MATH = BEAUTY

There is true “BEAUTY in Mathematics,” but do we enjoy and share it?  You might be thinking—Math? Beautiful? Starting with simple equations which are balanced and rule following. Equations are like the building blocks of mathematics and stimulate creativity and a mathematician’s brain to make order and find solutions. These equations provide the things we enjoy such as technology gadgets, medicine, appliances, the space program and most of our entertainment.

Think about math in music for a moment which is divided much like fractions.  Songs or pieces of music are separated into measures which are further “divided into beats” which are designated by notes, etc. If you have ever listened to a song mash up—you can hear the math in the rhythm, beat and pitch.

Nature is full of math including fractals which are a symmetrical pattern that continues to “fracture” or multiply the same pattern. Everyday examples of fractals  are tree branches, snowflakes, lightning, and seashells. Fibonacci’s sequence (the rule where the next number in a sequence is the sum of the previous two)  is found in everyday items such as the arrangements of leaves on a plant or a pine-cone.  Math truly is BEAUTIFUL.

Check out these examples from on May 19, 2014, The Guardian.

Our brain actually responds to math in a similar way as to art and music exposure. According to James Gallager (2014) in an article entitled, “Why the Brain sees Math as Beauty,” he states, “Brain scans show a complex string of numbers and letters in mathematical formula can evoke the same sense of beauty as artistic masterpieces and music from the greatest composers.” The brain accesses the orbito-frontal cortex when both learning math and studying art. This part of the brain controls your emotion and decision making. This part of the brain is centered on what information you bring in visually and where the brain reverses visual associations and information into other information.

So, what does that mean for educators?   In an article entitled, “Finding the Beauty in Math, Holly Korbey (2013) states, ” While research suggests that improving self-efficacy and providing math-positive role models can help spark interest and stave off math anxiety, what some mathematicians and teachers are looking for reaches beyond surviving or tolerating math class, but helping connect students to mathematics beauty.”  This sentence jumped off the page because it is a reminder that the “beauty” in math is what makes it enjoyable and fun. This helps to alleviate anxiety and motivate students. Somehow we need to capture the beauty and the content and as Korbey (2013) says, “fall in love with math.”

Falling in love with math requires us to make math real and interesting to students. Infusing math with the arts is a way to create excitement and fun but also to make connections to the math found in the every day world. How does math fit in their every day lives?

  • Shopping (All operations and Statistics on labels)
  • Lemonade Stands (All operations)
  • Video Games (Patterns and Sequences)
  • Nature (Patterns, Sequences and Geometry)
  • Architecture (Geometry)
  • Coding or Computer Programming (Patterns, Sequences, Number Operations and Equations)
  • Cooking (Measurement, Fractions)
  • Music (Fractions, Patterns, and Sequences)
  • Art (Geometry, Patterns and Sequences)
  • Eating Out (All operations)
  • Sports (All Operations, Patterns and Sequences)

Finding ways to infuse real world application into math makes the WHY stand out and helps students see the importance. Seeing the validity in math and how it fits in the real world helps to increase engagement and interest for students. We have increased the rigor and problem solving in our instruction but are we making this subject come alive?  Kylene Beers (in a FB Post on 2/26/2016) stated, “rigor without relevance is simply hard.”  Using a program, such as Engage NY, makes infusing engagement and relevance difficult but maybe by integrating some technology, art and music into our instruction it would be a beginning.

Finding the beauty in math and “falling in love” (Korbey 2013)–WHAT A GREAT CHANGE!

 

Resources Accessed for this Article:

James Gallagher (2014) in a BBC Post:  Why the Brain sees Math as Beauty accessed on February 24, 2016

Viewed photos from The Guardian on February 25, 2016

Holly Korbey (2013) article:   Finding the Beauty in Math  accessed on February 25, 2016

 

 

 

Effects Regarding the Neglect of Social Studies

Social Studies is the forgotten subject in our time of high stakes testing and the emphasis on proficiency in reading and math.  We have watered this subject down to a unit theme or topic that we use to guide our reading instruction.  I can hear you shouting at the computer, “I integrate!”  Yes, we do integrate social studies ideas but we rarely teach in our elementary schools to the depth of our standards. In reality, when we integrate our instruction, there is a “star” and a subject that supports.  When it comes to social studies, the “star of the instruction” is normally our reading because we are emphasizing how to apply reading skills or strategies in context. When we focus on social studies such as the Branches of Government, do we equally emphasize the reading skill and strategies?

 

When you examine Common Core K-5 history/social studies standards you will find that there are not any! Common Core only addresses the areas of reading and math.   Luckily, North Carolina adopted the Essential Standards to address the areas of science and social studies as well as health, world languages etc.  Here is where the integration is necessary because these two were not designed together.  Learning to integrate where social studies AND reading equally become the focus rather than social studies being the consistent supporting subject is our obstacle.  A problem we need to address to ensure our students cannot only read the words on a page but truly understand and make connections because they have the needed background necessary.

 

In 2001, with the enactment of No Child Left Behind, the Center on Education Policy did a study and found 44 percent of districts reduced the time and emphasis on social studies instruction.  This percent increased in schools that were failing because the focus was on “closing the achievement gap.”  Our neglect of social studies has serious effects that I believe we will feel as our students grow and begin to interact as citizens and become our work force and voters.

 

The National Council of Social Studies (NCSS) states that the purpose of social studies in the elementary grades “is to enable students to understand, participate in, and make informed decisions about their world. Social studies content allows young learners to explain relationships with other people, to institutions, and to the environment, and equips them with knowledge and understanding of the past.”  Social studies helps students become problem solvers and better decision makers because they have practice and instruction in analyzing historical events of the past. When you are able to think through situations and give decisions value, it helps you become better at evaluating your own actions and situations.  Debates and role playing helps students learn to think through multiple perspectives and to value ideas other than their own. Collaborative learning which is often employed in social studies projects and research allow students to learn how to communicate, become leaders and team members that can work towards deadlines and project completion.

 

Integration of social studies is better than not teaching the subject but as educators we must remember the importance of our social studies standards. It is imperative we create life long learners who understand how they can contribute to society as a good citizen.  Social studies helps students become adults who can listen critically, ask questions and think beyond the words being spoken to the effects of the actions.

 

I know that TIME is the barrier. My challenge is that we find opportunities to teach social studies to the depth of the standard and to ensure that students understand the concept not just in isolation but how it applies to the real world and bigger picture.  Our county ELA/SS Maps are a good beginning to see how we can address the standard and infuse ELA.  But, we must continually question as we teach from these maps, am I teaching the social standards or merely spending more time reading about a social studies topic? (There is a BIG difference!)  Vertical discussions and alignments are crucial to ensure we do not overlap instruction but build on concepts that broaden our student’s understanding of the world and community.

Together we need to keep in sight the importance of ALL our standards and that when we slight one for another—we are not giving a balanced education.   Balance is the message that needs to be sent to those that make laws and educational decisions.  Being proficient math and reading students is important but if they cannot think critically, exhibit characteristics of a good citizen, consider multiple perspectives, and know how to interact with others they will not be a productive and active member of the community. Isn’t that our ultimate goal?

 

 

Resources

Article Accessed on February 20, 2016:  http://www.socialstudies.org/positions/powerfulandpurposeful

 

 

Poetry- Reasons to Embrace it!

It is NO secret that I love poetry.  As an educator, you should too!  Poetry is a powerful vehicle of language.  Poems contain figurative language, grammar opportunities, and lessons on perspective and point of view in short manageable packages.   Rhyming poems offer an added benefit for younger readers because the rhyming helps them become better decoders. Rhyming improves phonemic awareness and learning of word families such as pill, will, chill, etc.

Poems are short but complex and offer a manageable way to expose students to rigorous text without overwhelming them.  They offer a way to build fluency for our readers. They help students build word recognition and automaticity with repeated readings and sometimes predictable rhyme patterns.

A missing element in our instruction is often GRAMMAR.  Poems offer educators text to examine punctuation and grammar “Do’s and Don’ts.”  Anyone who has looked at an e. e. cummings poem has been exposed to a new world of looking at words and punctuation. Students are able to look at the use of parts of speech in context in small phrases which makes it easier to study the purpose and impact.

Look at the following excerpt from Emily Dickinson’s poem Summer Shower

 A drop fell on the apple tree,

Another on the roof;

A half a dozen kissed the eaves,

And made the gables laugh.

 

A few went out to help the brook,

That went to help the sea.

Myself conjectured, Were they pearls,

What necklaces could be!

 

The dust replaced in hoisted roads,

The birds jocoser sung;

The sunshine threw his hat away,

The orchards spangles hung.

This excerpt was accessed from the following website on 2/12/2016:   http://examples.yourdictionary.com/descriptive-poem-examples.html#xvRjwpK0STsrgbAC.99

Within these three stanzas are opportunities to discuss verbs used in unusual ways.  The author creates images with nouns that are unconventional implying that the sunshine has a hat.   Diamante poems are an easy way for teachers to use poetry to focus on the power of grammar use in writing.  Helping children see why particular punctuation is being used such as the semicolon or comma, helps them understand their purpose within text.  Poetry offers these examples and allows the educator to teach skills at a sentence or phrase level rather than an entire paragraph or selection. When you are teaching skills remember that you teach first on a word or sentence level to paragraph to selection to multiple selections.  You do not begin teaching the skill of context clues within an entire selection because it is too much.  You must isolate the skill to one sentence until they understand and make the level more difficult and add more text. By moving through this progression level when you teach your skills, it allows students to grasp the concept on a concrete level before moving to a more complex abstract level.

Poems offer a way for students to apply their reading strategy and make true sense of text. When you read a free verse poem, the first response is normally—what? This response is that you did not comprehend the text and what you do next proves if you are a good reader. If you stop and say you hate poetry—you have just proved yourself not to be a strategic reader. If you apply reading strategies such as rereading, chunking the text, or applying context clues, etc. than you have proven you know how to apply the needed skills to make meaning of text. Poetry provides TONS of opportunity to TRULY engage students into using and applying skills and strategies as they read.  Some of our students do not even know they do not understand while others see that there is a break down in comprehension quickly.  It is this understanding that separates struggling readers from our strongest.  Strong readers make mistakes but they have “read attack” skills and apply them automatically. For the rest of our students, we must teach this skill.   It is rare for our higher students to truly grapple with text. Poetry is embedded with vocabulary and figurative language that even our strongest readers are not proficient. This ensures that ALL of our students are challenged with rigor and learn to see what it feels like when understanding is breaking down and how to apply reading comprehension strategies to fix it. For example, look at the excerpt from Emily Dickinson’s poem, I like to see it lap the Miles:

I like to see it lap the Miles –

And lick the Valleys up –

And stop to feed itself at Tanks –

And then – prodigious step

 

Around a Pile of Mountains –

And supercilious peer

In Shanties – by the sides of Roads –

And then a Quarry pare

This excerpt was accessed from the following website on 2/12/2016:

http://www.poetryfoundation.org/poem/24517

Immediately when students read the first stanza they think that the poet is describing an animal because of words such as lick, feed and lap.  The words tank and prodigious normally are skipped because they do not make sense for the reader at first.  The second stanza is usually where students stop and say, “I don’t get it.”  This should make you happy because they are realizing that they are decoding the words but not making  meaning of the text. Having students return to the beginning and begin to question the text and chunk the lines into phrases to really think about the meaning and hidden figurative language embedded in the words helps them think deeper.  The key word is “tanks” because this just does not make sense for an animal.  At this point, strong readers will realize that they must think figuratively.  Think of the opportunity here to model for students how to “fix their break down in comprehension” with modeling, guided questions and student discussion.

Finally, poetry provides creativity and the opportunities to see and think from other perspectives. Poetry is a world where any object or setting can take on a new persona.  Poetry is a world where “things are NUTS” and sometimes do not make sense but open to possibilities. Poetry provides a world of imagination and a place that educators should WANT to run towards.

 

Resources for you:

K-1 Exemplars 2-3 Exemplars 4-5 Exemplars

For TES specifically–

This Poem Is NUTS- strategy for testing– see Kelly or a 3-5 teacher if you want to learn more

 

Accommodations and Modifications and Educational Lingo–OH MY!

I recently was sitting in a meeting and heard words like accommodation and modification being used interchangeably and I sat wondering if we as educators speak as clearly as we should. Education is its own world or entity and sometimes those of us who dwell here forget that not everyone has the background or understands our unique “lingo.”  This blog entry will focus on clarifying academic terminology which is often misused or misunderstood.

First, the terms accommodation and modification which are similar because they both are designed to help a student be successful and mandated with the Individuals with Disabilities Education Act (IDEA).  The purpose of this law is to ensure all children have available and free appropriate public education specifically our special education students. Under this law, teachers and schools are required to provide both accommodations and modifications to students as needed to ensure that they are successful.  The main difference in these two words is that one changes the material or expectation while the other changes the environmental conditions. An accommodation is only changing how a student learns the material by allowing extra time, or giving more breaks. A modification is actually changing the material or expectation for the student. Seeing these definitions side by side, you can see the importance of clarifying in a conference or meeting the difference between the two. If you share with your principal that a child needs an accommodation, you are stating that the child can meet grade level expectations but needs you to level the playing field with environmental or procedural changes. If you are stating a child needs a modification, then you are explaining that the child cannot meet grade level expectations so you must change the material for success. Big difference!

chart accom

The second terms I would like to clarify are remediation and intervention which are similar in that they are both addressing weaknesses in a student’s education but should NOT be used interchangeably.  Remediation is a synonym for re-teaching and can be used reciprocally.  Remediation refers to  providing extra help or assistance to a child who did not previously master material when it was taught or they may have misunderstood a topic.  Most students need remediation at some point during their academic journey.  They may need material reviewed or small group help on a particular math problem or simply a peer tutor to review vocabulary they did not comprehend. Remediation is temporary and is not needed at all times.  It is a response to a child who needs to hear the material again.  Intervention is a more serious and targeted assistance. Intervention is provided to a small population of students unable to meet the challenge of daily curriculum and grade level expectations even with modifications and accommodations. Students who receive intervention are not responding to the normal class instruction (CORE) and routine remediation of material.  Intervention is provided for students who are several grade levels behind, receiving extra help AND are still not making adequate progress.  Interventions are not simply reviewing material or a quick impromptu lesson but are research based and targeted to a specific deficit which has been identified through assessment data.

interv

This leads me to the term progress monitoring which is similar to a temperature check. A teacher uses progress monitoring (a quick assessment or check) to ensure that students are making progress towards learning goals.  The best progress monitoring tools are  standardized or Common Formative Assessment to determine progress. Remember that interventions are the activities and lessons you are using to help the student and progress monitoring is the tool you are using to determine if the interventions are successful.

prog

When you hear the acronym MTSS, it probably begins a wordle in  your brain of terminology that is coming forth in education.  I hope this clarifies a few confusing terms that are being readily used in our transition to the MTSS process.  The list of words to cover is expansive but I will leave you with these today.

 

Research Resources

http://www.wrightslaw.com/

Acccomodations and Modifications  from Wrightslaw accessed on February 6, 2016

 

 

 

 

 

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