This is supposed to be MATH not READING!

 

Why are ‘Word Problems’ or ‘Number Stories’ such an issue? Because the Common Core State Standards from:

• Kindergarten OA “2. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.”

To grade 1 with the following Standard:

• “Operations and Algebraic Thinking: 1.OA Represent and solve problems involving addition and subtraction. 1. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.2 2. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.”

To Grade 4 – Measurement and Data 4.MD

• Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit.

And finally in grade 7

• Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers.

More than that the CCSS requres students learn to solve word problems, students need to develop their skills to decipher and solve word problems or number stories because they more accurately reflect real world experiences. It is not very often that you will be presented with simple mathematical equations where you have to add, subtract or multiply or divide numbers. The real world experience is:

I have $10.00. How many apples can I get at $0.35 a pound?

With this type of real world math challenge, there is estimation and rounding and division, and more. Students need to learn the proper sequence to perform mathematical tasks in order to determine the correct answers to real life situations.

Word problems are challenging enough to the typical student. What of our students with learning differences? How do we make this demanding mathematical process accessible?

Part of making math accessible is helping students acquire the vocabulary. Bill Atwood of Collins Education Associates has developed a fun and engaging, full body method of teaching the vocabulary of Mathematics as can be seen here in this video: https://www.youtube.com/watch?v=AOAJpcye7BI

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Learning the vocabulary of Mathematic helps demystify Mathematics and give students more confidence when approaching math word problems as they will have a better understanding of what they are reading. They will understand what a ‘Face’ is in math as they have the picture of it with their body.

This method of teaching the vocabulary hits various points of the UDL Concept, among them:

• Multiple Means of Representation – he use voice and gross motor movement – even the inflects of his voice changes.
• Multiple examples and Means of Expression – a ‘game’ he plays is to see how many the students can ‘teach’ others in the class, giving the students the opportunity to demonstrate their knowledge.

So now that they know what the words sound like and their meanings, how do the students recognize them when they see the words in the word problems?

Word Walls have been shown to have a positive impact on learning. It exposes the students to the words consistently, and provides a reminder when needed. Michèle S. Weiner, Regional Center II Instructional Supervisor created a marvelous Mathematic Word Wall available at: http://www.sas.com/content/dam/SAS/en_us/doc/event/math-summit/2014/112M.pdf

Some examples of the vocabulary words are:

The Virginia Family Special Education Connection has included a link to the Mathematic Word Wall as they recognize that it touches on several modes of learning for our students with difficulties.

These are two strategies to learn the vocabulary of math in order to help our students learn how to manage Word Problems. They meet UDL criteria of helping students develop the networks needed to recognize the information and concepts, to apply the information and, as Lev Vygotsky recommends, are engaging.

Resources

http://www.collinsed.com/resources.htm

http://www.onesassyteacher.com/2014/06/using-cubes-problem-solving-strategy-in.html 

http://www.attainmentcompany.com/sites/default/files/pdf/sample/SSS-Sample_0.pdf

http://www.ncpublicschools.org/docs/ccsa/conference/2013/presentations/48.pdf

http://tinyurl.com/z76gffw

https://udlstrategies.wikispaces.com/Math

http://www.ldonline.org/article/62401/

https://www.youtube.com/watch?v=AOAJpcye7BI

https://goalbookapp.com/toolkit/strategy/math-flashcards

https://goalbookapp.com/pathways/#!/strategies/d5d5297a-69f9-434f-9293-c75f6493c41c

https://quizlet.com/

https://itunes.apple.com/us/app/flashcards/id408490162?mt=8

https://vafamilysped.org/math

https://vafamilysped.org/Resource/JWHaEa5BS74tjB2sBVD-Mg/Resource-mathematics-word-wall

http://www.corestandards.org/Math/

 

 

Examples

• Board games– There are many board games available, such as Equate, Math Bingo and Allowance. These games can be incorporated into math lessons and address mathematical objectives. For example, having students practice creating and solving mathematical expressions while playing Equate would correlate with 6th grade Math Common Core Standard Expressions and Equations
• Playing Cards– Students can play a version of the card game War (addition, subtraction, multiplication, division). For addition, each student flips two cards over and adds the two cards together. The student with the pair that adds to the largest number wins. For more ideas, see math with playing cards.
• Math Jeopardy– There are multiple ways that Math Jeopardy can be played in the classroom. Some teachers prefer to use colored index cards with the points on one side and the Jeopardy question on the other side. The index cards can be easily taped to a classroom whiteboard under chosen math categories. Some teachers use a Powerpoint presentation or math Jeopardy games available online and a projector for whole-group instruction. When playing as an entire class, students typically break into two teams. Each team member has a mini-whiteboard on which to work out the mathematical problem. However, the teams must collaborate and agree on the correct answer (e.g., there cannot be more than one answer per team). The team that chooses the mathematical question has the opportunity to answer the question first. If the first team answers incorrectly, the next team has a chance to answer. Each team takes turns choosing the questions, and the teacher (or a student scorekeeper) keeps track of the score.

Implementation Tips

• Teach the rules to the students prior to playing. If you have a set of 3-4 basic math games, you do not have to re-teach the rules every time the students play the game, but you can change the parameters around playing (e.g. addition one day, subtraction the next).
• Math games are a great way to incorporate peer buddies or peer tutors for students. The peer buddies can help support students with learning the rules of the game, practicing math facts, and participating in class. You can differentiate the instruction of math games by thinking about how students are grouped together while playing the games.
• Always consider the mathematical objective that is being practiced. Make sure that the game matches the mathematical objective or educational outcome. Math games can enhance student learning and practice of mathematical skills. In addition, math games can become a part of the overall classroom structure. For example, some teachers have math learning centers once a week and have games available.

 

 

 

Flexibility – no yoga involved

Executive Functioning and Flexible Thinking

What is it?

“Executive Functioning’ has become a ‘buzz word phrase’ in the education field especially at Special Education Team Meeting discussing the needs of struggling students. Unlike some buzzwords in education, this one does have significance to our practices. The formal definition of the Executive Functions is ‘a set of processes that all have to do with managing oneself and one’s resources in order to achieve a goal. It is an umbrella term for the neurologically-based skills involving mental control and self-regulation.’   (http://www.ldonline.org/article/29122/)

In English – properly developed Executive Functioning Skills allow us to manage all the myriad details of our lives, among them planning for events, finding our way someplace (despite roadblocks and detours), making decisions and prioritizing. Please note the caveat of ‘properly developed’. If a person’s Executive Functioning skills are not properly developed or are hampered in some way, life can become very difficult as can be seen in this short animated video about a young person with ADHD (ADHD being one of the quintessential EF disabilities) and possible dyslexia.

https://www.youtube.com/watch?v=EQ71vgRzCA4

Our young person in the video is quite creative. While quite creative in keeping himself occupied, what he occupies himself with often has little bearing on the completion of the task at hand. His difficulty in focusing on tasks (as he becomes focused on other activities) has some rather unfortunate consequences. Fortunately, he has someone who appears to understand and accept his difference.

Sohlberg and Mateer categorized Executive Functioning into six categories in 2001.

• Initiation (Starting behavior)
• Response Inhibition (Stopping behavior)
• Task persistence (Maintaining behavior)
• Organization of Thoughts and Behavior
• Generative Thinking (being creative and flexible)
• Awareness (monitoring & modifying one’s own behavior)

Each one of these can be a challenge for a typical person of any age, let alone an atypical student whose brain is still developing. There are numerous strategies and technologies that can help students become organized, start or stop or maintain expected behaviors. In fact 5 of the 6 categories named above all deal with observable behavior. The other category alone deals with what is going on inside a person’s head – Generative Thinking: the Art of being Creative and Flexible.

Creativity and Flexible Thinking Skills are becoming more in demand by the world at large. They are now being recognized as skills that can be taught. Programs such as Destination Imagination and Odyssey of the Mind have been teaching Creativity and Flexible Thinking for years. Each program allows young people to develop both while developing solutions to open-ended challenges based around a variety of themes: technology, engineering, scientific, fine arts and improve among them.

Why are these skills important aspects of Executive Functioning? I’ll be focusing on Flexible Thinking for the rest of this article as the development of Creative Thinking Skills is could be an entire thesis in and of itself.

Flexible thinking is import as it helps one shift from one activity to another. What is frequently referred to as ‘multitasking’ is actually the ability to shift rapidly between several tasks. Flexible Thinking also allows one to more easily change direction when something is not working quite the way one expects. This skill is frequently needed in classroom situations as schedules frequently end up changing and while Math is supposed to start at 10:00, there may be a special speaker come in, there may be a fire drill, there may be any number of things that disrupt the standard day’s schedule. For the typical child, this is not a problem. They may even celebrate the change from routine. For our students with more rigid processes, change is a painful experience, and this pain can lead to disruptive behaviors as they express their discomfort. Preparing students before there are changes is one strategy which may help students cope with said changes.

Flexible Thinking and Reading

Flexible Thinking is important in learning to read. Just ask any English Language Learner! The ‘Lucy and Ricky’ video below demonstrates a difficulty faced in learning English in an amusing yet accurate manner.

https://youtu.be/MAL9VD6Lz9Y

Add to the variety of pronunciations possible with letter combinations with the words the meaning and pronunciation of which can only be determined by context:

Live fish live in water 

 the dove dove off the tree branch,

the wind will wind the flag about the pole 

the list goes on. A child needs to develop flexible thinking in order to understand the meaning of the phrases. Flexible thinking is also needed to understand idioms and puns. It is also needed to help understand inferences in their reading.

So how does one help young people develop their flexible thinking?

One proven strategy is to involve them in programs such as Destination Imagination and Odyssey of the Mind mentioned earlier, both of which help young people develop flexible thinking, along with many other 21^st skills and a variety of ways to express their skills which very much follow the pattern of UDL. http://www.destinationimagination.org/who-we-are/proven-results

One can play games that encourage thinking, flexible and otherwise. Understood.org has a number of games listed at https://www.understood.org/en/school-learning/learning-at-home/homework-study-skills/7-tips-for-building-flexible-thinking?view=slideview such as:

• “Fannee Doolee likes …” AKA “Martians like …”
• Tell riddles or puns. Most deal with language so they encourage the understanding of multiple meanings.
• Read “Amelia Bedelia” books and other that play with language.

The variety of games available allows young people a variety of ways to develop and express their skills which are key to following Universal Design for Learning precepts.

Flexible Thinking is a critical category of Executive Functioning. As such, care should be taken so that strategies are used to repair deficits in Flexible Thinking. This can be done by using any combination of the strategies described above among others. Many of these strategies can be quite fun for both parties in the experience.

Just be flexible in your thinking when it comes to finding means of assisting a young person to develop their Flexible Thinking.

Sources:

https://udlguidelines.wordpress.com/principle-ii/guideline-6-provide-options-for-executive-functions/

http://www.lcsc.org/cms/lib6/MN01001004/Centricity/Domain/21/LatestTechforExecutiveFunction_Handout.pdf

http://udltechtoolkit.wikispaces.com/

http://www.ldonline.org/article/29122/

https://www.understood.org/en/learning-attention-issues/child-learning-disabilities/executive-functioning-issues/6-ways-kids-use-flexible-thinking-to-learn

http://www.nesca-news.com/2013/10/executive-function-flexible-thinking.html

https://www.youtube.com/watch?v=EQ71vgRzCA4

https://www.understood.org/en/learning-attention-issues/child-learning-disabilities/executive-functioning-issues/6-ways-kids-use-flexible-thinking-to-learn

http://www.destinationimagination.org/who-we-are/proven-results

 

 

H.O.T.S. for Reading Comprehension

Reading is so much more than the ability to read the words on a page, application, website, e-reader,  road sign, or wherever the text is found. One must also be able to process and understand the information the text is conveying. It is essential for readers to develop their reading comprehension skills early as “A student’s academic progress is profoundly shaped by the ability to understand what is read. Students who cannot understand what they read are not likely to acquire the skills necessary to participate in the 21st-century workforce.” (page 1 Butler, Urrutia, Buenger & Hunt – 2010)

Reading Comprehension is not a skill that comes naturally for the typical learner. It is even more difficult for children with learning disabilities, thus, it is even more crucial they receive appropriate, and strategic instruction to develop their reading comprehension skills. There are many strategies used to teach reading comprehension, such as modeling, small group instruction using fish bowl exercises and Socratic questioning. In a 2010 research study observing methods used by teachers, the “most consistent finding was that teachers who emphasized higher-order thinking promoted greater reading growth.” (Page 5 – Butler, Urrutia, Buenger & Hunt – 2010).

 

“Good reading comprehension skills do more than allow students to make sense of what they read.  By using higher order thinking skills they can use new information to make help make sense of their world through analysis, synthesis, and evaluation.” (http://www.k12reader.com/reading-comprehension-and-higher-order-thinking-skills/) Higher Order Thinking is based on Bloom’s Revised Taxonomy. ‘HOT’ requires the learner to be actively involved in their learning, and not just regurgitate information that they quickly forget. By becoming engaged, learners activate several of the brain’s networks. As each learner is different, we want to use as many ways as possible to activate these networks, a central premise of UDL (Universal Design for Learning).

• To activate the affective network we want to provide choices in the learning context, the reward system, the levels of difficulty or challenge, and the tools and content used.
• Scaffolding the learners’ recognition networks include providing a variety of different exemplars with attention to highlighting significant aspects, provide information in a variety of modalities, and provide a firm foundation on which to construct the higher order thinking.
• When attending to the strategic networks, we must provide varied means of demonstrating mastery, provide timely and germane feedback, provide appropriate supports, and myriad models.

Higher Order Thinking can involve all three of the networks mentioned above. Asking more qualitative questions rather than quantitative questions is one way of helping learners develop their H.O.T. and stimulate the learner’s recognition networks. For example, rather that ask “Did Tom Robinson hurt Mayella Ewell in Harper Lee’s ‘To Kill a Mockingbird?’, which could be answered with a ‘Yes’ or ‘No’ the learner could be asked “Was Tom Robinson capable of hurting Mayella Ewell? Why, or why not, and how do you know?” This style of question requires the young person to use their HOTs of Analyzing and Evaluating in order to respond.

Brock Peters & Gregory Peck in To Kill a Mockingbird

A learner could be asked to demonstrate their knowledge of the extent of Tom’s abilities by drawing a picture, acting out the courtroom scene or finding the scene in the movie and creating a storyboard with a collection of stills from the movie, thus activating their strategic networks. They might demonstrate the difficulties Tom had doing things with one hand, develop a list of tasks that can be done one handed and compare/contrast it with things needing two hands. This strategy would engage their affective network. The graphic below of Bloom’s Revised Taxonomy offers a host of possible activities that could be used as a means of integrating UDL and HOT. All of our students, those with disabilities, and those without are capable of developing their Higher Order Thinking, and thus improving their Reading Comprehension. 

 

Below is a link to a list of sites and resources all focused on developing High Order Thinking Skills (HOTS), some of which can be used to help develop UDL-based reading comprehension lessons: http://www.techlearning.com/default.aspx?tabid=100&entryid=8519

This is a link to 30 strategies for Enhancing Higher Order Thinking, some of which may be helpful in developing reading comprehension: http://ueatexas.com/pdf/30strategies.pdf

Sources:

http://www.readingrockets.org/article/higher-order-thinking

http://www.readingrockets.org/article/how-increase-higher-order-thinking

http://www.readingrockets.org/article/universal-design-learning-meeting-needs-all-students

https://cortesfranciscojr.files.wordpress.com/2015/09/0dfb9413ee2b786c6d23358ec2ae0de2.jpg

http://www.readwritethink.org/parent-afterschool-resources/tips-howtos/encourage-higher-order-thinking-30624.html

http://www.readingrockets.org/article/response-instruction-and-universal-design-learning-how-might-they-intersect-general-0

http://udltheorypractice.cast.org/reading?4&loc=chapter5.xml_l1970066

http://www.k12reader.com/reading-comprehension-and-higher-order-thinking-skills/

A Review of the Current Research on Comprehension Instruction – 2010 – Shari Butler, Kelsi Urrutia, Anneta Buenger and Marla Hunt. Developed by the National Reading Technical Assistance Center, RMC Research Corporation – http://www2.ed.gov/programs/readingfirst/support/compfinal.pdf

 

 

 

New Beginnings …

So, start a new class and we start a blog! We will see where this takes us. The topic matters of the blog will focus on, hover about, flutter by UDL (Universal Design for Learners), tools and strategies, and how learners learn with maybe a few tangents on the way.