Guest Speaker Let's Sing about Rounding Let's Play! CLosing With a graded quiz. http://pisdtv.pisd.edu/dooley/features/188 You have been given a Math Journal.

The pages of the journal correlate with the number on each station.

Some centers are differentiated. Use the material labeled with the letter assigned to you.

Some centers have self correcting material.

One center is a folder for you to make and take.

There is a direction card with each center that also indicates which VAKT it represents. By an out of this world team!

Erik

Jeanine

Lori

Beth Understanding math

is like the structure of a building.

A good foundation must be built in order to learn a subject that compounds information. Math is the layering of skills. The continued learning of skills greatly depends on the quality of the floor of knowledge below. Our goal is to help each student build a sky scraper up to the stars. Vocabulary should be taught using explicit strategies.

As you are teaching math, help children understand that math is a language. Prior knowledge must be obtained before introducing new concepts.

A child's self confidence can plummet and the child is likely to give up and feel defeated. KEVA PLANK DEMO http://www.vdoe.whro.org/math-strategies/FLA_DOE_11/fla_doe_11.swf http://www.flocabulary.com/pythagorean-theorem/ Credits: Wall of Thinking Maps Thought Processes:

Used for Analogies

Identifies Differences/Similarities between relationships

Must have relating factors

Can read like a sentence:

______is ______ as ______ is to _____

Adding a frame of reference:

What are the relating factors?

What are the analogies?

How did you know this? Bridge Map Thought Process:

Sequencing

Ordering Processes

Adding a frame of reference:

What is the sequence?

How to you know what order to use?

What are the stages?

What are the sub-stages? Flow Map Thought Process:

Classifying

Vocabulary & Word Problems

Equations

Parts

Order

Adding a frame of reference:

What are the main ideas?

What are the supporting ideas?

What are the details in this map? Tree Map Thought Process:

Compare/Contrast

Can be adjusted for ELL students

Adding a frame of reference:

What is similar/different to you?

What qualities are the same?

What qualities are different?

Which qualities do you like the most? Double Bubble Map Thought Process:

Describing Qualities

Uses adjectives/adjective phrases

Thought Process writing or defining things

Adding a frame of reference:

How are you describing this?

What qualities do you like the best? Bubble Map 3-D Thinking Map More Circle Maps Thought Process:

Defining in a concept in context

Defining vocabulary terms

Vocabulary development

Brainstorming

Accessing prior knowledge

Adding a frame of reference:

Ask students to identify sources of prior knowledge.

What do you know about this?

How are you defining this concept? Circle Map Bridge Map: Flow Map: Student Generated Example: For Thinking Maps to be effective, the student must be the one who constructs the map. This gives the student the opportunity to cognitively

link the visual images to the content as well as incorporating the frames of reference that are individual to each student.

Teacher Generated Example: Incorporating Thinking Maps into

Explicit Instruction

Teacher Introduces the lesson

Activate prior knowledge

Use frame of reference

Introduce concepts and use questions to activate thinking

Initial Instruction

Teacher models several problems

Teacher provides explicit instruction for students to complete their thinking maps

Teacher-Guided Practice

Students use maps with teacher supervision

Teacher monitors student success

Students may work together in peer groups

Independent Practice

Students complete problems independently

Check for Understanding

Teacher checks for student success during independent practice

Re-teach Students Who are Having Difficulty

Identify students who are still having difficulty

Reintroduce concepts and re-teach Examples of Guiding Questions for adding a Frame of Reference Each thinking map is linked to a specific thought process

Connects a visual design with specific thought processes

Broadens critical thinking skills

Helps close achievement gap with ELL students

Provides a way to teach cognitive skills explicitly

Helps students become independent thinkers

Creates a mental visual pattern for thinking

Non-Linguistic Representation

Provides a frame of reference –> what influences a student’s thinking Thinking Maps: 8 Cognitive Skills

Many of our students have experienced repeated difficulties in math. They often get discouraged and feel like they will “never get it.” These negative feelings can persist and may become a self-fulfilling prophecy. Thinking maps are an evidence based practice to help students learn how to think. What’s going on in our students’ brains

during math instruction? THINKING MAPS A Language for Learning Multiple Maps

Same concept: multiple maps Thought Process:

Cause and Effect Relationships

Adding a frame of reference:

What are the causes?

What are the effects?

What happens next? Multi-Flow Map Thought Process:

Part to Whole Relationships

Reasoning

Structural Analysis

Adding a frame of reference:

What are the components?

What are the parts?

What are the subparts?

How to they fit together? A format for solving word problems Brace Map They are NOT graphic organizers!

Graphic organizers are flat, black and white, and very generalized.

Students need to learn more than how to graphically organize.

Graphic organizers don’t teach students how to think.

Important!

They are not teacher generated:

Students complete the maps themselves in order to allow them to make cognitive connections. Thinking Maps vs. Graphic Organizers

School/district wide method

Evidence Based Practice

Provides a Visual Scaffold for Learning

The brain can register 36,000

images an hour

90% of all information that comes

into our brains is visual

40% of nerve fibers that connect to

the brain connect through the retina*

Helps students conceptualize abstract

concepts such as:

Spatial Relationships

Distances

Sequencing

Multi-step processes

Compare/Contrast

Classifications

* Adapted from Brain Based Learning,

Eric Jensen, 1996

How Do Thinking Maps Work? Thinking Maps: Math Anxiety

Are your blinds open?

Are YOU afraid of math?

What about your students’

blinds?

Are they coming to you with “bugs”?

Do they already feel like they

will never understand math?

Do your students mentally shut

down during instruction,

independent practice, or tests?

Adding a frame of reference is the hook that allows the student to make cognitive connections to the new material. It is the “thinking” part of thinking maps.

Adding a Frame of Reference:

Ask the student questions that frame the new information.

How do you know about this topic?

What do you know already?

Did you get your information from a

specific source?

Have you seen this before?

Who could use this information?

Why is it important? Frames of Reference are thought processes. Each of the 8 thinking maps has a unique thought process. What is a Frame of Reference? •A Mnemonic is any procedure or operation designed to improve one’s memory

•A meta-analysis revealed that the effect sizes for these interventions were very large (Scruggs and Mastropieri, 2000)

•Forness (2001) demonstrated that these interventions had the largest and most consistent results of all special education intervention strategies.

•Useful across all subject areas

•Improve retention and recall information for all students but most importantly for students with disabilities Math Strategies

Mnemonics A nebulous journey Three types The Keyword

Method Letter Strategies Pegword Method •A keyword is used to connect a picture with information needed. The object in the picture has a sound that is similar to the word that needs to be remembered. Italian Vocabulary word

Lago = Lake

Keyword Image = log in a lake •Using a rhyming proxy for a number. Used for ordered operations.

(one is bun, two is shoe, three is tree) Acronyms STAR Letter strategy for problem solving

S earch the word problem, T ranslate the words into an equation in picture form, A nswer the problem,

R eview the solution My Very Excited Mother Just Served Us Nuggets

Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune Auditory Learners learn best by listening.

Auditory Learners do well with lecture and class discussions.

Auditory Learners tend to remember and repeat ideas that were verbally presented.

They can repeat and fulfill verbal instructions. Auditory Understanding the Learning Styles of your students

Assessments through Curriculum Based Measurement Learning Styles

VAKT Visual Learners prefer using images, pictures and colors to organize information.

Visual Learners like to read instruction on their own to increase understanding.

They learn by seeing and watching demonstrations.

They use the “mind’s eye” to conjure up images. Visual Conceptual Understanding – understanding mathematical concepts (word problems and integers) and operations (PEMDAS)

Strategic Competence – ability to formulate and conduct math problems

Procedural Fluency – ability to accurately and efficiently conduct operations and math practices

Adaptive Reasoning – thinking about, explaining and justifying math work

Productive Disposition – appreciating the useful and positive influence of understanding math and how ones attitude toward math influences success Math proficiency is the essential goal of instruction.

Math proficiency is what any student needs in order to acquire mathematical understanding.

Mastery – to be able to apply the concepts covered in class to “real world” situations.

How do we measure mastery? Math Proficiency A very important feature of a comprehensive math program is to teach concepts and vocabulary – to make sure students understand the language of mathematics. Learning Styles There are a lot of forces at work here.

There is a lot of diversity among the students as to their level of disability and cultural backgrounds.

This requires much attention and needs development of instructional interventions to meet the specific needs of the students. We cannot ignore the fact that our classrooms are a microcosm of languages and prior experiences. Diversity in the Classroom Kinesthetic

Visual

Auditory

Kinesthetic

Tactile 4 Types of Learning Styles In addition, we need to individualize the instruction for the children. We often assume an individualized program means the student works alone. Individualization refers to the program designed to meet the individual needs of the student. Despite years of research, no single method of math instruction has been proven to be significantly better than others. Individualization We know through the reading that students having difficulties in math often have other related difficulties that cause interference in learning math.

For example-

Students with learning disabilities often have difficulty applying learning strategies.

Students with emotional disturbances may have greater difficulties learning math than other subjects because it requires persistence and concentration.

(Parmar, Cawley, & Miller, 1994) Diversity in the Classroom Psychological Factors Personality Factors Educational Factors Neuropsychological patterns Intelligence

Cognitive ability

Distractibility

Ability to apply strategies Quality of past education

Amount of intervention

English as a second language Persistence

Self Confidence

Attitude Birth defects

Severe illness

Head Trauma Methods that can be used for studying math vocabulary.

Math journal; As you teach provide the child with a short explanation of the lesson to glue into a specific note book. Teach him how to use it as a reference book. Highlight all specific vocabulary.

.

Word banks; Provide word banks and posters that contain vocabulary words to increase the frequency of exposure.

Word webs and concept circles – The same types of materials used in a language arts class can be used for Math vocabulary

The Frayer Model - Thinking Map Tactile Auditory Teach children Math is not a black whole! Mathematics A Song for Geometry Auditory Songs Help http://www.sheppardsoftware.com/mathgames/earlymath/clock_shoot.htm Identify numbers

Count

Skip Counting

Add

Subtract

Calendar knowledge

Basic Shapes

Telling Time

Elapsed time

Multiply

Divide

Fact Families

Rounding

Estimation

Money recognitions Making Change

Place Value

Decimals

Measuring Angles

3D Shapes

Volume

Area

Perimeter

Circumference

Radius

Pie

Naming Angles

Measuring distance, weight and volume

Metric system

Converting base 10 to metric

Digits

Variables

inequalities http://animoto.com/play/5Jqq2Ka2jrUC56NJ4r0b5Q More ideas! Circle Maps are for defining things in context

Make a paper plate Circle Map defining your favorite number.

Put your favorite number in the middle of the plate.

Put everything you understand about the number around the circle. You Try! http://pinterest.com/search/pins/?q=math+thinking+maps

http://www.madzander.com/thinking_maps/Introduction%20to%20Thinking%20Maps/index.html

http://pinterest.com/search/pins/?q=math+thinking+maps

http://tellier.edublogs.org/2010/12/14/december-14-solving-multiple-step-equations/

http://www.doe.k12.ga.us/Curriculum-Instruction-and-Assessment/Special-Education-Services/Documents/Thinking%20Maps%20ppt.pdf

http://iriscenter.com/math/math_05_link_evidence_based.html

http://animoto.com/play/5Jqq2Ka2jrUC56NJ4r0b5Q

http://coachkessler.weebly.com/thinking-maps.html Credits: Acrostics Where do we begin? Where to Begin Learn through experience and physical activities like playing games or role playing

Benefit from demonstrations

They learn from teaching others what they know Process information best through a "hands-on" experience

Learn by touching and manipulating objects

Prefer a personal connection to the topic

Follow directions they have written themselves

First we need to determine the performance level of the students. For students with special needs, individually administered assessments yield the most information. (BRIGANCE Diagnostic Comprehensive Inventory of Basic Skills and the Test of Early Mathematics Ability provide information to assist with designing and monitoring instruction)

From there, “one would be hard-pressed to find a more effective technique than curriculum-based measurement (CBM) for directing, monitoring, and redirecting remedial efforts.” Bryant and Rivera 1997

From the individual assessments, we can pinpoint the concepts or operations where children are having trouble.

From there we define the goal which will help the student achieve mastery. Then we give a pretest to establish a measureable baseline of their current abilities. Then based upon their learning style, we individualize the instruction to best fit the child. The teacher and student meet frequently to discuss and track the student’s progress and modify assignments and instruction to help learning. This gives the student ownership of their progress and hopefully will positively increase their “disposition” towards math. How do we develop instructional programs for the students? So, we know where the deficits lie based upon the individual assessment we gave. We defined the goal we want them to achieve. From here we can individualize instruction. So what kind of strategies can we use to help kids with math deficits? What does “progress tracking” provide teachers? DATA for IEPs!! References and Resources

Scruggs, T.E., Mastropieri, M.A., Berkeley, & Marshak, L. (2010). Mnemonic

Strategies: Evidence-Based Practice and Practice-Based Evidence.

Intervention in School and Clinic. 46 (2) 79-86.

Forness, Steven R. (2001) Special Education and Related Services: What Have

We Learned From Meta-Analysis? Exceptionality. 9 (4)

Scruggs, T. E., & Mastropieri, M. A. (2000). The effectiveness of mnemonic

instruction for students with learning and behavior problems: An update

and research synthesis. Journal of Behavioral Education, 10(2-3), 163-173.

doi: http://dx.doi.org/10.1023/A:1016640214368 http://www.education.com/study-help/article/types-triangles/

http://www.mathsisfun.com/angles.html

https://www.google.com/search?q=types+of+triangle

http://www.lifestreamcenter.net/DrB/Lessons/thinking_maps.htm

http://neinursingonline.wordpress.com/maths/fractions-love-em-or-hate-em/

http://www.angelfire.com/ky2/LITTLEPIXEYDAYCARE/fingerplaysflannelboard.html

http://pisdtv.pisd.edu/dooley/features/188

http://secondgrademathmaniac.blogspot.com/2012_08_01_archive.html

http://www.cccphilly.com/moneylapbook.html

http://www.inspiration.com/Kidspiration

http://www.northcanton.sparcc.org/~elem/kidspiration/hlass/liquid.htm

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# Math Presentation for 628-677 GMU

Mathematics is a Nebulous Journey

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