Posts Tagged ‘Math’

Observing Best Practices in a Mathematics Classroom

Wednesday, May 18th, 2016

AUTHOR: Virginia Keasler, Secondary Math Specialist

Walking into a math classroom, an observer of the lesson may view many modes of instruction. The list may include:

  • Teacher shows students step by step problem solving and expects students to do problems in the way they are instructed
  • Students sitting quietly in rows
  • Students rotating around stations exploring challenging problems
  • Students are working on a problem together in groups, some individually, not necessarily doing exactly the same thing
  • Students engaged in critical thinking
  • A few students working at the board while others watch
  • Students who have completed their work and are waiting for the next problem
  • Teacher asking probing questions about the way students are attempting to answer questions

Generally you may see one or both of the two prevalent approaches to mathematics instruction. In the more traditional approach of instruction, skills-based, teachers may focus on how to solve the problem, show that problem solving strategy, and then require the students to quickly repeat that strategy. This method focuses on developing computational skills.

In concepts-based instruction, teachers have students solve a problem in a way that makes sense to them and then explain how they solved their problem. This method helps students be aware that there is more than one way to solve a problem.

You may be trying to decide what is the best way, but most researchers (e.g., Grouws, 2004) agree that both approaches are important, that teachers should strive for procedural fluency that is grounded in conceptual understanding.

There are three critical components to effective mathematics instruction (Shellard & Moyer, 2002):

  • Teaching for conceptual understanding
  • Developing procedural literacy
  • Promoting strategic competence through meaningful problem-solving investigations.

In an effective classroom an observer may see the teacher

  • Accepting students solutions to challenging problem which includes their explanation how they found their solution and the reason they chose to try their method.
  • Posing interesting questions to students to spur their interest in the problem.
  • Encouraging students to see that problems are challenging and that you sometimes have to search more than one method to find the answer.  
  • Instilling the belief that the goal of answering the question is attainable and worthwhile and can even be “cool”.  

In an effective classroom an observer may see the student

  • Solving the problem themselves and not just “mimicking” the procedure shown to them by others.
  • Challenging themselves to investigate a meaningful question.
  • Sharing their ideas with each other and as a group
  • Using various ways to show their work
  • Conducting an experiment by analysing data and coming to a conclusion
  • Are using calculators where appropriate
  • Using manipulatives to engage in problem solving to help form a concrete understanding of the concept where needed.

The National Center for Educational Achievement (NCEA, 2009) examined higher performing schools in five states (California, Florida, Massachusetts, Michigan, and Texas) and determined that in terms of instructional strategies, higher performing middle and high schools use mathematical instructional strategies that include classroom activities which:

  • Have a high level of student engagement
  • Demand higher-order thinking
  • Follow an inquiry-based model of instruction – including a combination of cooperative learning, direct instruction, labs or hands-on investigations, and manipulatives
  • Connect to students’ prior knowledge to make meaningful real-world applications
  • Integrate literacy activities into the courses – including content-based reading strategies and academic vocabulary development

Additionally, NCEA researchers found that it was important for teachers to create classrooms that foster an environment where students “feel safe trying to answer questions, make presentations, and do experiments, even if they make a mistake” (p. 24).

In summary, while both methods are important, teachers must reach students where they are and in the method that works best for each of their students.  While procedural learning is important to learn math facts and algorithms, students still need to be challenged, allowed to learn by exploring, and encouraged to keep trying knowing that math is meaningful and a huge part of the environment around us everyday.

References

The Education Alliance. (2006). Closing the Achievement Gap: Best Practices in Teaching Mathematics. Charleston, WV: The Education Alliance.

Grouws, D. (2004). “Chapter 7: Mathematics.” In Cawelti, G, ed., Handbook of Research on Improving Student Achievement. Arlington, VA: Educational Research Service.

National Center for Educational Achievement. (2009). Core Practices in Math and Science: An Investigation of Consistently Higher Performing Schools in Five States.  Austin, TX: National Center for Educational Achievement.

Shellard, E. & Moyer, P.S. (2002). What Principals Need to Know about Teaching Math. Alexandria, VA: National Association of Elementary School Principals and Education Research Service.

How to Create an Anchor Activity Using a Tic/Tac/Toe Board

Thursday, February 25th, 2016

AUTHOR: Virginia Keasler and Mary Headley, Math Specialists

How do we teach math to the wide range of diverse learners in today’s classroom? It is often difficult to match the readiness levels of every student and knowing where to start can be a challenge. Consider starting simple and celebrating successes along the way. Anchor activities can help you reach the diverse population in your classroom.

What are anchor activities? These activities are used for students to extend learning at their level. Student choice within these activities allows for students to apply and experience the learning in a variety of ways.These ongoing assignments are considered independent work and can be something students are working on for the next two weeks or something due in a few days. While some students are working on anchor activities, the teacher can utilize small group instruction to work with students who need more help.

Tic/Tac/Toe Boards: The content for this anchor activity can be modified to meet the needs of students at varied levels. Teachers may use Tic/Tac/Toe boards for extension, assessment, or as homework choices for the week. On a Tic/Tac/Toe board, the teacher can strategically place activities to enable students to get a Tic/Tac/Toe that demonstrates their learning.

Helpful Hints for creating a Tic/Tac/Toe board:

  1. Determine the content/topic for the board.
  2. Brainstorm activities, assignments, and products for the content/unit you have chosen.
  3. Check TEKS alignment.
  4. Write ideas on post-it notes.
  5. Sort activities based on learning styles (verbal, auditory, kinesthetic, etc…)
  6. Place post-it notes on the Tic/Tac/Toe grid.
  7. Check the configuration for variety to achieve a Tic/Tac/Toe. Move as needed.
  8. Type idea onto the Tic/Tac/Toe grid.

The following table gives an example of a Tic/Tac/Toe board for reviewing a math unit:

Explain the math steps that you would use to solve a problem from this unit Solve two of the problems in the “extensions” station Using the “beat” of a popular song create your own math song. See the choice board station for rules
Create two word problems that go with the concepts in this unit Student Choice Activity (with teacher approval) Define the unit’s vocabulary words with your own form of graffiti
Complete one mini-project from the project board Develop a game using skills you have learned in this unit Research and write how these concepts might be used in the real world

Variations:

  • Allow student to complete any three tasks–even if it does not make a Tic/Tac/Toe
  • Assigns students task based on readiness
  • Create different choice boards based on readiness (Struggling students work with options on one choice board while more advanced students have different options.)
  • Create choice board options based on learning styles or learning preferences. For example a choice board could include three kinesthetic tasks, three auditory tasks, three visual tasks.

Author Rick Wormeli offers the following Tic/Tac/Toe board based on Gardner’s (1991) multiple intelligences.

Interpersonal Task Kinesthetic Task Naturalist Task
Logical Task Student Choice Intrapersonal Task
Interpersonal Verbal Task Musical Task Verbal Task

To access a blank choice board to use in your classroom click on the following link: Blank Choice Board

Reference:

Wormeli, Rick. Fair Isn’t Always Equal: Assessing & Grading in the Differentiated Classroom. Portland, ME: Stenhourse 2006, pages 65-66

Mindsets and Math: Ideas for Helping Nurture Growth

Monday, December 7th, 2015

Author: Susan Hemphill, Education Specialist: Secondary Mathematics

Are you good at math? Do you believe you can learn math? These are central questions in ongoing research into how our beliefs shape our learning. Through getting to know what our students currently believe about how they learn and teaching them learning is a continuous process, we can help students understand that achievement in math is not a set ability but something that can be changed over time.

Dweck (2008) categorizes people into two groups: those with growth mindsets and those with fixed mindsets. People with a fixed mindset believe that you are only capable of a certain, set level of knowledge. Once one reaches this level, one can learn no more. If you find your students saying I’m not good at math and no one in my family is either, this may be a sign of a fixed mindset. People with a growth mindset believe that they can learn anything given time and effort. It is no surprise that students with a growth mindset are at an advantage.

So how do we nurture the growth mindset in the classroom?

A simple way to get started is to reflect on how you give your students positive feedback. Dweck recommends focusing on the processes students use in their learning. By focusing on strategies, efforts and choices, we promote the idea that learning is a path that is different for everyone. So while it might seem positive to say, “Wow! Excellent grade on that assignment,” rephrasing it as, “Nice work on that assignment. Your efforts show me you are learning new things every day!” would remind students the learning doesn’t have an end. Grades often provide unintended fixed mindset feedback. The 100% shows all is perfect and there are no mistakes and the student gets a boost in their beliefs about their abilities, but what about when something more challenging comes along? While perfect papers can be celebrated, think about what messages you are giving the students. What if you said, “It looks like I did not challenge you in your learning!” Similarly,,the student who earns a 60 receives feedback that can seemingly indicate that they aren’t able to learn the material that was graded. By getting kids to look at less than perfect work and inspecting their errors, you are encouraging students to understand this is not a final judgement on their abilities and they can still learn and grow.

Boaler (2015) has also researched learning math and mindsets and has found many strategies to help students succeed in math — even if they believe they can’t. Her Youcubed website shares various resources for teachers, parents and students. The website features ideas and information on getting kids to embrace the challenges in math. One of the videos of a classroom shows a poster that says, “Mistakes are expected, respected and inspected!” Boaler also suggests we adjust our classroom norms to promote the growth mindset to build a classroom community of math learners.

References

Boaler, J. (2015). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages, and innovative teaching. San Francisco, CA: Jossey-Bass & Pfeiffer Imprints.

Dweck, C. (2006). Mindset: The new psychology of success. New York: Random House.

Inspiring Students to Math Success and a Growth Mindset. (n.d.). Retrieved November 11, 2015, from https://www.youcubed.org

Place Markers: An Effective Reading Strategy Tool for Distracted Readers

Monday, December 7th, 2015

AUTHOR: Holly Salas, Instructional and Write for Texas Coach

Teaching children to read involves countless variables. However, strategies to teach comprehension, fluency, accuracy, etc., cannot be effective with students who are disengaged. Teachers regularly instruct students who are sleepy, ill, hungry, disinterested, or distracted. Often, a student’s distractibility is the result of a disability. Whatever the reason for distractibility, teachers must accommodate a student’s attention to instruction in order for quality reading development to occur. Teachers often have difficulty getting students to follow along while reading silently, as well as while listening to another reader. “The child’s difficulty in making left-to-right tracking movements while reading…disrupts sequencing of letters and syllables in words…and the inability to keep place also shows up when someone else is reading” resulting in reversal, rotations, inversions, omissions, substitutions, additions, etc. (“Visual-Spatial Dyslexia,” p.8 (n.d.)).

Teacher-monitoring for substantive comprehension breakdowns such as text inconsistencies, sentence scrambling, and misunderstanding with background information is difficult enough without the teacher’s ability to first monitor if the student is even attending to the text in the first place. For an already distracted student, the practice of interrupting reading for during reading strategies can further displace students from the meaning of text and impose a time-limit pressure that breaks down comprehension and enjoyment. “Heavy time pressure should not be imposed to individuals if they are to accurately complete important reading tasks” (Cauchard, Cane, & Weger, 2012). Metacognitive reading tasks are most effective when a student’s engagement with text is facilitated even while reading is stopped.

Before implementing other reading strategies, teachers need something that will help students focus. Only then will teachers be able to facilitate learning and assess ability. The place marker is a simple, minimal-preparation strategy with multiple implications that not only enables educators to modify and accommodate for students, and even assess the students’ task-compliance, but also provides opportunities for higher-level instructional strategies that scaffold students from decoding to comprehension to complex analyses. Although educators may purchase from a ubiquitous selection of marketed reading strategies and tools for engagement, the place marker requires no cost and almost no preparation. And because some students have difficulty transferring multiple reading strategies to settings outside of the classroom, establishing a procedure for the use of place markers allows for year-long instruction and may even facilitate independent reading for the student following graduation.

There is a seemingly limitless body of literature surrounding metacognitive monitoring, especially among distracted readers. From Mackey’s small-scale, easy-to-follow qualitative study (1991) that draws conclusions following Before, During, and After reading strategies, while accounting for context, content, and time; to Pan, Tsai, and Chu’s close look at fine motor skills within children with autism, children with ADHD (inattentive, predominantly hyperactive/ impulsive, and combined), and children without disabilities (2009), it is within a teacher’s own practice that she is best able to collect data for an isolated, a single reading strategy and its implications for large-scale conclusions.

Though conducted in the United Kingdom, the focus of Gillies and Robinson’s research on art-based strategies is particularly noteworthy (2012), because of its acknowledgment of the creativity within reading comprehension and beyond. Like the arts, reading and writing involve a human’s knowledge prior to the academic literary task, and that knowledge endures long after the academic setting, if not for the rest of the reader’s lifetime.

During a 2014 professional development research project at a Texas high school, teachers were asked to monitor the use of place markers as a during-reading strategy for a three-month period. Following data collection, teachers reported that 98% of students were less distracted than without the use of the place marker and that 98% of students transitioned more successfully back to reading after reading had been interrupted. The procedure:

  • enables distracted students to attend to the task.
  • creates student accountability.
  • facilitates before-, during-, and after-reading strategies.
  • enables students to self-monitor.
  • enables students to reflect on learning and evaluate progress.
  • enables the educator to monitor and track student compliance.

How it works:

  • Provide each student one place marker, three sticky notes, and an intentionally chunked or excerpted copy of a text, for multiple readings.
  • Instruct students to put a place marker under the title and read along until the teacher says, “Stop.”
  • Remind students that it’s important that the place marker follow along with the reader’s voice.
  • When all students have place markers ready, begin reading aloud the first chunk or excerpt of text.
  • After students complete the first section of text, say, “Stop. Leave your place marker where you stopped reading.”
  • Instruct students to write a brief summary or draw a picture of what was just read and give the summary or picture a one-word title or caption. Provide two minutes. Model and monitor.
  • Return to the text and read the next text excerpt. Say “Stop. Leave your place marker where you stopped reading.”
  • Continue through the end of the text, spiraling into independent reading, with teacher-directed stops. The goal is for students to eventually monitor their own reading by stopping at text points he or she deems significant.
  • Follow activity with Think-Pair-Share activity.

IMPORTANT: While students are writing, use teacher moves to check for understanding and collect data.

Before testing out the place marker theory with your own distracted students, reflect on your current practices:

  • What strategies are currently in place for enabling distracted students to attend to the task?
  • What strategies are currently in place to create student accountability?
  • What strategies are currently in place to enable the teacher to monitor and track student compliance and understanding?
  • How effective is each strategy in aiding students to visually attend to the text?
  • What strategies are currently in place to facilitate before-, during-, and after-reading textual interactions?
  • What strategies are currently in place that enable students to self-monitor?
  • What strategies are currently in place that enable students to reflect on learning and evaluate progress?

Before setting up the procedure with students, glean some information on their attitudes about their own reading. Consider asking the following questions:

  • Do you consider yourself a good reader, a fair reader, or a poor reader (circle one)? Why?
  • When do you most enjoy reading? Why?
  • When do you least enjoy reading? Why?
  • Where do you most enjoy reading? Why?
  • Where do you least enjoy reading? Why?
  • Why do you read?
  • Does reading make you feel comfortable or uncomfortable (circle one)? Why?

Collecting Data:

While monitoring, consider using a qualitative data analysis protocol such as the following:

  • Student is more, less, or just as distracted from text, using the place marker, as he/ she normally is during reading. Explain (body language, posture, eye tracking, expression, other unexpected physical reactions…?):
  • During the Stop-and-Jot activity, student transitions to task and then returns to text more quickly than without the use of place markers, at the same rate of speed as when reading without the use of place markers, or more slowly or disjointed than when reading without the use of place markers. How do you know?

The following Observation checklist may also assist in your data collection.

Student: __________________________________ Date ______

Please place a check in the box (more, just as, or less) that corresponds to the blank within each box to the left. Use the space to jot down observations (body language, posture, eye tracking, expression, other unexpected physical reactions…):

  MORE JUST AS LESS
During reading, the student is __________ distracted than without the use of a place marker.
After Stop-and-Jots, the student transitions back to text  _________ quickly than without the use of a place marker.
The teacher-participant is _____________ successful in student reading compliance than without the use of a place marker.

 

Lesson Plan PROCEDURE ACTIVITY TIME
1 Sponge Activity Before Reading Essential Question Quick WriteExamples:

“What happens to a person who always feels alone, even with those closest to him/ her?”

“Why do fractions matter in daily life”

“Why should we understand how organisms, places, and ideas have changed over time?”

“How do climate and natural resources affect the way people live and work?”

5 Min.
2 Set Induction Anticipation Guide 3 Min.
3 Pre-assessment of student understanding of the lesson concept/process/skill K-W-L:“Based on my prior readings (equations, lab results, etc.) what do I know about the _______________?” 3 Min.
4 Large Group Instruction Teacher reads aloud the first paragraph/ excerpt. Teacher models use of the place marker and where to put it. When she/he says “Stop,” the teacher also models summary or picture with one-word caption. Teacher monitors. 10 Min.+ 1 min. feedback
5 Independent or Group Work Students read silently, using place marker. Teacher says Stop. Students complete a Stop-and-Jot with one-word caption. Teacher models and monitors. 10 Min.
7 Evaluation –Post assessment of concept/ process/ skill K-W-L“Based on my prior readings (equations, lab results, etc.) what do I know about the _______________?” 3 Min.

References

Cauchard, F., Cane, J., & Weger, U. Influence of background speech and music in      interrupted reading: an eye- tracking study. Applied Cognitive Psychology, Appl.       Cognit. Psychol. 26: 381–390 (2012).

Gillies, V, & Robinson, G. (2012). Developing creative research methods with challenging  pupils. International Journal of Social Research Methodology. 15 (2).

Mackey, M. (1991). The association between reading strategies and reading histories of          adolescents: a qualitative study. University of Alberta (Canada): ProQuest. UMI          Dissertations Publishing.

Pan, C., Tsai, C., and Chu, C. (2009). Fundamental movement skills in children     diagnosed with autism spectrum disorders and attention deficit hyperactivity          disorder. Journal of Autism and Developmental Disorders. 39 (12), 1694-1705.          Visual-Spatial Dyslexia (n.d.). In A 2 Z of Brain, Mind and Learning. Retrieved     February 9, 2014, from http://www.learninginfo.org/visual-spatial-dyslexia.htm

How Well Did Our Math Resources Align to Our TEKS?

Friday, September 25th, 2015

AUTHOR: Virginia Keasler, Math Education Specialist & Susan Hemphill, Math Education Specialist

K-8 mathematics teachers have entered their second year with the new math TEKS while high school teachers are adopting updated math TEKS this year, with the possibility of new resources on the horizon.

What are some things to consider in matching up resources with the new TEKS?

In comparing the TEKS with our resources we should keep in mind exactly what the student expectation is asking. One way to do this is to break the student expectation into key concepts that we know we will need to deliver. Your district may have already broken down the SEs into key concepts for you. If not be sure to pay close attention to all the details in the SE. Keep in mind when lesson planning that these are the key concepts that need to be taught.

The next step is to look at your resources and note whether it covers all, some, or more of the key concepts than expected. Also check the depth and complexity of what is included in the resource. For example, if your TEKS have students using an operation to solve a problem, your resource should not just have them identify what operation is used to solve that problem. Check to make sure the verb of your SE matches the level in your resource.

The following SE is used as a model here. Again, you may not have time to formally write these down but keep in mind that all of these concepts must be included in your lesson planning.

4.2E: Represent decimals, including tenths and hundredths, using concrete and visual models and money.o Represent decimals to the tenths using concrete models.

o Represent decimals to the tenths using visual models.

o Represent decimals to the tenths using money.

o Represent decimals to the hundredths using concrete models.

o Represent decimals to the hundredths using visual models.

o Represent decimals to the hundredths using money.

Process StandardsAs you review your resources, consider evaluating your process standards, the released STAAR items from 2015, and your models and tools used to deliver the TEKS.

All math courses have the same process standards now from K-12. Our state assessments dual code process standards and content standards with each item. Did your resource take this factor into account? Do you need to add more to make it align?

Released STAAR Items from 2015

Released items from TEA are examples of dual-coded problems with process and content standards. It is important to refer to the released items as you review your resource. Released STAAR Items for 2015 Link 

Models/tools

In reading your TEKS, are all the models and the tools stated included in the resource and do they provide enough experiences for your students to have mastery? Our example above has concrete and visual models, so both must be included for this resource to be fully aligned.

We hope you will use some of these ideas this year as you acquire new resources.  Now it’s your turn….go forth and align!

Let’s PLAY!

Monday, April 20th, 2015

AUTHOR: Lori Reemts, Project Coordinator – Curriculum & Instruction

As adults, we long for the long weekend or holiday because we are eager for a brain break, a new adventure, or a chance to play in life. Play is our departure, our recreation, and sometimes our connection to the inner child or to memory lane. It is the opposite of what we consider work to be. As a result, we sometimes lose sight of the many benefits of play and how important these benefits are to our developing youth. Many of us feel happy when we see children playing; we may even recognize some general social and physical benefits. And yet some may question what they see when walking by a classroom full of 3-, 4-, or 5-year-old children who appear to simply be playing. Play is fun after all and classrooms are about working hard and learning. Still others may question the level of rigor or the relevance associated with this seemingly carefree whimsy and equate it with merely babysitting the students.

 

While there are many more notable quotes about play than the four below, these seem particularly noteworthy.

  • “Play is the work of the child.” Maria Montessori
  • “Play is the highest form of research.” Albert Einstein
  • “The creation of something new is not accomplished by the intellect but by the play instinct.” Carl Jung
  • “The playing adult steps sideward into another reality; the playing child advances forward to new stages of mastery.” Erik H. Erikson

 

Though there is research demonstrating the importance of play, logical understanding of play, and pure admiration for it, there are still those who react as if play is not a significant part of child development which impacts so many areas.

 

Consider academic, emotional, social, and physical development. Each of these areas impacts the others and retains its own set of milestones, prerequisites, and skill sets. In play, students work on these areas simultaneously and, because each experience of play is unique, students continuously develop and learn. They do not need a lecture or a worksheet to develop these areas–they need experience.

 

We know that best practice for an effective learning environment includes the need for meaningful engagement with information as well as interactions that occur within the context of the children’s daily experiences and development. For young children, and it could be argued older children as well, this engagement occurs through play. The phrase “hands-on, mind-on” is often used to describe interactive learning experiences that connect movement and physical experience to mental and learning experience. This is exactly what play is and what play does.

 

To understand and use children’s natural capacity for play as an effective classroom tool, it is important to also consider the stages of play.

  • Solitary
    • infancy to toddler years
    • plays alone; limited interaction with other children
    • separate toys
  • Spectator/Onlooker
    • begins during toddler years
    • observes others but does not play with them
  • Parallel
    • toddler years
    • plays side by side; lack of group involvement
    • similar toys
  •  Associate
    • toddler through preschool years
    • plays with similar goals; no formal organization
    • rules not set; may play with similar toys; may trade toys
  •  Cooperative
    • late preschool years
    • organized by group goals
    • typically at least one leader

 

By understanding the developing areas of a child along with the stages of play, educators are able to carefully plan purposeful and intentional play-based experiences that support student development aligned to Prekindergarten objectives. Children will benefit from play whether the experience has had enhanced opportunities provided through an intentional planning process or not. As educators, we can intentionally plan for and provide those enhanced opportunities so that our students’ growth, development, and success is even more robust. This is the difference between learning that occurs in a classroom where students are simply playing and learning that occurs in a classroom where students are playing in an environment designed for the purpose of mastering learning objectives. It is important to maintain a balance between free play and purposeful play, remembering that each kind of play serves a positive purpose for students.

 

Next time you set your sights on a weekend of recreational play in your adult life, consider the skills and interactions you use as second-nature and without even realizing it. Don’t just concentrate on your “work” too much—you might just forget to have fun!

 

 

Resource

Children’s Health. (n.d.). Retrieved April 6, 2015, from http://www.healthofchildren.com/P/Play.html

Maintaining Student Engagement in Math

Monday, April 20th, 2015

Authors: Virginia Keasler and Mary Headley, Education Specialists: Mathematics

The STAAR test is over, the students are trying to shut down, and field trips and awards ceremonies are on the horizon. How do I engage my students so that learning continues?

What do students really say about what engages them? A recent article published in Edutopia in February of 2015, “Kids Speak Out on Student Engagement,” addressed this question.  220 students were asked, “What engages students?” The responses received seemed to fall under ten categories representing recurring themes.

  • Working with peers
  • Working with technology
  • Connecting the real world to the work we do/project-based learning
  • Teachers should clearly love what they do
  • Get me out of my seat
  • Bring in visuals
  • Student choice
  • Understand your clients – the kids
  • Mix it up!
  • Teachers should show their human side

Mathematics can be an intimidating subject for students; however, with the right math teaching strategies, educators can engage students in the subject matter and help them to better understand complicated concepts.

Now is the time to try a few new strategies pertaining to the students’ list above.

Working with peers has the potential to create students who are highly motivated and have higher levels of participation. The following short video from the Teaching Channel showcases an example of peer teaching: https://www.teachingchannel.org/videos/student-peer-teaching

While the use of concrete manipulatives is a critical component of math instruction, virtual manipulatives add to the learning experience. One technology resource for the math classroom is the National Library of Virtual Manipulatives (NLVM). Virtual manipulatives give students prompts, feedback, and answers to problems while working on problems lets the students incorporate more self-exploration. As always, you will want lead with the TEKS as you select manipulatives with which students will master content.

There are many ways to get students out of their seats. One of the strategies you may not have heard of is called Brain Breaks. Brain Breaks are a great way to re-energize your students to get their blood pumping and their brains re-charged for learning. The following websites have information and/or brain breaks in action:

http://www.pgsd.org/cms/lib07/PA01916597/Centricity/Domain/43/Brain%20Breaks.pdf https://www.teachingchannel.org/videos/brain-break-classroom-transition-nea http://teachtrainlove.com/20-brain-break-clips-fight-the-fidgeting/

Allowing students to make choices for their learning is important in a math classroom. Choice boards allow for student engagement and are great for differentiation. A choice board is a tool that ensures students incorporate a range of multiple intelligences, and/or learning preferences.

Some of the benefits of choice boards include:

  • Allowing students more freedom with a choice of activities
  • Allowing students to work at their own pace
  • Promoting independence and responsibility
  • Promoting a more positive behavior

To explore choice boards visit: http://www.alexiscullerton.com/uploads/2/4/7/2/24729748/choice_boards_packet.pdf

It is important to keep students engaged in their learning process. Hopefully, these strategies will help you maintain student engagement after the STAAR test and give you several ideas to take forward into the new school year.

 

Reference

Heather Wolpert-Gawron. (n.d.). Retrieved April 1, 2015, from http://www.edutopia.org/blog/student-engagement-stories-heather-wolpert-gawron

Rigor and Relevance in the Math Classroom

Friday, February 20th, 2015

Author(s): Virginia Keasler and Mary Headley, Education Specialists: Mathematics

We read and hear quite a lot about rigor on the STAAR Mathematics test.  In the past few years the State of Texas has been trying to up the ante in students’ conceptual understanding of mathematics.  Let’s try to break down what rigor may mean.

In 2013, Linda M. Gojak, Past President of the National Council of Teachers of Mathematics, was discussing rigor with a group of mathematics coaches from around the country.  The coaches commented that many of their teachers were confused by exactly what was meant by teaching and learning with rigor and they were unsure about how to respond.  Together they began exploring the notion of rigor with an online search of the word “rigor.” The thesaurus led to a list of synonyms, including “affliction,” “inflexibility,” “difficulty,” “severity,” “rigidity,” “suffering,” and “traditionalism”—none of which describe characteristics of rigorous mathematics instruction. No wonder there was confusion! However, two additional words included in the list—“thoroughness” and “tenacity”—provided avenues for some serious thought about what “rigor” implies.

Without a common understanding of the meaning of the word rigor, how can teachers provide rigor in the classroom?

Take this quick true/false quiz.

  1. _____ If standards are rigorous, the course is automatically rigorous.
  2. _____ Rigor means using creative ways to solve relevant problems.
  3. _____ Rigor means more work.
  4. _____ Rigorous work should be more difficult.
  5. _____ Rigor means selecting highly rigorous content.
  6. _____ Rigorous instruction allows time and opportunity for students to develop and apply their understanding.
  7. _____ Younger students cannot engage in rigorous instruction.
  8. _____ In order to engage in rigor, students must first master the basics.

Rigor isn’t as much about the standards as it is about how you ask students to reach the standards. There are times when students are asked to achieve highly rigorous standards in un-rigorous ways. At other times, teachers are able to take mediocre standards and help students achieve highly rigorous learning by designing rigorous learning experiences that correspond with those standards. Therefore, statement one above is false.

While rigorous instruction may require that students put forth more effort, it is not based on the volume of work students complete. Rigor is about the quality of the work students are asked to do, not the quantity. More assignments or more reading does not guarantee more rigor. In fact, rigorous classrooms often have fewer assignments and less homework. Therefore, statement three is false.

Rigorous classrooms do present more challenge to students but there is a difference between challenge and difficulty. Challenging work requires students to stretch and reach for new understanding. Work can be difficult for a variety of reasons. Examples include unclear instructions, a lack of necessary resources or adequate support, and demands that are too great for the time allotted. We can all think of assignments we endured that were difficult without being intellectually challenging. Thus, it is a mistake to think that just because students had difficulty completing their work, they have engaged in a rigorous assignment. Therefore, statement four above is false.

Selection of highly rigorous content does not guarantee a highly rigorous learning experience for students. How we ask students to engage in the content determines the level of rigor for the course. Therefore, the answer to statement five above is false.

Even young students can think and interact with material in highly rigorous ways. If given the opportunity, students will naturally take what they are learning to solve challenging problems. The key is for teachers make sure that rigorous instruction is developmentally appropriate. Therefore, statement seven is false.

Rigorous thinking is involved in learning even the most basic material. Students can learn the basics in highly rigorous ways. They can learn how to build adequate representations, organize those facts in some way, analyze and construct relationships among those facts, and make inferences beyond what is explicitly presented while they are mastering the basics. Therefore, statement eight is false.

Rigorous instruction allows time and opportunity for students to develop and apply their understanding by using creative ways to solve relevant problems. So, if you were thinking that statements two and six were true, then give yourself a pat on the back!

 

Study the following International Center for Leadership in Mathematics Education–Rigor/Relevance Framework®

 

Rigor 1

 

 

Looking at the examples in the above quadrants, where do you see yourself and your classroom on this framework?

Quadrant A – Relevance and rigor are both low for the student as the task has no real meaning and is fairly easy for students.

Quadrant B – Relevance is high since it is associated to a real example for the student but rigor is still low.

Quadrant C – Rigor may be high in this activity but relevance to real world examples is low for the student.

Quadrant D – Relevance and rigor are both high for the student in this task. Here the student must understand what is being taught as well as understand how to apply knowledge to relevant situations.

 

Characteristics of a rigorous classroom include:

  • Instructional environments that encourage students to take their learning one step further
  • Teachers facilitating learning and using higher level questioning strategies
  • Students pursuing deeper understandings through thoughtful investigations into the concepts they are learning
  • Students applying new learning to other disciplines and to predictable and unpredictable real-world situations
  • Evidence of teachers spending the majority of their time in quadrants B & D in the ICLE Rigor/Relevance Framework®

In conclusion, here are two scholarly definitions of rigor.

“The goal of helping students develop the capacity to understand content that is complex, and personally or emotionally challenging.”  (Strong, et al., 2001)

Jeff Paulson: “Rigor (n) An expectation that requires students to apply new learning to other disciplines and to predictable and unpredictable real world situations.” (Quoted in Paulson, n.d.)

By agreeing on what rigor means, educators are better able to provide and recognize rigor in the classroom in a consistent way, and this benefits all students.

 

References

Strong, R., & Silver, H. (2001). Teaching what matters most: Standards and strategies for raising student achievement. Alexandria, Va.: Association for Supervision and Curriculum Development.

Marcy Paulson. (n.d.). Retrieved February 5, 2015, from https://suite.io/marcy-paulson/181b2m1

Rose Colby, Patsy Dean, A Framework for Rigor. National Association of Secondary School Principals, Retrieved February 8, 2015, from http://www.nassp.org/Content.aspx?topic=57403

Making a Case for Information Literacy

Friday, November 21st, 2014

Author:  Leslie Barrett, Education Specialist: Technology & Library Media Services

Information literacy. What is it? Quite simply, it is the ability to sift through an abundant quantity of information to find what you need to accurately answer a question you have. It is knowing how to refine an information search to get a smaller but more accurate selection of resources to answer your question (i.e., “puma NOT shoes”). And it is knowing when one source (National Geographic) may be more reliable than another source (Bob’s Blog About Cool Science Stuff).

So why does it matter? The information landscape of today’s digital world is changing at incredible rates. According to Gonzalez (2004), the “half-life of knowledge,” or the time between acquiring knowledge and the obsolescence of that knowledge, is shrinking. Effectiveness in today’s workforce requires knowing how to stay current on the most up-to-date information possible. “As knowledge continues to grow and evolve, access to what is needed is more important than what the learner currently possesses” (Siemens, 2005). Knowing how to find out is rapidly replacing knowing. Information literacy is knowing how to find out.

We are seeing more and more digital devices being included in classrooms to facilitate the learning process. This creates perfect opportunities to make sure we are integrating information literacy skills into our content area instruction. Fortunately, some common threads of information literacy are already woven into the process standards of the four major content area TEKS. Consider the following TEKS examples:

 ELAR Research Strand

Students are expected to know how to locate a range of relevant sources and evaluate, synthesize, and present ideas and information.

ELAR Figure 19

Students are expected to apply deep comprehension strategies when reading such as:

establish a purpose for reading,

ask questions of the text,

make connections (text to self, text, community),

make inferences and support with text evidence,

summarize, and

monitor and adjust comprehension.

 Social Studies Process Standards

Students are expected to use a problem-solving process to identify a problem, gather information, list and consider options, consider advantages and disadvantages, choose and implement a solution, and evaluate the effectiveness of the solution.

Science Process Standards

In all fields of science, students are expected to analyze, evaluate, and critique scientific explanations by using empirical evidence, logical reasoning, and experimental and observational testing, including examining all sides of scientific evidence of those scientific explanations, so as to encourage critical thinking by the student. In addition, students will evaluate the accuracy of the information related to promotional materials for products and services such as nutritional labels.

Mathematics Process Standards

Students will use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.

In creating learning activities around these standards, teachers can incorporate opportunities for students to search the web and databases of scholarly resources to find information to support their content understanding. When Google searches produce information that is inaccurate or too broad, the opportunity exists to teach students ways to refine searches or access more scholarly sources to yield more effective results. With the return of state funded database access through www.texquest.net teachers in Texas public schools and open enrollment charter schools will have free/low cost access to digital academic resources to support information literacy integration. Your campus librarian can be a fantastic resource to assist teachers in integrating information literacy skills into instruction, but it is important that information literacy skills integration is occurring regularly in classroom activities and not just on occasional library visits.

As the “basis for lifelong learning” (ACRL, 2000), information literacy is one of the greatest skills we can instill in our students. The increasing availability of technology in our classrooms makes integrating information literacy skills into instruction an attainable goal.

 

References

ACRL. (2000). Information literacy competency standards for higher education. Retrieved from http://www.ala.org/acrl/standards/informationliteracycompetency#ildef

Gonzalez, C. (2004). The role of blended learning in the world of technology. Retrieved from http://www.unt.edu/benchmarks/archives/2004/september04/eis.htm

Siemens, G. (2005). Connectivism: A learning theory for the digital age. Retrieved from http://www.elearnspace.org/Articles/connectivism.htm