Managing Math Intervention

In a recent post I had Jim Wright's ideas on how to meet the needs of intervention students, this post builds off his other ideas from www.jimwrightonline.com.  A few points I will build off of is:

• Applied Problems, and encouraging students to draw and clarify understanding by drawing pictures.  
• Have students solve 2-3 sheets of problems in a set amount of time assessing the same skill.  The teacher determines whether the student is at frustration, instructional, or mastery level.
• Increase student engagement and improve group behaviors with response cards.
• Teachers should also change speech patterns to increase student comprehension.  This includes facing the students, paraphrasing often, clearing indicating most important ideas, limiting asides, etc.
• Maintain a supportive atmosphere for classroom "math talk."
• Always re-loop, a process of always bringing in previously learned material to build on each day so that students have a base knowledge to start with and so that learned structures are constantly reinforced.
• Unlock the thoughts of reluctant students through class journaling.
• Have the students use the vocabulary from the class in these journals.  Using brief assessments to help students build basic subject specific vocabulary and also gauge student retention of subject specific vocabulary.

100th Post

This is the 100th post so far, so I am celebrating by giving away another free book.  Since this doesn't seem real that I have made it this far, the book I am giving away is Imagining Numbers by Barry Mazur.

All you have to do is comment below with your name and address and I will ship the book to you free of charge for being such a loyal patron.

Imagining Numbers is Barry Mazur's invitation to those who delight in the imaginative work of poetry—and who may or may not have a background in math—to leap into the world of imaginary numbers.

http://us.macmillan.com/academictrade/imaginingnumbers

Multiple Representations

The algebra standard emphasizes relationships among quantities, including functions, ways of representing mathematical relationships, and the analysis of change.  But, algebra is more than moving symbols around!  Algebra should not be taught as a collection of tricks, students should see algebra as an aid for thinking rather than a bag of tricks. 

Multiple representations should incorporate verbal, concrete manipulatives, numerical, graphical, and algebraic representations of a topic.  The need to read problems carefully is vital and to learn the importance of re-reading and determining what is given in a problem and what is being asked.  Also, encourage student refelctions on their problem solving process.  Teachers should assist students in moving among different representations to generalize strategies and solve problems.

Technology enriches the range and quality of investigations by providing a means of viewing mathematical ideas from multiple perspectives. 

For example a common problem in algebra is the "Umbrella/Cap" problem:  Given two umbrella's and one cap costs 80$, but one umbrella and two caps is 76$.  Which one costs more?  What is the price of one umbrella? What is the price of one cap?

Writing Examples in Math

Using metaphors in the math classroom in class journaling helps teachers learn more about students and their relationships with mathematics.  For example, if math were a food, what kind of food would it be?  If math were weather, what type of weather woudl it be?  If math were a building what kind of building would it be?  If math were an animal, what animal would it be?

Gathering other valuable information at the beginning of the year or another class journal entry might be:  What do you like for a teacher to do in math class?  How can a math teacher be helpful?  What do you hate for a math teacher to do?  Is there something I need to know about teaching math?  One time math class... have students finish the sentence, telling the teacher about something that happened and how they felt about it.  Lastly, tell me something about yourself that I don't know that I need to know.

Having them journal a mathematical autobiography.  What year in school was math the best for you?  What made it a good year in terms of math?  What year in school was math one of the worst for you?  What made it a bad year in terms of math?  Think about mathematics and describe a concept or skill that you can do well. 

Incorporating vocabulary is a critical component needed for learning mathematics is a complete understanding of the language of mathematics.  The Frayer Model, picturing in your mind what a rectangle is, dual meanings of words in math and everday use, and having an alphabet book.

Other journal entries can be higher ordered thinking questions you can look over, such as can three angles be supplementary? If yes give an example? If no, explain why not?

• Having students write in journals helps studetns form views about mathematics.  It helps student-teacher interaction, improve writing skills, have individual diagnosis and evaluation, and help students make connections between topics.

More information can be found at NCTM and the article Can Writing be the Missing Link for Mathematical Understanding by Dr. Connie Shrock.

Response to Intervention (RTI)

Response to intervention is a multi-tiered approach to help struggling learners.  Students's progress is closely monitored at each stage of intervention to determine the need for further research-based instruction.  Their are three tiers for math instruction:  math instruction that all students recieve, school provides additional assistance to students who demonstrate difficulities, and lastly students who need more intensive assistance.  There are eight recommendations used by educators to help students who struggle with mathematics.

1. Screen all students to identify those at risk for math difficulties.
2. Instructional materials for students recieving interventions should focus intensely on in-depth treatment.
3. Instruction during the intervention should be explicit and systematic.
4. Interventions should include instruction on solving word problems that is based on common underlying structures.
5. Intervention materials should include opportunities for students to work with visual representations of mathematical ideas.
6. Interventions at all grade levels should devote 10 minutes in each session to building fluent retrieval of basic arithmetic facts.
7. Monitor the progress of students receiving supplemental instruction and other students who are at risk.
8. Include motivational strategies in tier 2 and 3 interventions.

Information was found at Response to Intervention: A introduction to the process... by David Pugalee.

Using the Response to Intervention helps students at all grade and age levels get the best education process for each student.  It also helps the teacher become more fluent in teaching practices that they aren't comfortable or are use to using in the general education process.

happy teaching!!

Discussion Boards

Discussion boards are reflective in nature.  They force students to read other perspectives and carefully consider a response.  The social aspects of face-to-face classroom are very intimidating for many students, especially for ESL speakers, new students, and those who are simply shy or quiet.  Often large enrollment classes often suffer from a lack of student participation.  Sometimes I don't necessarily go to Wallwisher for a discussion board, I have my own classroom discussion board.  On the walls in my classroom I set up different parts of an equation and how to solve the problem.  Below this is a blank sheet of paper where students can write ideas, what's important, and looking and seeing what is important in the equations before they ever use it.

Positive growth in class community is reflected through a sense of cohesion with other students, a higher degree of trust between students, an increased number of inquiries and questions between students and the instructor, and a general sense that the class is valuable and applicable to student needs.

Discussion boards are an active method of learning and encourage an active engagement with the course content and gives power to the students and lead to a more interested and motivated.

Thanksgiving Math

The focus of this lesson is for the students to explore the Pilgrims and Wampanoags experiences, actions, and decisions as they relate to the settlement of Plymouth colony.http://www.scholastic.com/teachers/lesson-plan/thanksgiving-lessons-grades-6-8  Throughout the activity students will develop an understanding of historical events from different perspectives while practicing research skills, reading comprehension, and various forms of writing.

The lesson resources are located at the link provided above, for math students I would have them relate the topic they are covering right now the Pilgrim and Wampanoags experience and how they could benefit using the math they are learning right now. 

To assess the students have the students come up with a math story problem relating the Thanksgiving story to math.

Peer-Guided Pause

During large-group math lectures, teachers can help students to retain more instructional content by incorporating brieft Peer Guided Pause sessions into lectures.

During each Peer Guided Pause, students are given a worksheet that contains one or more correctly completed word or number problems illustrating the math concept(s) covered in the lecture. The sheet also contains several additional, similar problems that pairs of students work cooperatively to complete.

• Students monitor their understanding of lesson concepts.
• Students review the math model problem
• Students work cooperatively on additional problems
• Students check their own answers.

http://www.interventioncentral.org/

Math Art Projects

While the connection between geometry and art is very strong (particularly similarity and symmetry), we are looking for projects that connect a broad spectrum of mathematical topics to artistic projects.  In our call for projects, we are motivated by topics taught in a “liberal arts math class” – classes aimed at students in the humanities to satisfy a quantitative or mathematical requirement. 

Guiding principles for activities:

• Intrinsic math: For all projects, the mathematical content should be intrinsic to the activity.  That is, the mathematics should be a natural, integral part of the artistic project rather than an added, superficial aspect
• Transference: In all cases, there should be a clear indication of why the student should find the mathematical content useful and/or interesting.  There should be an expectation that students will be able to transfer the skills gained from the project to other parts of their lives.
• Analysis/creation balance: In all cases, we are looking for a balance between analyzing art and creating art.  Students should have an opportunity for both activities. 
• Connections to professional work: When possible, there should be documented evidence of artistic work related to the activity. 

Artistic content should have an opportunity to experiment with style, medium or other aspects of artistic content.  The following list of projects provides a sense of kinds of artistic activities my class envisions:  Celtic knots, conceptual art, Dahlia designs, fractal design, Frieze and wallpaper patterns, Inca quipus, Islamic tilings, kaleidoscope design, mosaics, Kirigami (paper cutting), logos and symbols, network schematics, Origami (paper folding), polyhedral sculpture, sona sand drawings, and Temari balls.  Links for great ideas to get started on your math art projects are listed below.
http://www.princetonol.com/groups/iad/links/artlessons.html (High school)
http://www.education.com/activity/middle-school/arts-and-crafts/ (Middle-school)

Math Aerobics

The purpose of doing math aerobics is two-fold. First, you create movement opportunities and engagement for students. Plus, you can give students math facts and have them respond using their bodies instead of giving verbal answers. This makes a great transition activity for any time of day.

Below is a featured YouTube video that has no words, but I can assume that this is a great way for students to learn about lines and properties of lines using aerobics.  You can see the gestures the teacher does when she encounters parallel lines, perpendicular lines, parabolas, and you could extend this great activity further if you wanted to.

Math Tic-Tac-Toe

Tic

The activities vary in content, process, and product and can be tailored to address different levels of student readiness, interests, and learning styles.  The center square may be left open for the student to select an activity of their own. Tic-tac-toe activities may be given to every student in the class, high ability students for extension activites, or lower students for review and practice.

Some websites that are great for math tic-tac-toe examples and in-depth articles:

http://daretodifferentiate.wikispaces.com/file/view/tictactoe.pdf

http://www1.cbsd.org/sites/teachers/middle/csikora/DI%20Handouts/Choice%20Boards%20Packet.pdf

http://sites.google.com/site/mssowerssuperstars/news/tiic-tac-toe-homework

-tac-toe, also known as Think-tac-toe, is a differentiation tool that offers collection of activities from which students can choose to do to demonstrate their understanding. It is presented in the form of a nine square grid similar to a tic-tac-toe board and students may be expected to complete from one to “three in a row”. 

Math Icebreakers

At the beginning of the year, you want to create a sense of community.  That each classroom should be their own little microcosm, but sometimes they are not, sometimes schools are so large that all students don't know the names of people in their class or their entire school (this was shocking to me).

Math Icebreakers are a great way to get students interested in math in the first few days of school.  But, before I get started on a few of my favorites, I am going to give you a list of links, not too many, but im not going to list 300 icebreaker games you can play with your students in one blog post.

http://www.educationworld.com/a_lesson/lesson/lesson074.shtml (Good)
http://adulted.about.com/od/teachers/tp/warmupsforlessonplans.htm (Better)
http://www.ehow.com/list_6559009_math-icebreaker-games.html (Great)
http://tips.atozteacherstuff.com/220/icebreaker-activities-getting-acquainted/ (Good)

Math About Me
Students create Math About Me sheets. The Math About Me information might include birthday, address numbers, phone number, sports number, favorite number, number of pets, number of people in the family, etc. When the students gather together to share their numbers, they see what numbers they have in common with their classmates, and everyone learns a little bit about one another. The numbers are then used to make a Math About Me poster. I take a snapshot of each child for the center of the poster.

Fizz Buzz
Is a fast pace and silly way to help kids relax, and forces players to quickly analyze a number in several different ways.  It helps push certain multiplication facts in to long-term memory by associating them with strong emotions.  Students stand in a cirlce and one student begins by picking a number from 1 to 99.  The next peron in the circle says the next number in the sequence, and so on.  However if a number has a five in it or is divisible by 5, the person must say "fizz" instead of the number.  And if a number has a seven in it or is divisible by seven, the person must say "buzz".  For example the number 35, you would say "fizz buzz". You continue until you run in to a mistake.

Using Humor

"A good joke is like a good math problem... the punch line is unexpected, and you have to think to get it."

Education is about relationships and humor facilitates social interaction.  It can also portray math as a fun topic.  Children laugh 400 times a day, adults laugh 15 times.  Most teachers think humor causes rowdyness and chaos, but humor can do more for students such as reducing anxiety, lowering blood pressure, motivate and energize, and students will have better retention for information.  It does more than have physical effects, but also psychological benefits as well, it hones prediction and decision making skills, improves communication, and develops a positive attitude. 

Classrooms can lose control if a classroom is a joke-fest, but 2-3 well placed jokes creates a friendly environment.  A couple rules I have of humor in the class is never be hurtful or offensive, make humor relevant, and laugh at yourself. 

A common classroom activity that I have adopted overtime is:

1. Pick a common cliche.
2. Modify the cliche to make it silly.
3. Write a story to set up the modified cliche as the punch line of a joke.
4. (I try have the students incorporate math terms or concepts as well)

An example is:  One-Half was chatting with a blue jay, but One-Half could barely hear what the blue jay was syaing.  "Speak up!" yelled One-Half.  The problem, of course, is that fractions speak louder than birds.

A great website I found is: http://mathjokes4mathyfolks.wordpress.com/

(Most of this information can be found on NCTM website, under e-seminars.  It is called Using Jokes and Humor Effectively in the Mathematics Classroom.)

Award Certificates

Everyone loves to be recongnized.  Yes, writing good job at the top of a long paper or getting a good grade on a test is a great way to be recongized, but those tests get thrown away and lost forever.  Math award certificates are a great way to show that you care about your students.  There are links below for free printable certificates that you can create for your students. 

http://www.hayespub.com/wtemp.php is a website that gives templates in microsoft word.
http://www.123certificates.com/math.php are math certificates you can use for the you can use for math contest winners, best mathematician certificates, math awards to print for kids, most improved math student, completing math worksheets, or other mathematical success.
http://www.123certificates.com/ has more formal math certificates for end of the year graduation type templates.

Completing the Square (Geometrically)

As teachers how many of you know how to complete the square on an equation?  Quite a few I am guessing.  How many of you know why you complete a square? Probably less than the first question.  Can you represent completing the square geometrically?  OH, Yes! Below features an activity guide using geometry to portray completing the square.  Normally after we do the complete a square as a regular lesson, we go over what it looks like geometrically the next day.

When you have students see the geometric way after going about and doing the algebraic way, it helps students memorize and visualize what completing the square is and it is a small fun acitivity that you can change to many different ways and levels.
Completing the Square (Geometrically)

TouchMath

TouchMath is a multisensory program that uses its signature TouchPoints to engage students of all abilities and learning styles.  Each numeral 1 through 9 has TouchPoints corresponding to the digit's value.  Numeral 1-5 have single TouchPoints, numerals 6-9 have double TouchPoints, as students count the TouchPoints they associate numerals with real values.  They learn that a number has a meaning and is not just a squiggle on a page. http://www.touchmath.com/

I have been trying to adapt TouchPoints in to higher education, so far they only have activities until general math (multiplying and dividing), but I am sure I can come up with represenational ways of higher mathematics using TouchPoints.  If anyone has any suggestions, please don't hesitate to comment below.

Touch Point Math

Math Tattoos

Just to make sure, I am not one for getting tattoos or condone anyone getting a tattoo.  But I had to share some remarkable tattoos.  A few are featured below:

Sharon is an undergraduate math student at Arcadia University. A while ago, I decided that I wanted a tattoo that showed my love for mathematical formulas and equations. I got the quadratic formula on the back of my neck. The quadratic formula has been my favorite equation ever since I learned to sing it to the tune of “pop! goes the weasel.” My tattoo is also useful for anyone who happens to sit behind me on an exam!”

A Ph.D. student studying maths in Australia. The the tattoo on the top, I got about three years ago in Berkeley, CA. The other tattoo I got about a year later in Sydney, Australia. Both these tattoos are closely related to the research I’ve done for my Ph.D., which is in the area of elliptic partial differential equations. The top equation is called the Monge-Ampere equation and is the archetype of the equations I currently study. The bottom equation is called the ‘Infinity Laplacian’ and was chosen because it is correlated to variational theories which I find to be beautiful.

A Mechanical Engineering undergrad at UC Berkeley and  got this tattoo about a month ago. It’s the golden ratio in the shape of a rectangle, with the ratio of the sides of the rectangle actually being the golden ratio! I have been obsessed with this number since I heard about it in high school, and it is the reason why I became so fascinated with mathematics. The golden ratio is known to be the closest mathematical explanation of beauty.

Math Without Borders

Found a great lesson idea that incorporates vocabulary.  Copied straight from http://www.weareteachers.com/ideas/partnerask/teachingidea?app=9503&grantId=43 the site We Are Teachers I have found recently has been a great website that has some of the best teacher ideas and connections across curriculum. 

Students will be using their skills in language and mathematics to create math concept books for a sister school. My class is a majority second language learners and they love finding ways to reach out to other cultures. We will be creating illustration modeling the math concepts and adding the text to help students in another country who have few or no books to help them learn math in engaging ways. The books will be presented at an author signing and celebration/family math activity day.

Students will learn to write clear, engaging sentences expressing mathematics concepts for other learners. They will connect these written concepts with visual models as they create their illustrations. Students will have the option of photography and manipulatives to further illustrate the concepts they are learning. They will also have the opportunity to present their book as a lesson to an appropriate grade in our school as a pre-publishing check for clarity, quality, and feasibility.

Students have been studying how to be productive citizens in a global community. With our sister school and with other lessons we have been looking for ways to share with other students around the globe. Writing about math concepts will help my students become more solid in these concepts as well as allow them to share in the excitement of publishing a quality product for other students. Project based learning has proven to be very effective in my diverse, multi-lingual class.

Flatland

But, this is a free prize post!!  Comment below with your name and address and you can get a copy of Flatland: A Romance of many Dimensions. 

In my classroom (specifically geometry), normally I print off a section of Flatland: A Romance of many dimensions.

Place a penny on the middle of one of your tables in Space; and leaning over it, look down upon it. It will appear a circle.But now, drawing back to the edge of the table, gradually lower your eye (thus bringing yourself more and more into the condition of the inhabitants of Flatland), and you will find the penny becoming more and more oval to your view; and at last when you have placed your eye exactly on the edge of the table (so that you are, as it were, actually a Flatlander) the penny will then have ceased to appear oval at all, and will have become, so far as you can see, a straight line.The same thing would happen if you were to treat in the same way a Triangle, or Square, or any other figure cut out of pasteboard. As soon as you look at it with your eye on the edge on the table, you will find that it ceases to appear to you a figure, and that it becomes in appearance a straight line. Take for example an equilateral Triangle - who represents with us a Tradesman of the respectable class. Fig. 1 represents the Tradesman as you would see him while you were bending over him from above; figs. 2 and 3 represent the Tradesman, as you would see him if your eye were close to the level, or all but on the level of the table; and if your eye were quite on the level of the table (and that is how we see him in Flatland) you would see nothing but a straight line.

Normally I do this before we get to three dimensional shapes, it shows that students that there are different ways of viewing the world. The world we are hearing about is the 2nd dimension, we live in the the 3rd dimentions, is there a 4th or 5th dimension? How many dimensions are there?

This mini-lesson helps students think critically and begins them on their way of becoming great mathematicians. In my classroom, I like to think that everyone is a mini-mathematician and some of the hardest math problems are some of the easiest thinking problems.

Teaching Tips

Recently I have found a website with great teacher tips for teaching.  http://www.nea.org/tools/BrowseAllTips.html  some of my favorite tips that I saw are:

Park Your Questions:  I have a poster-sized piece of paper decorated with yellow parking stripes. The poster is labeled "Parking Lot." There are usually a short stack of sticky notes near the poster. When those random questions come up, I (and sometimes other students) just say, "Parking Lot." Students know to bring up their pencil, jot the question down, and we'll address it when there's time.

Stocking Your Class Library:  It was only in the last few years of my teaching career that I truly felt I had enough variety in ability and interest level for my classroom library, thanks to the Reading a-z Web site.

The website also has Teaching Strategies: http://www.nea.org/tools/TeachingStrategies.html
School life: http://www.nea.org/tools/SchoolLife.html
Classroom Management: http://www.nea.org/tools/ClassroomManagement.html
Lesson Plans: http://www.nea.org/tools/LessonPlans.html

At the National Education Association, they put the best ideas and strategies for students and their master teachers are the ones that are putting lessons out for upcoming teachers.  The site only offers about 57 different lessons for mathematics, though.

Math Trading Cards

There are different types of math trading cards: vocabulary, history, and concept cards.  These are great ways to build a foundation of mathematics and math understanding.  This gives students meaningful ways to practice and comprehend word definitions.  Words I include on some of my math trading cards include: array, symmetry, polygon, congruent figures, parallel lines, and sphere.  This practice helps students practice, develop mastery, and retention of math skills.

http://mathscience.mt.gov/MSICards/cards.htm is an article where the govenor of Montana gave math and science cards to students as they travel across the state.  The cards included facts and statistics about Montana history.  Below features a youtube video of Xeko is an adventure game for children and students.

(Move in about to 1:30)

Google Forms

Google forms is a great tool for for educators to use and get great feedback from students quickly.  Teachers who use google forms know that it helps get information from students and checks for understanding.  If you have a google account, on the top or under the drop box there is a tool called documents, click documents and select the button to create a new document select forms and I made a survey for a journal article I have done for gender equity in the classroom.

When students or teachers submit a survey, the survey is sent to a ready-made excel document with the title of the question at the top and the side is timestamps of the number of students.

Happy Teaching!

Multicultural Mathematics

In this post, im going to hit you with a lot of information about culturally and linguistically diverse learners (CLD).  Mathematics offers a great challenge to CLD learners, challenging them with its own symbols, syntax, and vocabulary. 

Links below feature online lesson plans and materials for CLD students.

http://www.wfu.edu/~mccoy/mathstuff.htm is a site with lessons, technology, history, and diversity.

http://www.teachersdesk.com/lessons/lessons_math.htm presents lesson plans in english and spanish.

http://math.rice.edu/~lanius/Lessons/ presents fun interactive math lessons, many in spanish.

http://www.esc4.net/default.aspx?name=math.home holds a host of support material for CLD students.

http://www.todos-math.org/ dedicated to helping the mathematics education of CLD students.

http://a4esl.org/ Quizzes, tests, exercises and puzzles to help you learn English as a Second Language (ESL)

http://homepages.rpi.edu/~eglash/csdt.html helps students learn standard based curriculum as simulate original artifacts.

http://recursostic.educacion.es/descartes/web/matemagicas/index.htm spanish mathematics page

Multicultural Books with a Mathematical Theme:
A Million Fish... More or Less Patricia McKissack  Native American
Anansi the Spider: A Tale from the Ashanti Gerald McDermott  African
Arrow to the Sun Gerald McDermott  Native American
The Balck Snowman Phil Mendez  African American
Grandfather Tang's Story Ann Tompert  Chinese
The Paper Crane Molly Bang  Asian
Something Special for me Veria Williams Latino
The Rajah's Rice Dave Barry  Indian

(Kane Press at http://www.kanepress.com/ has created the Math Matters Series of Storybooks in Spanish)

Values of Pi

The refinement of Pi is an interesting exploration.  Early societies used 3 as the circumference/diameter ratio, but soon different cultures extended the value.  In my classroom one of the group projects I have during the year is students report on methods used by these mathematicians and their cultures.  They could also compute the circumference of a pool or traffic circle to discover the margin of error for early pi values.

Approximations of Pi throughout history

2200 BC     Babylonian     3 1/8
1650 BC     Egyptian        (16/9)^2=3.16
250 BC       Archimedes   3.14099<Pi<3.142826
150             Ptolemy         3773/130=3.1466
263             Lui Hui          3.14159
1200           Fibonacci      3.141818
1424           al Kashi         16 digits

Multicultural Math Fair

A multicultural math fair is one way to display mathematics from different cultures.  The fair could be held within a single classroom or involve an entire school.  Students could work in small groups to present their projects.  The fair might be open to parents and community members in addition to the school community.

A good place to get ideas for example math fair activities can be found here:

• http://math.youngzones.org/MathFair.html
• http://www.galileo.org/math/puzzles.html
• http://mypages.iit.edu/~smile/mathinde.html

Happy Teaching!!

Geometers Sketchpad

Sketchpad gives students a tangible, visual way to learn mathematics that increases their engagement, understanding, and achievement. And it’s not just for geometry. Use it for elementary and middle school math, algebra, precalculus, and calculus.  Sketchpad’s online Learning Center provides videos, tutorials, tip sheets, and additional resources to help you quickly learn the software. To learn even more, try our webinars, online courses, and in-person teacher training.  You can now get the Sketchpad Explorer iPad app to interact and investigate any mathematical document created in Sketchpad.  Sketchpad Explorer also comes with ready-made explorations, so you can dynamically manipulate visual mathematical representations to investigate concepts in elementary mathematics, geometry, algebra, trigonometry, and even calculus.

Sketchpad offers ready made classroom activities listed here: Classroom Activities

Sketchpad also offers proffesional development for teachers: Professional Development

At Risk Students

Why do students struggle with math, there are many different answers to this question such as: special needs, math anxiety, reading deficits, gaps in basic skills, language and cultural differences, family issues, and difficulty focusing or maintaining concentration.  Most of these are obstacles no teacher can overcome, but sometimes there are situations teachers can prevent or change to have students have a more positive impact. For example:

• Cluttered handouts, tests, and quizzes.
• No room for answers.
• Writing in cursive.
• Presentation materials that are too small.
• Poor graph paper.
• No routine.
• Readability level of teacher generated material.
• Class notes.
• The "Welcome" mat is not out.
• IEP accomdations and modifications are not met.

Math Bulletin Boards

Every good teacher knows that the walls are prime real estate, the place where you reinforce rules and routines, encourage students to do their best, and celebrate everyone's achievements. Too often bulletin boards are just thought of as decoration, when they really should emphasize the learning that is taking place in the classroom.

• Be interactive and make the classroom "come alive" with the curriculum material being studied.
• Give students a sense of ownership of the classroom by surrounding them with examples of their work.
• Be mostly created by students.

Having interactive boards lets the media specialists and students use library materials to create questions and quizzes and develop entertaining ideas that will hopefully attract more patrons to the library media center. When you put something on your bulletin boards that presents a challenge to students, they get interested in meeting that challenge.

An excellent bulletin board is one that makes students think. That can be as simple as a thought of the day or as complex as an interactive lesson in bulletin board form.  For example: introduce concepts, prove a place for a daily review of concepts, provide information about seasonal topic that the classes might not be studying.

A great link for secondary math bulletin boards can be found here: http://faculty.kutztown.edu/  

Metaphors

Metaphors can be a powerful tool to help students make connections between new material and ideas with which they are already comfortable.  Whether student created, or teacher created, metaphors help expand thinking sills and help students make meaningful and important bridges of new and familiar ideas.

Metaphors involving “warm” and “cold” evoke a sensory experience, and so could be called an image as well.  In math education, the phrase “concept image” means the mental structure associated with a concept, so there may be no direct connection with sensory experience.   I will usually use the phrase “metaphors and images” to talk about all our mental representations, without trying for fine distinctions.

Happy Teaching!!

Sona

Sona designs of the Chokwe people of Angola and the Congo are a particularly attractive form of mirror curves.  These curves are drawn through a lattice of dots, bouncing off edges of the lattice.  Most designs are drawn as a single, uninterruped line and containing some symmetry.  The mathematics of the designs reflect issues of common divisors of numbers, Eulerian cycles, and symmetry groups.  The Chokwe people of Angola and Congo have a drawing tradition, done both in sand and on more permant objects. 

GCD investigations are discovered through experimentation.  In my classroom during the end or beginning of the year I would give a station that had a sona and pose a few of these questions.

• If a single dot is erased from a corner of a rectangle, when will the resulting sona be monolineal?

Answer: If, and only if, the rectangle dimensions have a gcd of 2.  meaning the dimensions of the rectangle saym x n will give a monolinear sona when they have no common factor or when the gcd(m,n)=1.

More questions and information you need is posted here: www.beloit.edu//Sona_BridgesWorkshop.pdf