materials before they will benefit from the use of continuous materials. This is because discrete materials have defining characteristics that students can easily discriminate through sight and touch. As students master an understanding of specific readiness concepts for specific measurement concepts/skills through the use of discrete materials (e.g. counting skills), then continuous materials can be used.

Types of manipulatives used to teach the Base-10 System/place-value (Smith, 1997):

Proportional - show relationships by size (e.g. ten counting blocks grouped together is ten times the size of one counting block; a beanstick with ten beans glued to a popsicle stick is ten times bigger than one bean).

Non-linked proportional - single units are independent of each other, but can be "bundled together (e.g. popsicle sticks can be "bundled together in groups of 'tens' with rubber bands; individual unifix cubes can be attached in rows of ten unifix cubes each).

Linked proportional - comes in single units as well as "already bundled" tens units, hundreds units, & thousands units (e.g. base ten cubes/blocks; beans & beansticks).

Non-proportional - use units where size is not indicative of value while other characteristics indicate value (e.g. money, where one dime is worth ten times the value of one penny; poker chips where color indicates value of chip; an abacus where location of the row indicates value). A specified number of units representing one value are exchanged for one unit of greater value (e.g. ten pennies for one dime; ten white poker chips for one blue poker chip, ten beads in the first row of an abacus for one bead in the second row). See example - 1
Suggestions for using proportional and non-proportional manipulatives with students who have learning problems:

Students who have learning problems are more likely to learn place value when using proportional manipulatives because differences between ones units, tens units, & hundreds units are easy to see and feel. Due to the very nature of non-proportional manipulatives, students who have learning problems have more difficulty seeing and feeling the differences in unit values.

Examples of manipulatives (concrete objects)

Suggested manipulatives are listed according to math concept/skill area. Descriptions of manipulatives are provided as appropriate. A brief description of how each set of manipulatives may be used to teach the math concept/skill is provided at the bottom of the list for each math concept area. Picture examples of some of the manipulatives for each math concept area can be accessed by clicking on the numbers found underneath the title of each math concept area. This is not meant to be an exhaustive list, but this list does include a variety of common manipulatives. The list includes examples of "teacher-made" manipulatives as well "commercially-made" ones.

Counting/Basic Addition & Subtraction Pictures

Colored chips
Beans
Unifix cubes
Golf tees
Skittles or other candy pieces
Packaging popcorn
Popsicle sticks/tongue depressors

Description of use: Students can use these concrete materials to count, to add, and to subtract. Students can count by pointing to objects and counting aloud. Students can add by counting objects, putting them in one group and then counting the total. Students can subtract by removing objects from a group and then counting how many are left.

Place Value Pictures

Base 10 cubes/blocks
Beans and bean sticks
Popsicle sticks & rubber bands for bundling
Unifix cubes (individual cubes can be combined to represent "tens")
Place value mat (a piece of tag board or other surface that has columns representing the "ones," "tens," and "hundreds" place values)

Description of use: Students are first taught to represent 1-9 objects in the "ones" column. They are then taught to represent "10" by trading in ten single counting objects for one object that contains the ten counting objects on it (e.g. ten separate beans are traded in for one "beanstick" - a popsicle stick with ten beans glued on one side. Students then begin representing different values 1-99. At this point, students repeat the same trading process for "hundreds."

Multiplication/Division Pictures

Containers & counting objects (paper dessert plates & beans, paper or plastic cups and candy pieces, playing cards & chips, cutout tag board circles & golf tees, etc.). Containers represent the "groups" and counting objects represent the number of objects in each group. (e.g. 2 x 4 = 8: two containers with four counting objects on each container)
Counting objects arranged in arrays (arranged in rows and columns). Color-code the "outside" vertical column and horizontal row helps emphasize the multipliers
.
Positive & Negative Integers Pictures

Counting objects, one set light colored and one set dark colored (e.g. light & dark colored beans; yellow & blue counting chips; circles cut out of tag board with one side colored, etc.).

Description of use: Light colored objects represent positive integers and dark colored objects represent negative integers. When adding positive and negative integers, the student matches pairs of dark and light colored objects. The color and number of objects remaining represent the solution.

Fractions Pictures

Fraction pieces (circles, half-circles, quarter-circles, etc.)
Fraction strips (strips of tag board one foot in length and one inch wide, divided into wholes, ½'s, 1/3's, ¼'s, etc.
Fraction blocks or stacks. Blocks/cubes that represent fractional parts by proportion (e.g. a "1/2" block is twice the height as a "1/4" block).

Description of use: Teacher models how to compare fractional parts using one type of manipulative. Students then compare fractional parts. As students gain understanding of fractional parts and their relationships with a variety of manipulatives, teacher models and then students begin to add, subtract, multiply, and divide using fraction pieces.

Geometry Pictures

Geoboards (square platforms that have raised notches or rods that are formed in a array). Rubber bands or string can be used to form various shapes around the raised notches or rods.

Description of use: Concepts such as area and perimeter can be demonstrated by counting the number of notch or rod "units" inside the shape or around the perimeter of the shape.

Beginning Algebra Pictures

Containers (representing the variable of "unknown") and counting objects (representing integers) -e.g. paper dessert plates & beans, small clear plastic beverage cups 7 counting chips, playing cards & candy pieces, etc.
Description of use: The algebraic expression, "4x = 8," can be represented with four plates ("4x"). Eight beans can be distributed evenly among the four plates. The number of beans on one plate represent the solution ("x" = 2).

Suggestions for using manipulatives:

• Talk with your students about how manipulatives help to learn math.
• Set ground rules for using manipulatives.
• Develop a system for storing manipulatives.
• Allow time for your students to explore manipulatives before beginning instruction.
• Encourage students to learn names of the manipulatives they use.
• Provide students time to describe the manipulatives they use orally or in writing. Model this as appropriate.
• Introduce manipulatives to parents

Representational

What is it?

At the representational level of understanding, students learn to problem-solve by drawing pictures. The pictures students draw represent the concrete objects students manipulated when problem-solving at the concrete level. It is appropriate for students to begin drawing solutions to problems as soon as they demonstrate they have mastered a particular math concept/skill at the concrete level. While not all students need to draw solutions to problems before moving from a concrete level of understanding to an abstract level of understanding, students who have learning problems in particular typically need practice solving problems through drawing. When they learn to draw solutions, students are provided an intermediate step where they begin transferring their concrete understanding toward an abstract level of understanding. When students learn to draw solutions, they gain the ability to solve problems independently. Through multiple independent problem-solving practice opportunities, students gain confidence as they experience success. Multiple practice opportunities also assist students to begin to "internalize" the particular problem-solving process. Additionally, students' concrete understanding of the concept/skill is reinforced because of the similarity of their drawings to the manipulatives they used previously at the concrete level.

Drawing is not a "crutch" for students that they will use forever. It simply provides students an effective way to practice problem solving independently until they develop fluency at the abstract level.

Examples of drawing solutions by math concept level

The following drawing examples are categorized by the type of drawings ("Lines, Tallies, & Circles," or "Circles/Boxes"). In each category there are a variety of examples demonstrating how to use these drawings to solve different types of computation problems. Click on the numbers below to view these examples.

Abstract

What is it?

A student who problem-solves at the abstract level, does so without the use of concrete objects or without drawing pictures. Understanding math concepts and performing math skills at the abstract level requires students to do this with numbers and math symbols only. Abstract understanding is often referred to as, "doing math in your head." Completing math problems where math problems are written and students solve these problems using paper and pencil is a common example of abstract level problem solving.

Potential barriers to abstract understanding for students who have learning problems and how to manage these barriers

Students who are not successful solving problems at the abstract level may:

• Not understand the concept behind the skill

Suggestions:

Re-teach the concept/skill at the concrete level using appropriate concrete objects (see Concrete Level of Understanding).
Re-teach concept/skill at representational level and provide opportunities for student to practice concept/skill by drawing solutions (see Representational Level of Understanding).
Provide opportunities for students to use language to explain their solutions and how they got them (see instructional strategy Structured Language Experiences).

- Have difficulty with basic facts/memory problems

Suggestions:

• Regularly provide student with a variety of practice activities focusing on basic facts. Facilitate independent practice by encouraging students to draw solutions when needed (see the student practice strategies Instructional Games, Self-correcting Materials, Structured Cooperative Learning Groups, and Structured Peer Tutoring).
• Conduct regular one-minute timings and chart student performance. Set goals with student and frequently review chart with student to emphasize progress. Focus on particular fact families that are most problematic first, then slowly incorporate a variety of facts as the student demonstrates competence (see evaluation strategy Continuous Monitoring & Charting of Student Performance).
• Teach student regular patterns that occur throughout addition, subtraction, multiplication, & division facts (e.g. "doubles" in multiplication, 9's rule - add 10 & subtract one, etc.)
• Provide student a calculator or table when they are solving multiple-step problems.

Repeat procedural mistakes

Suggestions:

• Provide fewer #'s of problems per page.
• Provide fewer numbers of problems when assigning paper & pencil practice/homework.
• Provide ample space for student writing, cueing, & drawing.
• Provide problems that are already written on learning sheets rather than requiring students to copy problems from board or textbook.
• Provide structure: turn lined paper sideways to create straight columns; allow student to use dry-erase boards/lap chalkboards that allow mistakes to be wiped away cleanly; color cue symbols; for multi-step problems, draw color-cued lines that signal students where to write and what operation to use; provide boxes that represent where numerals should be placed; provide visual directional cues in a sample problem; provide a sample problem, completed step by step at top of learning sheet.
• Provide strategy cue cards that student can use to recall the correct procedure for solving problem.
• Provide a variety of practice activities that require modes of expression other than only writing

The Big Idea

Student learning & mastery greatly depends on the number of opportunities a student has to respond!! The more opportunities for successful practice that you provide (i.e. practice that doesn't negatively impact student learning characteristics), the more likely it is that your student will develop mastery of that skill.

It's funny as teachers we build culture in our classroom and it becomes "the way things are done." We hard to build it so that everyone soon becomes a family. We never give a second thought to what our School Building Culture is. We may think we know what it is such as warm and welcoming; everyone shares ideas; everyone has an open door. But is it really.? I think about School Culture the same way I do in my class.

I would like to offer here an approach to learning where the locus of classroom standards is centered neither in the teacher nor the individual student, but rather in a classroom culture, imbedded in a consonant school culture. This classroom culture contains the teacher and each individual student, the peer groups of students, but also transcends them: it is a framework which governs the learning and social interaction of all classroom members, and builds norms for a new peer culture.

Culture is a powerful concept. It goes deeper than what is spoken, deeper, even, than what is consciously understood Students in my classroom probably couldn't articulate exactly why they try so hard at their work and probably haven't even stopped to fully analyze it. Similarly, as members of a larger culture, we rarely stop to think about how many of our personal attitudes and actions are simply reflections of cultural norms. Culture defines how people function, and to some extent, even how they think. If a notion of high standards is not simply included in classroom culture but is actually at the core of this culture, then high standards become the norm.

This is all fine in the abstract, but a picture and understanding of how this culture looks in practice is needed. Painting this picture is, for me, a difficult task. A visit to my classroom in action, where I can often leave the room for twenty minutes and students don't even notice, as they are gripped in project work, would be much more compelling and persuasive than my words here could hope to be. Even this, however, would be inadequate, as it would fail to disclose how the environment was built, and what unspoken norms define its social structure.

Schools can sometimes take on the feel of a production shop, students cranking out an endless flow of final products without much personal investment or care. The emphasis is on keeping up with production, not falling behind in classwork or homework, rather than in producing something of lasting value. Like a fast food restaurant, the products are neither creative nor memorable. Teachers create and fuel this situation, despite the fact that we grow tired of repetitive, trivial assignments, and dread correcting piles of such work.

Turning in final drafts of work every day, often many times in one day, even the most ambitious of students must compromise standards continually simply to keep up with the pace. Internalized high standards are no defense against a system which demands final draft work at this rate. If an adult writer, scientist, historian, visual artist, was asked to turn in a finished piece of work every day, two or three finished pieces on some days, how much care could he or she put into each?

An alternative is a project-centered approach. In this structure, students still work hard every day, but their work is instead a small part of a long-range, significant project. Daily work entails the creation or revision of early drafts of a piece, the continued research of a topic or management of an experiment, or the perfection of one component of a large piece of work. Final drafts or presentations of completed projects are no longer trivial events occurring every day, but are special events, moments of individual and class pride and celebration.

Universal success does not mean uniformity. Though the structure which braces and guides student progress is common to every project, each student's project is unique. The structure provides a frame for common learning and critique, as well as appraisal of progress, but it also has room for significant creative expression and direction by individual students. If every student in a classroom prepares a guidebook to a different local building, the steps and skills involved may be somewhat prescribed: conducting interviews, researching local history, consulting city records, trying to obtain blueprints, doing sketches, taking photographs, preparing diagrams, writing and proofreading drafts of text, preparing illustrations, composing book layout, and learning book binding. Within this frame though, individual students have substantial latitude for artistic choices: the choice of building, the choice of whom to interview, the use of research and interviews, the nature of text and illustrations, the balance of text and illustrations, the use of photographs or diagrams, the tone of presentation, and the layout of the finished book.

My comments thus far may have raised a lot of questions. What about "untalented" students? Or teachers, for that matter. People who feel incompetent in particular academic or artistic areas. What about students with pronounced disabilities in perception, memory, or motor skills? If high standards are applied to the work of everyone, won't it just emphasize the painful weaknesses of some?
What about assessment? If so much of project work is creative and individualized, and even deadlines and requirements often differ from student to student, how can fair and constructive assessment take place?
What about a sense of community? If you work to dissolve the boundaries between school and outside life, don't you destroy the precious asylum of school which provides safety and security to children?
What about the cultivation of positive personal qualities in students: politeness, thoughtfulness, cooperation, initiative, self confidence, equanimity. Environments of "high standards" are often high-stress; a high standards classroom often means fighting for teacher recognition.

I'd like to say that I, and my school, have found the definitive answers to all these questions. Of course, we haven't. We are forever confused with trying to fashion a schoolwide assessment system which fits our teaching approach and documents student progress for the community or district in a real way. We are just now undertaking an effort to begin using student portfolios as archives of individual projects and achievement, as many schools have already done. And we are continually trying to restructure our school resources and community traditions to make the school more supportive for students with disabilities, insecurities, or other factors which make them "marginal".

Nevertheless, I think there is much going on in my classroom and school that addresses these questions in powerful ways. Despite having a full range of "academic abilities" in my students, and even students of real special needs, visitors to the classroom are often bemused and skeptical that this is a "regular" group of students. The work on display looks too impressive, the focus, cooperation, investment, and friendly ease of children too good to be true. The answer, I believe, is that students in my classroom are deeply and genuinely supported in countless ways to do their best and act their best, and have been so since Kindergarten. To a great extent, this is due to the ways in which the school culture deals with issues of assistance and assessment for students, and also for teachers.

People often say to me that this learning approach works in my classroom because I am a strong teacher, or works in the school because the school has strong teachers. In fact, they say, it's importance is trivial, because it can only work with strong teachers. Your school has strong teachers, but you don't know the teachers at my school. I would never contend that this approach is easy to use, nor that my colleagues are not full of talent.

First, it is suspiciously similar to that of teachers who visit my room and tell me: "Oh, but your kids are all bright (or artists, or interested, or well-behaved), you should see my kids. This would never work with my class." Now the kids in my class are no special group, but somehow they seem to shine. Is it because they're inherently strong , as the school's teachers are described, or is it because the structure and culture inspires them to do their best? Granted, children are more malleable and open than adults, particularly schoolteachers (we tend to be a defensive and protective bunch). I would argue, though, that the school culture where I teach inspires teachers to do their best (though this is an argument which might generate some laughter at times in my staff room). In addition to searching for strong teachers, school cultures can be building strong teachers. Perhaps more accurately, school cultures can inspire and reward teachers for displaying their strengths more fully, by taking risks, working together, and assuming substantially more decision-making power. I would guess that children too good to be true. The answer, I believe there are more "strong" teachers than people realize, teachers whose strengths are hidden by isolation, lack of power, and lack of inspiration. The talent and spark in these teachers can be fueled with the same approach used with students in the classroom. If teachers are expected and supported to design curriculum and projects, to take risks, be original, to work together in critique and learning, teachers can often blossom just as "weak" students do. I don't mean to trivialize the difficulty in effecting teacher change, but I think it's crucial to emphasize that standards for teaching are as much a product of school culture as standards for student learning: teachers, like students, tend to settle into surrounding expectations, standards and norms.

Second, on a classroom level, saying that this approach needs a strong teacher may be true, but it doesn't begin to reveal why the approach works. The power in the approach it is that it is based in a classroom community which shares a culture. The assessment, encouragement, accountability and teaching which goes on in the classroom is vastly wider than that which emanates from me, as teacher it is a continual and ubiquitous process among students. When I think of a particular student I had last year, a painfully shy girl who was new to town, I would be crazy to take credit for her astonishing emotional and academic growth-- I could hardly get her to speak to me during the year. I take credit only for managing a classroom where countless students took time to tutor her, support her, welcome her, and guide her success.

Again, where do student standards originate? Partly from me as the teacher, but very much from watching each other. Students did quality work, treated each other well, because that is what their friends did, it was the "cool" way to be, it was what the culture supported. How do students decide what is "good enough" as work, what is good enough behavior? Teacher standards only define the minimum standards allowed, they can't define the upper limit of care. Students in my classroom look to each other, help each other, critique each other's work, most of all, push each other to achieve their best. For all of my teacher power, the power in this total culture is infinitely greater.

The culture is rooted in a class community in which the first priority is supporting everyone. The responsibility for each person's emotional well-being and success is shared by everyone; the teacher bears more of this responsibility, but each student is encouraged and expected to help his or her peers. As a teacher, this means setting up a classroom structure which allows time and space for peer collaboration and tutoring; it means complimenting students, rather than complaining, when they abandon their own work at times to assist others. Supporting others means emotional support and care as much as it means academic support and care. In this team concept, the hope is that no student will be left out, left behind, allowed to fail or feel like a failure. It's everybody's job to look out for others.

For me, a culture of high standards means high standards for kindness and cooperation as much as for academic work. In the same way that careful quality in work is stressed over fast production, careful attention to treating all students fairly and thoughtfully is stressed over efficiency and speed in school logistics. "Simple" classroom decisions, such as which students should make a presentation or attend a limited event, often take a long time as they are discussed carefully with students to insure that all feelings are considered. Events and honors which are exclusionary or individualistic, displays of the "best" work or awards for the "best" students or athletes, are avoided in favor of whole-class, whole-school pride. When visitors to my classroom are impressed with student work, it is often due not to specific outstanding examples but rather to the absence of careless work, the uniform commitment to quality. This is a testament to the degree of cultural pride and peer support in the classroom.

 My teachers in elementary school often instructed us to try to do your best". This isn't a bad motto; I'd use it with my class today, and most schools would embrace it without a thought. There's a big step between teachers saying this to students, and students actually doing it. Not too many schools seriously look at what aspects of their structure and culture support and compel students to do their best, to act their best, and what aspects undermine this spirit. Rather than searching for individual teachers or principals who they hope can demand high standards, I feel that schools should be looking at how they can create a spirit of high standards, a school culture of high standards.

What's your building culture like? Have a great week! Say cool:)