## Archive for the ‘Math’ Category

### Exploring Integration in Elementary Curriculum, Part 2

Friday, November 2nd, 2012

### Author:  LoriReemts – Education Specialist: Elementary Generalist

Part 1 of this series focused on laying the foundation and seeking common language when referring to integration. There are as many ways to connect and integrate ideas as there are ideas themselves.  By defining differences between Curriculum Integration, which can be found described on documents and the like, and Instructional Integration, which can be artfully woven into the course of learning over time, we are able to identify what we can control and how that influences student success in our classroom. This series focuses on these choices: Instructional Integration.

As promised, this installment continues the conversation and begins the process of identifying key points of intersection within the curriculum by exploring two key ideas: Direct Connection and Purposeful Awareness.

There are times when different subject areas align with one another through TEKS that are directly linked. Meaningful links may be found in a direct relationship between two concepts, such as money in Math with the economics in Social Studies.  A direct connection might also be found within the language or concept of the Student Expectations themselves. Consider the 3rd Grade standards below.

Science

Earth and Space. The student knows that Earth consists of natural resources and its surface is constantly changing.  The student is expected to:

3.7b       investigate rapid changes in the Earth’s surface such as volcanic eruptions, earthquakes, and landslides

3.7c        identify and compare different landforms, including mountains, hills, valleys, and plains

Social Studies

Geography. The student understands how humans adapt to variations in the physical environment.   The student is expected to:

3.4c        describe the effects of physical processes such as volcanoes, hurricanes, and earthquakes in shaping the landscape

3.4a        describe and explain variations in the physical environment, including climate, landforms, natural resources, and natural hazards

Direct (Explicit) Support

As a third grade teacher looking at any one content area it may be easy to miss. However, a third grade teacher looking across content areas should be able to identify two direct connections within the above sets of TEKS.  In third grade, students investigate rapid changes to the Earth’s surface (Science) and the effects these changes have (Social Studies).  These do not need to be separate and isolated ideas, nor should they be.  Looking at the other pair of standards listed, another direct connection between studying landforms in Science and landforms in Social Studies is easily identified.  These are connections found no further than the TEKS themselves and points of intersection that teachers can use not only to save themselves the time spent in isolated planning, but also to make authentic and meaningful content  connections in a way that benefits all learners.

Purposeful Awareness

While not as overtly apparent as Direct Support, the use of Purposeful Awareness is key in applying knowledge and skills to new and novel situations.  These transferrable skills are the very things we seek to build in our students so that they continue to grow and learn throughout their lives while being productive and contributing citizens in the process.  Furthermore, it is precisely this type of thinking that STAAR requires as well.  This type of thinking is more difficult to “teach”, as it must be consistently modeled and practiced using a myriad of examples and scenarios. The beauty of employing Purposeful Awareness lies in the world of possibilities and potential connections that exist within students’ minds. There is no reason that the teacher need be the expert in the room as the goal is to expand student thinking beyond what may be easily apparent or written on a worksheet.  Purposeful Awareness may often come through the use of vocabulary in new contexts to strengthen the comprehension of the language.  Other areas such as big ideas, (i.e. human impact, conservation), relationships, and skills also provide breeding ground for cross-content connections.  Consider the following vocabulary words as examples.

Interdependence

– A standard concept and vocabulary term in Science, this term can apply in other contexts with very little change to the working definition.  To understand the concept is to be able to apply it to new and novel situations.

– Language Arts:  interdependent characters, parts of speech, cause/effect relationships

– Social Studies: global economics, countries, opposing sides of conflict, money

– Math: sides of an equation, factors/multiples

Consumer

– Basic definition in science: an animal that cannot produce its own food and eats plants and other animals (as opposed to a producer–which makes its own food)

– Basic definition in Social Studies: A consumer is a person who buys and uses goods and services. A producer is a person who makes goods or provides services.

– “to consume”

There are obvious differences when applying these example concepts in different content areas but the core meaning remains the same.  It is the context which changes. Too often we label concepts as “terms” to be used in a particular class or within a particular scheduled part of the day.  Although we have the best of vocabulary intentions, we may inadvertently silo language in such a way that students are not readily and easily applying concepts across areas. A student identifying a word as a “science word” may easily not be able to transfer the actual comprehension of that word/concept when viewing it in a new context.  Whether units occur during the same grading period or not, using Purposeful Awareness keeps these connections alive, albeit in smaller chunks than stand-alone units.  When working in the social studies context of “consumer,” for example, we need to purposefully connect back (or forward) and point out the similarity to other areas.

Well-placed questions and quick tie-ins are another way to utilize Purposeful Awareness. Consider the following example. As a teacher you may be introducing the accomplishments and contributions of various citizens in Social Studies. This is actually a standard in all levels of Social Studies. One such person may be Robert Fulton, credited with inventing the first operational steamboat. This invention opened the waters of the Mississippi, which in turn had great impact on the U.S. economy and growth of the day.  During instruction, the teacher may ask questions such as those that follow.

• What type of landform is the Mississippi River? River
• Is it salt or fresh water? Fresh
• What landform is created when it meets the ocean? Delta
• What Earth processes are at play and shape the earth? Weathering, erosion, deposition

The kinds of questions enable the student to concentrate on the Social Studies message at hand, while simultaneously connecting it with concepts from science. This is done in a low-intrusive manner requiring nothing more than planned questions to tie things together. Often the best approach to these connections is simply to plan to ask the students how things may connect to one another.  Something as basic as “How does this ______ in our current unit connect with _______, our previous unit?” can be very effective in forcing students to think beyond what is in front of them and to remember previous concepts in the process.  There is always a connection to be made.

This process takes time. A solid knowledge of the TEKS, or a consistent referral to them, remains, as always, the starting point.  While everyone has the ability to see connections, some people may seem to see them more quickly or more easily.  While we desperately seek these points of intersection, it seems we have somehow trained ourselves not to.  Of the two techniques listed here, begin with seeking Direct Support within the standards themselves.  From there, be comfortable opening your mind to what may be less obvious.  The more this is practiced the easier it becomes.  Don’t be afraid to bring your students into this thinking journey with you. It can actually be quite fun when taken together!

The next installment will focus on the area of skill building.  All of the core content areas, health and technology standards include similar skills.  When we view these as a whole, in addition to the student and the learning day, we are able to better capitalize on the intent of the standards while fostering deep and critical thinking for ourselves and our students.

### Understanding the Geometry STAAR EOC

Friday, August 24th, 2012

### Author: Emily Gray, Secondary Math Specialist

As we enter our second year of STAAR EOC exams, many of our mathematics students and teachers will be faced with the challenge of an End-of-Course exam in Geometry.  While the Algebra exams are relatively easy to understand (nearly all of the Algebra I TEKS have been tested before, and none of the Algebra II TEKS have ever been tested), the transition from the assessed Geometry TEKS on TAKS to the Geometry STAAR EOC is not so easy to understand.  Let’s look at a few facts to help illustrate this transition.

FACT: The Exit Level TAKS test has some Geometry questions on it.  The graphic below illustrates the percent of questions on the Exit Level TAKS that come from Grade 8, Algebra I, and Geometry TEKS.

The intention of the Exit Level TAKS test was to be a comprehensive exam over a broad range of topics.  The STAAR EOC exams, on the other hand, are designed to target the material from only one year of content in much greater depth.

FACT: The Exit Level TAKS test did not cover all of the Geometry TEKS.

As you can see above, the Exit Level TAKS tested 51% of the Student Expectations (SEs) outlined in the Geometry TEKS, while on the STAAR EOC for Geometry 97% of the SEs will be eligible for testing.

FACT: On Exit Level TAKS, all SEs were created equal.  This usually translated to every SE eligible for testing being tested once, or occasionally twice.  This is not the case on any of the STAAR exams.  For STAAR, standards are designated as Readiness or Supporting.  For Geometry, 12 standards are deemed Readiness standards and will comprise 60-65% of the test (or 31-34 questions).  It seems likely then, that these standards will be assessed two, three, or even four times.  The remaining 24 Student Expectations eligible for testing will comprise 18-21 of the test questions.  Clearly, some of these standards will not be tested in a given year (although they may reappear the next year).

FACT: Knowing is half the battle!  You’ve taken the right first step by reading this article!  Want to know more?  Visit Region XIII’s STAAR Website (http://www.esc13.net/staar/) or TEA’s STAAR Website (http://www.tea.state.tx.us/student.assessment/staar/) to get even more information.  Want more that’s Geometry-specific?  Start by taking the FREE one-hour online course through Region XIII titled “Geometry STAAR EOC – I Can’t Believe They’re Testing the Whole Thing”.   To register for this course, go to http://ecampus.esc13.net , login or sign-up for an account, and search for Workshop # FA1224480.  Click “Register” at the bottom of the page to get started!

### Exploring Integration in Elementary Curriculum, Part 1

Friday, August 24th, 2012

### Author:  LoriReemts, Elementary Generalist

There is a place where the learning process, fueled by pure motivation, engages everyone in the room and authentically integrates critical thinking with content concepts. This place operates beyond barriers, perceived or otherwise, and capitalizes on the efficient and effective use of talent and time.

Although this may sound unattainable to some, the reality is that this place can often be found within our own instructional choices.   Of course we, as professionals, operate within larger systems and, of course, these systems each have their own issues, but when it comes right down to it the largest influencer and indicator of student success is the classroom teacher. (Stronge,  2010)  While respect should be given to the realities of life and teaching in today’s world, it is imperative to acknowledge and appreciate that educators do not have a simple or easy task;  it benefits no one to dwell on daily challenges when our energies could better be spent upon enacting change in our own classrooms.  Educators everywhere collectively cry out for the path and the simple answer to integration.  The goal of this series is to focus on this desire and suggestions for steps toward accomplishing this as we journey to this place we so covet.

In this first installment, it may be an excellent time to try to define “integration” so that our conversations center on similar ideas and starting points.  Believe it or not there are many variations in how we use this word which are quite dependent upon the person using the term and in what context.  Obvious historical examples exist referring to actual student integration during the Civil Rights movement, but in this context we are referring to skills and concepts addressed  in our classrooms.  The term itself has been thrown around for a number of years and has recently regained momentum; unfortunately for some, it has become a symbolic “buzz word” without substance.

Humphreys (1981) offers a basic definition: “An integrated study is one which children broadly explore knowledge in various subjects related to certain aspects of their environment.”  That is a wonderful academic definition of integration but let’s get to the practicality of the concept. Curriculum itself is the relationship between three main components: the written curriculum, the taught curriculum, and the tested curriculum.   Ideally this triad operates in balance and responds to each of the other sections.  The written curriculum would be that which we find on our documents. Components such as scope and sequence, vertical alignment, and unit guides exist to help teachers identify and define the “what,” the student expectations.  While important, this written curriculum exists and is effective only when brought to life through the taught curriculum, or instruction. This speaks to the art of teaching. These are the two areas with which to begin the conversation.  As written curriculum is built from the state standards, it is dependent upon those standards. Content area standards do change and not at the same time.  Aligning and integrating them within a written curriculum, therefore, takes time and may be at a slower pace than the call for it would like it to be.  One must know and understand the separate content areas’ requirements in order to accomplish the task of integrating them effectively.  This is not to say it cannot be done, but the reality is that written curriculum, as dynamic and living a document as it may be, is not equipped to change on a daily basis when classroom teachers must make instructional choices and connections, nor could it and remain credible and consistent.  What, then, is a teacher to do?

We turn to instructional integration.  This is where educators can capitalize on the information a written curriculum provides to them by seeking commonalities.  Learning does not occur on a bell schedule or subject shift during the day. Children and adults alike learn throughout the course of experiences rather than isolated skills or facts.  By embracing this continuous learning idea, even when operating on a much-needed school schedule, we can build transferrable skills in a more effective manner rather than feeling the need to “close out” Subject 1 in order to begin Subject 2.  These same real-life skills can be found within every content area as can almost endless content/concept connections. The key to locating these areas lies in working toward a core and solid understanding of what the most recent and required student expectations actually communicate.

Our next conversation will continue with this idea and explore how to use the required state standards and other information found within our written curriculum in order to effectively utilize and maximize the integration potential.

Humphreys, Alan, Thomas Post, and Arthur Ellis. Interdisciplinary Methods, A Thematic Approach. Santa Monica:

Goodyear, 1981.

Stronge, James. Effective Teachers = Student Achievement: What the Research Says. Larchmont: Eye on Education, 2010.

### Math with Mary!

Friday, August 24th, 2012

### Author: Mary Headley – Elementary Math Specialist

The introduction of new math concepts can be described using three stages:

I. Concrete (the “doing” stage) – This stage involves both teacher and student modeling.

II. Pictorial (the “seeing” stage) – This stage transitions the concrete model into a representational level such as  drawing pictures or using dots or tallies, etc.

III. Abstract (the “symbolic” stage) – This stage uses numbers and mathematical symbols.

Using concrete models is the first step in building the meaning behind mathematical concepts.  These models include a variety of math manipulatives, measuring tools, and other objects that students can handle during a lesson. Research-based studies show that students who use concrete materials develop more precise and more comprehensive mental representations, often show more motivation and on-task behavior, understand mathematical ideas and better apply these ideas to life situations.  (Harrison & Harrison, 1986; Suydam & Higgins, 1977)

Pictorial representations help teachers provide the perfect bridge between concrete representations and abstract algorithms. Pictorial representations include drawings, diagrams, charts and graphs that are drawn by the student or provided for the students to read and interpret. Pictured relationships show visual representations of the concrete manipulatives and help students visualize the mathematical operations. It is imperative that teachers explain how the pictorial examples relate to the concrete examples.

“Up the Hill” Manipulatives stmichaelschool.us

Connecting the dots between the concrete, pictorial, and abstract is the glue that cements the learning for students. This connection provides the understanding that students need to demonstrate a problem or operation using symbolic representations such as numbers. The meaning of symbols and numbers must be rooted in experiences with real objects (concrete) and pictorial representations. Otherwise the symbolic operations (abstract) become rote repetitions of memorized procedures with no understanding.

The gradual movement from concrete to pictorial to abstract benefits all students and helps to prevent the frustration that some students feel when instructed only with abstract processes and procedures.

Perhaps this article has caused you to think about exploring multiple ways to teach math.  Would you like to observe and experience the conceptual development of content? Do you want to give students multiple strategies for success? Would it help you to see how manipulatives can be used to build the meaning behind math concepts?

If the answer to these questions is yes, you may be interested in Math with Mary, an online resource tool that offers professional learning modules designed to build teacher content knowledge and teacher confidence with the use of manipulatives. These modules are hosted by Mary Headley, Education Specialist for K-5 Mathematics at Education Service Center Region XIII, and will walk participants through the use of a specific manipulative which will allow students to explore and develop a variety of math concepts. Using the strategies presented, students will be able to visualize the math while engaging in strategies that build conceptual understanding.

The first course module, Math with Mary: Multiplication with Base Ten Blocks (FA1224478), is appropriate for grades 3-6 and is currently available on E-Campus. This course lays the foundation for understanding multiplication of 2 digit numbers and beyond. Student expectations related to Number and Operations emphasize the use of concrete models and visual representation of numbers and operations. The Multiplication with Base Ten Blocks course supports student expectations outlined in the TEKS and will help teachers build the bridge between concrete models, pictorial representations and the abstract multiplication algorithm. (2 hours CE credit)

Sources

Harrison , M., & Harrison, B., “Developing Numeration Concepts and Skills,”  Arithmetic Teacher 33 (1986): 1–21.

Suydam, M. N.; & J. L. Higgins,  Activity-based Learning in Elementary School Mathematics: Recommendations from Research. Columbus, OH: ERIC Center for Science, Mathematics, and Environmental Education, 1977.

### TEKS Referenced / TEKS Based Resource Calibration

Monday, February 13th, 2012

There is so much “stuff” here …what do I use?

I don’t seem to have any “stuff” to use…what do I buy?

Money to spend this year?  Budgets to create for next year?

These are but a few questions heard in meetings, hallways, teacher lounges and the like.  Sometimes the sheer volume of materials to wade through is overwhelming while other times it may feel as if there just isn’t any resource to be found.  This may differ from content to content and even differ from unit to unit within any given content.  If you have ever felt as though you are simply racing against time and the system itself to “fit it all in” or as though you are spinning your wheels because students seem to “have it” only to just as easily have “lost it” over any given time frame, perhaps simplifying the instructional decision process by simply targeting the intent of the TEKS will help.  Admittedly this is far easier said than done, but wouldn’t we all love it if at the end of day we had a base of solid “go to” resources absent of ambiguity and rich with potential?  As the practice becomes second-nature, arguably an art form, we are able to focus our time and energy on each of our students with confidence that we are covering appropriate content and at the appropriate cognitive levels for our students.

Certainly we can launch an in-depth study of works by Robert Marzano, Mike Schmoker, and others noteworthy in their field…but really?  Do we all have that kind of time?  Although their work on defining Standards-based vs. Standards-referenced education serves as wonderful appetizers to full blown educational debate, when push comes to shove we are in our classrooms with our students each day and we make countless instructional decisions fueled solely by the intent to help and serve our children in their journey.  Part of the beauty of teaching is keeping hold of an eclectic set of items and resources because you just never know when or if you can use it again. Part of the danger of teaching is keeping hold of an eclectic set of items and resources and pulling from this comfort zone regardless of assignment or how many years have passed.  Admit it: there is a purple mimeograph copy somewhere in your files.   It may even be entitled something very similar to something you currently teach.  Does that make it the best instructional choice?

Consider this:  TEKS based vs. TEKS Referenced Materials.  Has a ring to it, doesn’t it?  If we focus on TEKS based materials in our original or main instruction we are then able to support and supplement with TEKS referenced and additional TEKS based items.  After all, we teach children, not subjects.

TEKS based:  resources tightly aligned with the content and cognitive level of the standards

•  Example: A lesson addressing Science TEKS student expectation 2.7c focuses on distinguishing natural vs. manmade resources; combine this with Scientific Investigation and Reasoning TEKS student expectation 2.2d where students record and organize this information using pictures, numbers, and words within their science notebooks (TEKS 2.4a).

TEKS referenced:  resources loosely aligned with the direct standards but support the overall understanding of the concept; they may be considered “in the same ball park.”

• Example:  In addition to reading non-fiction text on natural vs. manmade resources, a guided                         reading group explores a fictional leveled-reader short story in which the characters choose resources to gather and build a class project.

We would not rely on the TEKS referenced story to address the TEKS directly or to support student experiential learning, but we would choose this title to help support and solidify the idea of choosing and using resources which in turn helps the overall conceptual learning related to the standards.

One final word of caution:  sometimes less is more.  Let’s suppose that you begin your elementary unit on life cycles and you have come across a poster that you believe includes your grade level’s standards.   All six of the elementary grade levels contain TEKS related to life cycles.  For argument’s sake we will take the role of a 4th grade teacher covering 4.10c: explore, illustrate, and compare life cycles in living organisms such as butterflies, beetles, radishes, or lima beans.  Does the poster below support this student expectation in the TEKS?

image found, February 2012 at http://www.biographixmedia.com/index.html

One could argue that the basic information is indeed found within this poster (content).  Of course just having a poster doesn’t elicit the required cognitive level of the standard and that would have to be incorporated into the lesson itself, but take another look at the content.  Sometimes resources are lacking content but other times, as in this case, they contain too much content and the original intent is lost for many students.  The extraneous information can easily muddy the water for many students.

What is the moral of our story? When considering resources, whether to utilize for TEKS based instruction or to purchase for future use, one must consider three questions:

1. Does the content align to the TEKS?

• (Consider: TEKS based or TEKS referenced. This impacts how you would use the resource.)

2. Is the student cognitive level at the depth and complexity required in the TEKS?

• (Consider: Are there means to combine a content student expectation in the TEKS with a process skill or other skills-based TEKS to increase the rigor?)

3.  If the answer to Question 1 and/or Question 2 is no, then you must ask if a small adjustment or tweak (resource calibration) could be made relatively easily to calibrate the resource to the standards.

• No?  Then it is time to “retire” or share this resource with another grade level or course, if appropriate.  By the end of the unit, you will have streamlined your toolkit and saved time in the long run.

Remember, we all have favored lessons, resources, and vendors.  Companies and non-profits may even provide a correlation document aligning our state standards to their product.  For example, textbook publishers assign TEKS throughout the publication. As professional educators, there is no substitute for evaluating and calibrating resources before we use them.

Of course we know that things are much easier to say than to do in real time, but this practice can easily become second-nature and prove invaluable when designing lessons.  Want more information or practice evaluating and calibrating a variety of resource types?  Region XIII has offered several professional learning sessions doing just that; keep an eye on E-Campus, join the content list-servs, or request a visit from a specialist to learn more.

### Making Connections: Points of Instructional Integration and Skill Building

Monday, December 12th, 2011

Our goal as educators is that our students grow into productive citizens with a wealth of skills to draw from. We want to foster learning so that students are critical thinkers and problem solvers who are able to make connections and apply their learning in new and novel situations. The TEKS call for critical thinking, problem solving, and making connections. STAAR calls for critical thinking, problem solving, and making connections. Life calls for critical thinking, problem solving, and making connections.  This necessitates that our instruction include and build critical thinking, problem solving, and making opportunities for students to make connections.

In modern education, we are under more and more time constraints with fewer resources. We often feel we are trying to do it all and it seems there just is not enough time. It is easy at times  to become focused on the pure content within our grade level or subject matter, and forget that the skills we wish to build are transferrable skills that apply to all content and simply may look slightly different based upon the context.

As a result, we sometimes find ourselves and our lessons looking somewhat like a solved Rubik’s cube. Although within this particular game, getting all colors onto one side and isolated from the rest of the colors indicates you have “solved” the puzzle; in education this represents ideas, skills, and learning in isolation.

We want students to be able to operate within all of the colors and, in fact, NEED students to be able to operate in a more integrated fashion for STAAR and beyond.

Consider the term interdependence for a moment. What does it mean?

A dictionary definition would be “a relation between its members such that each is mutually dependent on the others.”  For students understanding content and their world, such a definition means nothing and holds little relevance. We learn about interdependence within Science. In fact, this is a key concept in science.  For example, the entire understanding of food chains relates to this idea among many others. Students may build an understanding of this vocabulary word within the Science context and examples, but can they apply it outside of these specifics?

•  What might “interdependence” look like within Language Arts?

Characters are often interdependent.

• What might “interdependence” look like within Social Studies?

Countries in time of war and peace are interdependent upon each other. Economic systems, global economics, are interdependent upon one another.

• What might “interdependence” look like within Math?

Concepts such as part/part/whole and balanced equations include ideas of dependence and interdependence.

Would it be better to build on the idea in its entirety with multiple examples in order to assure students can transfer and apply knowledge or would it be best to know this term simply through a dictionary definition, a specific example such as a food chain, or within a specific content? Even if the word is introduced as a new vocabulary term in science, we want and need students to have word study skills that might enable them to determine what this unfamiliar word means, especially within multiple contexts.

That is one specific example with the intention of planting the seed for making connections and continuing learning throughout the day rather than in isolated periods of time or content.

Aligning TEKS to TEKS, side by side can be a daunting process when one considers the number of standards Texas has and how little time there is within a given day.  However, there are a few manageable ideas to begin to take the first small step(s) toward integrated learning throughout the day.  By doing so educators are able to “shave” time off of discreet stand-alone lessons and students are able to see connections and apply their learning across content and contexts.  These processes have the potential to increase efficiency and effectiveness by capitalizing what already exists within the TEKS and conceptual connections.

Within lesson design, we must look for opportunities to make connections and build skills across content.

1. Look across content units within the same time period: big ideas/concepts.

Are there opportunities for direct and explicit support or purposeful awareness or both?  For example, in 3rd grade Science your landforms unit may be within the same time frame as the Social Studies unit on landforms.  This is direct explicit support.  Or perhaps you teach English in 7th grade and the Texas History class covers political change in Texas as a result of the Civil War.  Through resource choice, instruction can support purposeful awareness and support the overall connections and learning associated with the Texas political climate without actually directly teaching the Social Studies TEKS within the English classroom.

2. Focus on transferrable skills across content and context:  TEKS skills strands

Every content has a skills strand, or skills-based student expectations, embedded within the course TEKS.  These are the very skills needed to approach and access content in order to make connections and increase comprehension.  Focusing on the skills across the course of the day rather than “period to period,” regardless of the content, builds practice and repetition and therefore increases skill levels.  For example, if we consider the 3rd grade TEKS and the skills embedded, we can identify basic skill categories, including data collection, analysis, inferring, forming conclusions, and problem-solving.   Similar skills found within these and other categories can be found in Language Arts, Math, Science, Social Studies, Health, and Technology Applications.  Learning effective data collection across content areas allows the students to see the skill applied within different contexts and in new and novel situations, resulting in deeper and broader understanding.

In the end it is the student who ultimately benefits from this direct explicit support and purposeful awareness.  We know the brain is wired for making connections.  By asking where there are opportunities to make connections and build skills during the lesson design process, we make more efficient use of our time while increasing the overall effectiveness of our instruction.

### STEM: Top 10 Resources

Monday, December 12th, 2011

### Transformation 2013 T-STEM Center

http://www.transformation2013.org

Transformation 2013 T-STEM Center is a partnership between ESC Region XIII in Austin and ESC Region 20 in San Antonio. Transformation 2013 T-STEM Center serves central Texas and El Paso T-STEM Academies as well as other schools focusing on innovative Science, Technology, Engineering, and Math (STEM) instruction. The vision of Transformation 2013 is to provide the highest quality professional development, curriculum, and outreach programs emphasizing hands-on problem-based learning to create superior STEM scholars. Our “Top 10 STEM Resources” are cited below including a summary of each resource and a hyperlink to each full-text document.

1. Bybee, R. W. (2010, September). Advancing STEM Education: A 2020 Vision. The Technology and Engineering Teacher, 70(1), 30-35. http://curriculumreform.wikispaces.com/file/view/Advancing+STEM+Education.pdf

This document details the phases and goals of a decade-long STEM action plan to move STEM education beyond the slogan to make STEM literacy for all students a national priority. Initially, the purpose of STEM literacy must be clarified, and then the challenges to advancing STEM education must be addressed. Furthermore, the STEM curriculum will be advanced by presenting challenges or problems framed in life and work contexts involving STEM to engage students.

2. Fulton, K., & Britton, T. (2011, June). STEM Teachers in Professional Learning Communities: From Good Teachers to Great Teaching. Retrieved November 2, 2011, from National Commission on Teaching and America’s Future: http://www.nctaf.org/documents/NCTAFreportSTEMTeachersinPLCsFromGoodTeacherstoGreatTeaching.pdf

The research compiled in this executive summary is based on a National Science Foundation‐funded project: STEM Teachers in Professional Learning Communities: A Knowledge Synthesis. The NSF Knowledge Synthesis indicates that STEM learning teams have positive effects on STEM teachers and their teaching, and students of teachers participating in STEM professional learning communities achieve higher success in math.

3. Hill, C., Corbett, C., & St. Rose, A. (2010). Why so few? Women in Science, Technology, Engineering and Mathematics. Retrieved November 2, 2011, from American Association of University Women: http://www.aauw.org/learn/research/upload/whysofew.pdf

This study was conducted by the American Association of University Women (AAUW) on the underrepresentation of women in science, technology, engineering, and mathematics. The summary emphasizes practical ways that families, schools and communities can create an environment of encouragement that can overcome negative stereotypes about the capacity of women in these demanding fields.

4. ITEEA. (2003). Advancing Excellence in Technological Literacy: Student Assessment, Professional Development, and Program Standards. Retrieved November 2, 2011, from International Technology and Engineering Educators Association: http://www.iteaconnect.org/TAA/PDFs/AETL.pdf

As a companion document to the Standards for Technological Literacy listed below, this document provides a guideline for implementation of the standards in K-12 classrooms. It details important topics such as student assessment, professional development, and program enhancement, while leaving specific curricular decisions to teachers, schools, districts, and states.

5. ITEEA. (2007). Standards for Technological Literacy. Retrieved November 2, 2011, from International Technology and Engineering Educators Association http://www.iteaconnect.org/TAA/PDFs/xstnd.pdf

The content standards and related benchmarks indicate what all students need to know and be able to do to achieve technological literacy. The Standards for Technological Literacy provide the foundation upon which the study of technology is built.

6. Langdon, D., McKittrick, G., Beede, D., & Doms, M. (2011, July). STEM: Good Jobs Now and for the Future. Retrieved November 2, 2011, from Department of Commerce, Economics and Statistics Administration: http://www.esa.doc.gov/sites/default/files/reports/documents/stemfinalyjuly14_1.pdf

Growth in STEM jobs occurred three times as fast as growth in non-STEM jobs in the last ten years and as a result, U.S. businesses are expressing concerns with the availability of STEM workers. STEM occupations are projected to grow 17% between 2008 and 2018 compared to less than 10% growth for non-STEM occupations; therefore, STEM workers will play a significant role in future growth and stability of the United States.

7. Sanders, M. (2009, December/January). STEM, STEM Education, STEMmania. The Technology Teacher, 20-26. http://www.iteaconnect.org/Publications/AAAS/TTT%20STEM%20Article_1.pdf

The origin of STEM, the current status of how integrative STEM education is addressed for teachers and students, and the systematic changes that are needed to approach integrative STEM education are discussed. In a world where the STEM pipeline problem has been widely publicized, this article addresses the question “Why Integrative STEM Education?” rather than conventional STEM education to achieve technological literacy for all.

8. Texas High School Project. (2010, November 15). T-STEM Design Blueprint. Retrieved November 2, 2011, from THSP: http://www.thsp.org/assets/ee/uploads/pdf/TSTEM_design_blueprint_11-15-2010.pdf

Used by T-STEM academies, the T-STEM design blueprint, rubric, and glossary serve as a guideline for building and sustaining STEM schools. The blueprint addresses seven benchmarks: 1) mission driven leadership; 2) school culture and design; 3) student outreach, recruitment, and retention; 4) teacher selection, development and retention; 5) curriculum, instruction, and assessment; 6) strategic alliances; and 7) academy advancement and sustainability.

9. The President’s Council of Advisors on Science and Technology. (2010, September). Prepare and Inspire: K-12 Education in STEM for America’s Future. Retrieved November 2, 2011, from The White House: http://www.whitehouse.gov/sites/default/files/microsites/ostp/pcast-stemedreport.pdf

The recommendations in this report suggest five priorities that provide a roadmap for achieving our STEM vision: “(1) improve Federal coordination and leadership on STEM education; (2) support the state-led movement to ensure that the Nation adopts a common baseline for what students learn in STEM; (3) cultivate, recruit, and reward STEM teachers that prepare and inspire students; (4) create STEM-related experiences that excite and interest students of all backgrounds; and (5) support states and school districts in their efforts to transform schools into vibrant STEM learning environments.”

10. U.S. Department of Education, Office of Planning, Evaluation and Policy Development. (2010, March). ESEA Blueprint for Reform. Retrieved November 2, 2011, from United States Department of Education: http://www2.ed.gov/policy/elsec/leg/blueprint/blueprint.pdf

In providing students a complete world-class education and college and career readiness, we must strengthen STEM instruction and standards. The availability of grants will support the strengthening of state-wide STEM programs, and support districts in identifying effective instructional materials and improving teachers’ knowledge and skills in STEM instruction for all students.

Article by Karissa Poszywak
STEM Specialist
Transformation 2013 T-STEM Center at ESC Region XIII
Email: Karissa.poszywak@esc13.txed.net
Phone: 512-919-5139
Website: www.transformation2013.org

Special thanks to Joules Webb, STEM Specialist at ESC Region 20, for recommending these top ten resources.

### What Does Progress Monitoring Really Look Like?

Monday, December 12th, 2011

We are almost at the halfway point in the year and you have groups all over your classroom and so does everyone else in the school.  The questions start to echo off the walls: Is Mary in the right group?  Are they progressing fast enough to close the gap by the end of the year?  Am I doing this strategy correctly?  How do I group the students to get the most progress in the least amount of time?  Is this strategy working or not?

A critical key component to successful progress monitoring is setting reasonable goals.  We do not want to waste time implementing an ineffective strategy or taking data and then not using it to help guide our instruction.  If you have not set goals for your class as a whole and for individuals who are struggling, then you are going to have a very difficult time trying to get them where they need to be.  Consider the following analogy (Adapted from V. Lynch, C. McGuigan, and S. Shoemaker, “An Introduction to Systematic Instruction”).

Suppose you are taking a trip.  Contrast the difference between taking that trip having specified your destination and taking the trip with no special endpoint in mind.  For example, you leave Seattle this morning with a goal to reach Mexico City by nightfall three days hence, as opposed to merely leaving Seattle.  Without a specified destination and projected arrival time, you know neither in which direction to go nor how fast to travel; having established a goal, you know both these facts (head south and really hustle).  With this information you can judge whether the direction and the rate at which you are traveling will get you to your final destination on time.

If you have not set specific goals for the end of the year yet, it is not too late.  You need to meet with your colleagues/team and decide what the specific end of year goal is for each of your students.  Look back at your data and determine how many students have already met the goal, how many are close to reaching the goal already and how many students have a long way to go.  There are many research based standards for establishing performance goals using baseline data including DIBELS (http://dibles.uoregon.edu/), AIMSWeb (http://aimsweb.com/), and “Formative evaluation of academic progress: How much growth can we expect?”  School Psychology Review, 22, 27-48 (http://www.studentprogress.org/library/articles.asp).  You can also use normative peer data to establish a reference point for the initial goal for an individual. Not only is it critical to set a goal for your students but a key factor in determining success is teacher responsiveness to the data.  “Goal ambitiousness seems to positively affect student achievement.” (Fuchs, Fuchs, & Deno, 1985)  In other words, teachers and students who set their goals higher and continue to increase those goals progress at a more rapid rate than do peers who select lower performance goals and do not change them.  It is also crucial for teachers to follow specific rules for how to be responsive to the data instead of just collecting and graphing it.  Having clear and measurable goals allows teachers  to work as a team with other teachers and with the students.  There can be meaningful and concise communication with regard to how and what students need to improve, and whether they are indeed progressing.  Student progress will help keep the groups flexible as teachers adjust the groups according to student level of progress and program modification.

Let’s look at how to use goal setting, scores along the goal line, and program modification to make decisions about student progress.  If the student’s current level of performance is more than one-half of the peer norm, and if we had more than 30 weeks left in the school year, we would consider setting the goal at the current peer norm.  Since we do not have 30 weeks left in the year,  we need to reduce the goal to a level that we estimate to be attainable.  Initial goal setting may be done through estimation because it can be adjusted if the goal turns out to be unreasonable.   The main point here is to set a goal for every student so you know where you are headed.  Progress toward that goal is then represented on a student graph using a goal line.  When 4 consecutive scores exceed the goal line, raise the goal.  In contrast, when 4 consecutive scores fall below the goal line, modify the program.  Draw a vertical line on the graph to indicate where the program was modified and continue to graph the scores.  The new goal line will need to be parallel to (but lower than) the goal line beginning at the student’s present level of performance.  You may also adjust your groups at this time to regroup students who are progressing without modification and students who will all need an adjustment to the program.  Keep in mind that you will need to progress monitor the lowest 40% of your students more often than the others.  You will also need to monitor the programs in which more students are struggling more often than the programs in which most of the students are progressing along their goal line.

Program modification includes a myriad of options.  It is important to first look at the implementation integrity to make sure the program is being used in the way it was designed.  There are a number of implementation integrity checklists created by Alecia Rahn Blakeslee at http://www.aea11.k12.ia.us/idm.  Once you have determined the integrity of the intervention, you can start to look at ways to modify it in order to meet the needs of your students and your campus.  Deb Simmons has created a chart that displays alterable variables in programs. This chart is available at http://oregonreadingfirst.uoregon.edu/inst_swrm.html.  There are several other guidelines to consider when modifying any program.  Supplemental groups should optimally include no more than five or six students.  Intensive groups should optimally include no more than three or four students.  Put the most qualified staff with the neediest students.  Your campus may want to do a personnel resource inventory with ALL staff (general education, Title l and special education teachers, G/T, ELL specialists, paraprofessionals, trained volunteers) to see who has knowledge, skills and experience with the strategies you want to put in place.  Scheduling is another important factor.  Possibly have teachers teach core subjects at different times of the day or different periods so the support staff can schedule time in each classroom and students can access additional time in other classrooms.  You can list each teacher and support personnel’s schedule in 15 minute increments.  Any 15 minute section that they are not teaching core content is a possible intervention time.  This could be a way to provide the additional intervention time for the supplemental and intensive groups.

RtI implementation takes a commitment from all the staff and administrators.  Students will be successful if we use our time and resources effectively and efficiently.  At this point in the year teachers and the leadership team need to be looking at the goals for all students and their progress towards those goals.  It is critical to be responsive to the data that have been collected to modify the program after implementation fidelity has been established.  There are many resources to guide you through this process.  For more information please refer to the RtI Blueprint for Implementation- School Building Level at www.nasdse.org and the Progress Monitoring Leadership Team Content Module at www.rti4success.org.

### Formative Assessment in Mathematics

Wednesday, October 12th, 2011

“Formative assessment is an active and intentional learning process that partners the teacher and the students to continuously and systematically gather evidence of learning with the express goal of improving student achievement.” (Moss and Brookhart, 2009)

This definition implies three phases of formative assessment.  In order for the assessment to be intentional and systematic, there must be a planning phase.  Once planned, we move into the evidence-gathering phase, making sure that the methods used are active and produce clear indications of the level of student understanding.  Finally, the data must be used to provide feedback and adjust instruction in order to improve overall student achievement.

So how does this process of formative assessment work for a math teacher?  Let’s take a look at how formative assessment can be imbedded throughout your unit planning to maximize student success.

Planning

First, take a look at your topic, and ask yourself three questions:

• What are the essential understandings that students should take away from this lesson or unit?
• What are common misconceptions that will need to be addressed?
• What is the learning target for lesson or unit?

An example might be adding and subtracting fractions with unlike denominators.  Students need to understand the importance of writing fractions with a common denominator before adding or subtracting.  It is common for students to think that they would then just add the “tops” and add the “bottoms” in order to arrive at their answer.  A clear learning target for students (such as “I can add fractions with unlike denominators”) is critical for the formative assessment process.  Once you and your students have a clear understanding of the goal and the common missteps along the way, you can begin to plan the learning experiences and formative assessment checkpoints that will lead to this goal.

Evidence-Gathering

As the learning process proceeds, it quickly becomes time to gather evidence of student learning.  This evidence can be formal or informal, verbal or written, or linguistic or non-linguistic, but it must be planned for, gathered, and used.  In mathematics, there are generally two forms of knowledge that you may be formatively assessing: procedural and conceptual.  As you introduce the concept of a common denominator, it is important to gauge student understanding before you proceed.  Some ideas for formatively assessing conceptual mathematical knowledge may include:

• Hand signals, such as thumbs up/thumbs down, 1-2-3-4-5, etc…
• Timed writing in response to a question or prompt, perhaps including a sentence stem such as “I can’t add ½ and ¼ without finding a common denominator because ________.”
• Colored response items, such as red/yellow/green triangular prisms, blocks, cups, or plates
• Timed pair share, giving students a chance to explain the concept to a partner, and also listen to their partner’s explanation

Once students have some conceptual understanding, you will then spend time helping students understand the process of getting a common denominator and using these new fractions to add and subtract quantities.  This will create new opportunities for formative assessment.  For procedural knowledge, some methods to gather evidence of student learning may include:

• “What’s Wrong?” analysis of incorrect work to help students begin to identify common errors and misconceptions
• Response Cards, where students hold up their answer to either a multiple choice or free response question simultaneously, using colored paper, white boards, or perhaps an electronic response system
• Take and Pass, where one student begins the work and then passes the work to another student who does the next step, who then passes to another student, etc.  Could be done as a relay race as students become more proficient
• Scavenger Hunt (also called Around the Room or I have/Who has), a circular set of problems, where one answer leads to another question and the student ends where they began
• Side-by-Side Problems, in which two students work two columns of different problems that have the same result (For example, the answer to #1 on both columns might be 5, but the two problems are different.)

Notice that both the conceptual and procedural formative assessments provide quick, timely feedback to both you and the student about their level of understanding.

Once an evidence-gathering method has been selected and carried out, you are ready for the most important step – using this information to adjust instruction to improve student achievement.  If you discover some of your students are still struggling with the concept or procedure, some options for adjustment include:

• Small Group Instruction, so that re-teaching or enrichment can take place as needed
• Discussion of misconceptions, either with a small group or the whole class
• Clear, targeted feedback to students making common and consistent errors

Once an adjustment is made, the cycle continues.  Another round of evidence-gathering gives another chance to assess and adjust, as you and your students work toward developing student mastery and success!