21st Century Learning

21st Century Learning occurs around the core subjects: reading, writing, and math.  The 21st century skills occur when the teacher or classroom ties career skills, critical thinking skills, and technology into the core subjects.  These have more connections in the 21st Century classroom by standards, curriculum and instruction, professional development, and the students learning environment.  Featured below are 3 different 21st Century Learning tools you can include in your classroom.

Virtual Environments
An understanding of complex causality is a necessary foundational skill for advanced science and mathematics. Ecosystems science, an important strand of the life science content standards, requires an understanding of complex causal relationships. However, even after instruction, students often retain inaccurate interpretations about ecosystems’ structural patterns and systemic causality. To address this issue, we are developing a Multi-User Virtual Environment (MUVE)-based ecosystems science curriculum called EcoMUVE, based on middle school life science standards.


The goal of this new curriculum is to immerse students into virtual environments to help students develop a deeper understanding of patterns that have the feel of video games.  Such as SecondLife.
http://ecomuve.gse.harvard.edu/
http://wowinschool.pbworks.com

Google SketchUp
Google SketchUp is 3D editing tool that can be used to design basically anything you can see.  Area, Perimeter, and Volume concepts- Download a living room and create story problems for students to solve based on the dimensions in the room. Or you can have students create problems for their classmates to solve in a blog or wiki. Trigonometry- Ever wonder why the proofs in trigonometry work? Have students create triagles and predict the lengths and angles using trigonometry formulas. Prove concepts in class.Technology Education- Students design a room based on a blueprint they create in the classroom. Design objects in Sketch-up and allow students to find missing angles and measurements. 
http://edupln.ning.com/google-sketchup-math


Project Based Learning
PBL is a method of instruction that can help engage students in active learning by providing relevant, challenging curriculum.  The focus is to foster an understanding of project-based learning, particularly in mathematics education; to explain the factors for making a conscious decision to implement PBL in middle grades mathematics classrooms; and to provide insights about the possible realized effects when mathematics-based PBL is implemented.  The characteristics PBL holds is that students and teachers are engaged in active learning, curriculum is relevant, multiple learning approaches to student diversity, and assessments that promote quality learning.
http://www.bie.org/project_based_learning_in_mathematics

Using Google Apps

Self Grading Rubrics
Using Google Forms you can create Self Grading Rubrics.  When you create a new Google Form, I have my  students add their period along with their first and last name as the first part of the self-grading rubric.  Then you are ready to start the questions.  Using the rubric from a project, you have students answer questions about the rubric and how they did accordingly.  Here is a how-to video about how to create self-grading rubrics Self-Grading Rubric

Digital Kits
Digital kits are nothing more than collections of content: still images, video clips, audio clips, passages of text - connected to the topic being studied that teachers assemble for their kids before a project even begins.  Then, students use the content in digital kits to assemble their final products.  When you search for images directly in Docs, Google ONLY returns images that are licensed for reuse and modification.  For more information and a step-by-step tutorial you can click on the link: Digital Kits


Test Feedback
State Standards and NeSA scores in the state of Nebraska are what teachers are worried about and students brains become fried when the week of NeSA testing is over.  However, to make your lives a little easier there is a way to use Google Spreadsheet to input grades for all of your students and should take about 15 minutes to complete. When students have access to the spreadsheet, they input the marks that they received for each question. Each question has been given a category. Once all the marks have been input, the relevant percentages for each category are displayed, giving an indication of strengths / areas for improvement. Here are some screenshots of the spreadsheet.

Observation and Attitudes

Student, teacher, and even parent attitude all are what students are affected by on a daily basis.  If your friend doesn't like Coldplay, neither will you.  But, if your parents feel like math isn't something you need then you wont excel at it either.  Students, teachers, and parents play a primary role in what students want to learn.  Everyday I try to bring enthusiasm for math in to the classroom.  I feel like math is a great tool that every student needs.

The first is observation of students: I care for my students.  Caring is one of the ways to express yourself in students.  For instance, she can tell if a student in the back has done his/her homework by his facial expression and body language.  Teachers must know the students well.  Find a link to this article with more examples and more in-depth knowledge: Effective Teaching Observation

Attitudes from the parents: Experts in research and policy have examined different ways to enhance and promote STEM education, but most of these efforts are focused in the classroom. A new study published states that STEM needs to go beyond the walls of the classroom to examine the unique role parents play in promoting STEM motivation.  Many math and science classes are not required after the first two years of high school.  Student enrollment may be a fundamentally important issue than student motivation, but the findings provide evidence that interventions with parents could be a useful tool for boosting enrollment in STEM courses and could help close the gaps in student enrollment that result from differences in parental education.  For more information follow the link here: Get Teens Interested


Attitudes from the teachers: All teachers feel differently about the use of technology, based on a survey 67% of teachers use technology in every class and 85% of teachers use it every day.  The main skepticism is proof that technology tools provide real value for student learning.  Teachers choose to use technology to help their students; they believe technology can help bolster engagement and find richer context for their studies.  Teachers who are not comfortable with technology are making a stronger push in school districts than teachers who are tech savvy.  Teachers biggest complaints are: access to computers, personal comfort levels, time for planning, students' access at home, lack of training, and knowledge of effective software programs.  But, I have seen teachers out-right refuse to use technology or receive technology training from those who offer it, but as we move to better access to technology, the only re-occurring excuse is time and as a teacher you have to make time for personal development.  Even if it means sitting down on a Friday night looking over Khan Academy, the small time you put in provides large benefits for your students.  For the link with more information than I provided check out: Teacher Attitudes


For those teachers who actively pursue new material on Twitter, Professional Learning Communities, EdCamp, and rarely Pinterest; I applaud your dedication you make to your students.  I believe that you are the rarity in schools and the best 1% of any school district.  In my opinion you deserve more gratitude than you receive.  You and I both know that this hard work will pay off, because the other 99% will give up and you will succeed!

Storytelling in Math

There are many different ways you can use storytelling in math class, featured below are three distinct ways you can use storytelling in the classroom and there are web 2.0 tools and extra technology that you can incorporate to make the storytelling more fun and engaging.

Using QR codes
QR codes can be integrated into a larger instructional strategy that incorporates game play and storytelling.  QR codes are a fun way to get learners to explore stories in non-traditional locations.  You can require to watch a story and solve a problem.  Learners can be required to text answers to a mystery question when they read the QR code.

This QR code takes you take this video.  Which is the Number Devil: Chapter 1.  You can have multiple QR codes attached to questions that the students are suppose to answer.  You can create this with any video and any QR code generator.

Create Your Own Story
Have students create their own story about the previous chapter.  You can create a rubric for you students to use and have them go through a story problem for the previous chapter have them work it out and then have a character in the story come up with the answer.  You can have students use story rules that sound close to mathematical exploration.

• Come up with the ending before you figure out the middle.
• When you're stuck, make a list of what wouldn't happen next.
• Pull apart the stories you like.
• Take apart movies you like and rearrange them.
• Keep in mind what's interesting to you as an audience.
• You admire a character for trying more than for their successes.

Working backwards, like proofs, helps you understand by working on details that used for problem solving and exploration in math class.

Extra Resource: http://web2012.discoveryeducation.com/Digital-Storytelling

Using Google Doc's

Have students use Google Doc's and presentation to come up with a story like the comic strips.  Students create a story that goes over a particular story problem.  Students can use Google Doc's to write out a scripts and even use Sock Puppets (which is a free presentation application for the iPad).  Students can share the script with the teacher and even collaborate with the teacher on particular ways that the story can go.  The best thing about this is, I am horrible at English and writing papers, but the students can send a link to collaborate with the English teacher and they can work together cross curriculum to help them with their story.

Determining Educational Games

One of the best things that game-based learning is bringing back to the education reform discussion is the value of play and a playful approach to learning. he value, here, is in encouraging learners to “play” with ideas.  In doing so, the idea of failure is either not possible or is an accepted part of the process.  Using this sort of approach also provides learners with opportunities to test ideas and hypotheses to solve ill-defined problems.  Though an integral part of game-based learning, it’s a only a component of the bigger picture.  


The most important thing to determine about games, is it a simulation or a game?   Simulations provide experiences through which participants experiences concepts, but they lack the elements that games bring to the learning process.  The definition of a game is a system in which players engage in an artificial conflict, defined by rules, that results in an quantifiable outcome.  You can find more here.


If you want to know why people get addicted to games, it’s probably this: games are filled with rewards.  Earning rewards is what keeps us going. Extrinsic rewards (a certain number of points, a flashy animation, or a grade on a report card) fail to compel gamers.  Intrinsic rewards, or rewards that once gained allow you to play the game better, compel gamers immensely.  Unfortunately to design true, educational games, we are stuck with a major throwback.  Kids (and adult gamers, mind you) are wary of something labeled an “educational game.”  Fore more information you can find it here.


To know what is quality material for educational games and game play, there are 5 steps a teacher can use to evaluate educational games.

1. Define the Learning Objective: for math games I started with State Standards and looked at what students needed to know.
2. Describe the Learning Mechanic: The learning mechanic represents the actions we want students to take that will reinforce the learning objective.  If our primary learning objective was to improve sped and accuracy then we would want the learning mechanic to include an element of time.
3. Imagine what the students are Thinking: What do we want going through students' heads as they are playing the game.  
4. Pick a Game Mechanic: This is different than the learning mechanic, the game mechanic are professional designers of games.  Certain designers look and use different teaching strategies to use in their software. Look at many different examples and when you seem comfortable with one, use that one across the board.  It also comes in handy if you have questions about the game!
5. Create a Theme:  The games worked from a mathematical perspective and our student testers seemed to enjoy them. They were thinking the thoughts we wanted them thinking. However, we wanted more engagement, and a bit of whimsy to bring a smile along with mathematical challenges. Our creative artists threw out a bunch of wacky ideas.   We’re working to build educational games, not games with some education tacked on. Keep that in mind as you look at the educational game options for your students and children.

Feedback, Engagement, and Alternatives, Oh My!

Feedback
Kids that would leave any worksheet blank are asking for more problems. It really has been a fantastic transformation in my class.  The answer is immediate feedback to all students, not only the ones that will raise their hands and ask "is this right" has changed my classroom.  They are working harder and doing more problems, they are trying and building confidence. Why? Because they know immediately if they have the problem correct. And they love it. Can we do this on the computer is always asked.

After some confidence is gained there is still so much value in getting them able to do the work on paper. And being able to finish something that they started is so valuable (even with out the feedback.) But getting to that point has been so much easier in my Algebra 1 classroom with the help of the computers and two simple, free, online programs.


http://algebra1teachers.blogspot.com/2012/06/immediate-feedback-increases-math.html


Engagement
Three words seem to be dancing around in my head of late when it comes to current thinking about education: “personalization,” “engagement” and “flip.”  We don’t need personalization as much as we need to promote and give opportunities for our kids to do personal learning. And while they come from the same root, those two words are vastly different. “Personalized” learning is something that we do to kids; “personal” learning is something they do for themselves. In a world where we can explore almost every interest or passion in depth on our own or with others, it’s crucially more important to have the dispositions and the skills to create our own educational opportunities, not be trained to wait for opportunities that someone else has selected for delivery.


http://missnoor.visibli.com/share/xNXcjo


Alternatives

It used to be so much simpler. When asking a student to display mastery of some material, a professor would ask for a 10 page paper. The student would research the topic, type up the contents, maybe include an image or graph, add the bibliography, and turn the paper in. The professor would walk out of class with a stack of papers to grade. This was all so predictable.

Well, not any more. The opportunities for displaying mastery are probably limited most by the professor’s imagination more than either the students’ abilities or the technical tools. Here I will go through some of the ideas for new types of projects that have crossed my mind recently as I have been planning my courses.

http://www.samoore.com/2012/07/05/digital-alternatives-to-written-report/

The Chimera Prophecies

The Chimera Prophecies by Elliott Ostler

My rating: 5 of 5 stars

Great math book, not all mathematics, but introduces higher education in to a real-world setting. It has the pace of Dr. Horrible's Sing along Blog with Limitless. It is a fast-paced read with twists and turns everywhere. I know the author of this book personally and it reads as he teaches, fast paced and he explains everything in detail.

For teachers it is a great way of incorporating mathematics (especially higher mathematics) in to the curriculum.

View all my reviews

When a subtly brilliant mathematician known only as Number Six discovers a way to mathematically predict human behavior, the simple life that suited all his academic interests changes forever.  Evil men seek to obtain his formulas, and the young mathematician is forced into a life and death intellectual battle with the very company who employs him; a company consumed by power and driven by spite and greed.  Operating in secrete, Number Six explores the dangerous options that brings him face to face with a question that challenges the core of his beliefs... can mathematics provide a solution to every  problem.

Twitter for Classrooms

I've seen the and even re-pinned the twitter classroom door and twitter classroom bulletin boards which is great for the classroom.  If you going to use the brand name and the same concept of twitter, why not use Twitter in the classroom.  Even though most schools are reluctant to use Twitter there are many different tools and uses of Twitter that go beyond the classroom and into the classroom.

Geometry through Twitter
So now what? I had a Twitter account, but what should I tweet? A few days later I found myself at the Texas Rangers baseball game thinking about a problem we had done in class about finding the location of the perfect bunt a few chapters back. Hey, I wonder if the students really learned anything from that chapter and remember the answer? So I took a picture of the field and tweeted it out asking the students for the answer. I was shocked when only minutes later I had several replies. I was so excited.  Link to article.

Using Twitter to engage students in and out of the classroom is a great idea and using the homework to post extra problems for a "surprise" or using them as quiz questions is a great way to introduce twitter into the classroom.


Classroom Communication
Twitter can benefit your classroom by using it as a means of communicating assignments and homework. If you and  your students have a twitter account, then you can use Twitter as another means of reminding students of their assignments. Also, you will want to use hashtags to denote the purpose of the tweet. If the tweet is an assignment, then use #assignment or if it is homework, then use #homework.


Using Twitter for students to know what homework is due or any changes you may make to the homework is a great way of publishing and using Twitter as a communication device to the students outside of the classroom.


Managing Twitter
Twitter has become a powerful tool for teachers, the community, and others who want to share and receive information in a fast, friendly environment.  Twitter, using the tool to connect students, share information with parents, and finding useful resources.  Here is a link to 100 tools for the twittering teacher. http://www.bestcollegesonline.com/top-100-tools-teacher/


Finding Resources
This is the biggest part of why I use Twitter.  Using hastags such as #mathchat and #edtech I use these hastags to search for what other teachers are using in their classrooms.  If they worked for one teacher, they must work for another teacher.  Using this is my own type of PD, where I can find material or interesting activities that I can use in the classroom that are ready to go.

Tech-Shy Students

I use to think that all students know how technology works and since I love using different types of technology in the classroom, that all students of the high school and middle school setting love using technology in-and-out of the classroom.  This may not be the case for some students who either can't afford high-end technology or have other means.

Encouraging these students to become more comfortable using technology is vital, in order to prevent them being left behind by the educational technology bandwagon. Moving education on in new and exciting ways is fantastic progress, but it is vital to make sure that nobody is being left behind. It would be tragic if the advancement of education technology meant a growing learning gap between the most privileged pupils and the most disadvantaged.

1. Identify tech-shy students: students who don't know much about computers and technology might be much more shy and embarrassed about it.  Observe students and pair them up with students who have a deep understanding of technology.  Once you identify the students who need help, your in a position to get them the resources they need.
2. Partner Up: Allowing students to teach each other is a great way of encouraging correct communication skills.  It allows the students to look like they don't need the extra help, even though they are getting it.  It normalize the situation which allows learning to take place.
3. Encourage Device Sharing: Even though BYOD (Bring your own device) seems common-place inside school districts allowing students to bring in their own devices and share them makes sure everybody has access to the same resources.
4. Use Simple Resources: Students who use technology everyday use complex, high-tech programs to get their information, which is great, but students who are just learning to use technology and the material need less complex online resources that are easy to navigate.
5. Praise: As with any new skill, students who are learning how to use technology in the classroom for the first time need plenty of praise and encouragement to celebrate their achievements and stay positive.  Not one child needs to be criticized of using technology, if they turn off of technology because of it then it will be harder later on to turn them on to it when you are trying to complete projects or assignments.

More information can be located here: http://www.fractuslearning.com/encourage-tech-kids/

Located below are two great resources for emerging technologies and technologies set in place that teachers can use to engage and motivate students to use technology in their classrooms.

http://www.onlineschools.com/blog/top-10-emerging-technologies-in-education

http://njtechteacher.blogspot.com/2012/07/teaching-math-four-years-later.html

Standard Badges

Today, I will start with a quote. "A number of initiatives and start-ups are hoping to offer ways to give people some formalized recognition for their informal learning- or at least the skills they possess for which they don't have official diplomas or degrees, such as Open Badges, Degreed, and LearningJar."

This is due to the concerns of high cost of higher education.  Nowadays a college degree isn't necessarily the best or only indicator of a person's skill-set.  Badges create a potential for creating alternative forms of certification that would benefit more people more broadly.  Who will Benefit from Badges

I thought to myself, badges aren't a bad idea to incorporate to the classroom, not in a higher level education. Instead I would create badges about what I think the students should learn and I also create a few badges for State Standards.  There is an example picture below of one that I easily created in Google Draw and could easily upload to a Google Doc and print them off on to stickers.

When students take a test on a particular section of the test there are normally problem sets that relate to a particular concept you went over (hopefully!) and if the students met a particular master level or were proficient in that area I would attach a sticker to that part of the test (like the one below).

Next year, I am thinking about basing all grades on the stickers they receive since they should be meeting these proficient levels and be able to obtain all the stickers.  If you get 6 of the 7 stickers you would receive a 85% since they mastered that much of the material.  Then if they want to retake the test they would just need to retake the part they didn't master.

Substitute Teaching Math

Many people are not fans of being a substitute teacher at the high school level. This is because many substitute teachers believe that they lead the class either by intimidation or by being the class hero. Neither of these approaches work very well in high school. There are some simple guidelines that make most high school substitute teaching assignments work. For those who are making their first foray into this arena, these tips should give you help to get going in the right direction.


Here are some resources that a substitute can use in the math classroom.


http://www.educationworld.com/a_curr/curr359.shtml
http://www.educationworld.com/a_curr/curr157.shtml
http://www.educationworld.com/a_lesson/lesson/lesson220.shtml

Facebook Page

Hope all teachers are enjoying their summer and taking it easy before the new school year begins.  As the summer winds down more updates and changes will happen before the months end to prepare teachers for the upcoming school year.  With more updates Math Techniques and Strategies just created a Facebook page, the link is here: https://www.facebook.com/mathtechniquesandstrategies

We hope to be unveiling new guest posts.  More user responses to reach and accommodate all teachers.  You can follow Math Techniques and Strategies on Twitter and Pinterest.

After our first full year of blogging about education and mathematics our blog has evolved from a sweet baby to an adolescent teen.  Hopefully after this successful year we will have more success in the future and get the educational knowledge and news out to users more quickly.

Lastly, enjoy the rest of summer.  Have a great school year.  Happy Teaching!

Trever Reeh

Docs Teach

http://docsteach.org/ is a great resource for all teachers.  It uses primary resources from the National Archives for ready-to-use tools for teaching with these documents in the classroom.  It brings history to life!

Teachers can even create their own activities or find already made activities.  In no time at all I created this activity where students have to use their knowledge of the Louisiana Purchase to tell if the United States overpaid or underpaid for the land they bought.  http://docsteach.org/activities/11133

There are about 1000 pre-made activities ready to teach, most concerning History classes.  To sign-up it is free and a great resource to implement in the classroom, especially in the middle and secondary grades.

Higher Reading for Math

I believe reading above your grade level helps students expand their knowledge and when you go over a text with the teacher, lends itself to ask and answer questions (even if the teacher doesn't have the answers).  Having teachers who teach just not their subject areas, but reaching reading across the curriculum let's students know that reading is important.  This post includes reading strategies for math class along with higher level math texts that secondary math students can grasp, even though they are challenging reads.

Here are some reading strategies for math classrooms: http://sharepoint.chiles.leon.k12.fl.us/lcsreadingstrategies/Reading%20Strategies%20for%20Math%20Teachers/Forms/AllItems.aspx

A Mathematicians Lament
Two Cultures of Math
On Proof and Progress
What is good Math?
Truth as Value and Duty
Mathematical Knowledge
Birds and Frogs
Advice to a Young Mathematician
Who Can Name the Bigger Number

If you have any other suggestions for upper level reading for secondary students, feel free to post them below.  I only included PDF's that teachers can take pages from or use the entire article.

Models in Math

The use of models as an instructional tool is to teach abstract and complex concepts.  The focus is on the use of models in the mathematics classroom, although, this course is beneficial to teachers of all disciplines. Students often have a difficult time understanding mathematics and the importance of learning the topic; they simply memorize and implement formulas.

YouTube is a great site to find effective models of mathematical concepts.  You can find videos that involve math above.

Essentially, a model is a tool used to make learning easier by simplifying the target in some way. For example, a science teacher could use a diagram of a solar system to illustrate the proportional size of all the planets. What you are trying to simplify is called a target, and the simplified version is the model. In our example of the solar system, the target is the entire system and the model is the diagram.

There are different types of models you can implement in to the classroom.

Conceptual Models

• Conceptual models illustrate a concept, or "units of thought".  For example, a model could be used to represent a flood. A flood is a concept, because by itself 'flood' does not mean anything, but the category of flood is associated with its appearance, importance, images, personal experiences, and other weather phenomena.

Concrete Models

• The most common type of model is a concrete model. These are "tangible material models that we can generally interpret with relative ease."  A model airplane is concrete model because it is something we can physically touch, and most everyone will know that it symbolizes a real airplane.

Scale Models

• The purpose of a scale model is to look like the object we are representing. A blueprint is a scale model because the shape and size of each room is proportional to each other.

Function Models

• Functional concrete models are intended to represent certain functional relationships of their targets. They have relatively less emphasis on retaining scalar relationships and on accuracy of appearance. A classroom model is an example of a functional model. It is not intended to represent the solar system to scale is a very difficult thing to do in a classroom. Instead, this model's purpose is to illustrate the relative positions and motions of the sun, planet, and moon in relation to each other.

Similes, Analogies, and Metaphors

• These models are often used when it is important to make abstract ideas more concrete.

There are two main components of a model; the target and the analog. The target is the complex item, concept, or idea we are trying to represent. The simpler item, concept, or idea used to explain or the first is known as the analog. The similarities between the objects are the correspondence.

For a model to be effective it must:

• Be engaging for students: if students are engaged throughout the entire activity, they are more likely to understand and think about what they learn from the analogy.
• Require high-level thinking: models are effective when students create models themselves, explore and explain ideas, given time, and express high-level thinking.
• Be familiar and interesting to students: analogies that are familiar to students and connected to familiar things.
• Include multiple models to reinforce the same concept: incorporate several activities, analogies, and discussions.

Reducing Student Stress

Why do many students come to the school counselor? Why do students continually do poorly in certain classes? Why does sleeping in class seem to be an international epidemic? Why does the use of stimulants among students seem to be skyrocketing? One component in all of the above is student stress.

Often teachers confuse the affects of quantity versus quality, in the work they assign to students. Teachers tend to plan for covering the content of a course and achieving objectives or learning outcomes, but often fail to account for the innumerable distractions, interuptions, and teachable moments that put these best laid plans to waste.  Another common complaint; students assignments require too much time to do well. In order to achieve quality, develop critical thinking and problem solving abilities, and review and revise work, time must devoted to actually think, analyze, and evaluate; this time is often completely removed from an instructors frame of reference, when considering student assignments.  

How can we modify the effect of stressors on students? Usually, stress advice is given to those who are experiencing it's ill effects. In this instance, as educators, we are doing what we do best; taking care of our students.

Types of Stress Buffering Support that instructors can provide to students.

1. Informational support – offering suggestions and direction when students are confused. Being available for questions; proving feedback on student work prior to evaluation (and after) can all help alleviate students level of stress.

2. Instrumental support – helping students directly by allowing an extraday when students are overwhelmed, providing greater scaffolding when students become confused, etc. can bring great stress relief. Often teachers feel they are playing favorites and feel if they do this they will not be treating students equally and fairly. In terms of stress, the same for everyone may not be fair. Different students have different needs. Some have very few demands, while others collect an unbearable number of responsibilities.

3. Esteem support – It’s easier to repeat what we have done that’d right than not do what was done wrong. An important concept when giving feedback to students on submitted work. This doesn’t mean we can’t tell a student they an answer is incorrect but that we try to keep criticism constructive and focused on aspects of the work that can be changed.

4. Increasing student control over their educational environment and outcomes. Allowing greater flexibility in how students show achievement of outcomes or objectives in regards to learning has benefits to both the student and the instructor. Give students options for increasing performance on learning objectives and the grades associated. 

Advanced Organizers

Advanced organizers are an instructional unit that is used before direct instruction, or before a new topic; this is sometimes called a hook, set induction, or anticipatory set.  Advanced organizers can be many different things, such as a narrative, expository, skimming, graphic organizers, or a KWL chart.

For this activity, you will carefully read through a lesson plan. Notice and reflect upon the use of an advance organizer and answer the following questions:

1. Which type of advance organizer was used?

2. How was the organizer used? Was it used to present information or to make connections from previously learned information to new information?

3. Was it used effectively? Did the use of the advance organizer serve a purpose? Why or why not?

4. Reflect upon how you would or would not change this lesson and provide reasoning for your response.

Lesson Design Project

1. Now that you have choosen the topic of your lesson, go ahead and choose which advance organizer would best suit the needs of both your topic and students. Consider how will you present this advance organizer- on a chalkboard, overhead projector, or via power point?

2. Design one strong lesson that exemplifies the appropriate and effective use of an advance organizer.

Teacher's Beliefs

When you first interviewed for your job you get question like "Do you think all students can learn?", "What's your favorite thing about teaching?", and "How do you make students feel comfortable in your classroom?"  I believe some teachers lose sight of these questions and how they answered these questions from when they joined the profession.


A substantial body of research suggests that teachers' beliefs and values about teaching and learning affect their teaching practices Influencing teachers' beliefs, therefore, may be essential to changing teachers' classroom practices. The goal is to better understand the nature of teachers' beliefs about mathematics teaching and learning and the links between their beliefs and practices. Hopefully professional development approaches will increase inquiry-based teaching of mathematics in classrooms.



The NCTM Standards stipulate that students need opportunities to communicate math ideas and solve problems with others, that they should engage in mathematical activities with confidence and enthusiasm, and that teachers should use assessment strategies that focus on understanding rather than on right answers. Teachers are encouraged to value and reward students' effort and persistence, and to give children some discretion in how they approach mathematical problems and encourage them to use a variety of approaches to mathematics tasks.


This article comes from a study done at UCLA that teacher beliefs about math affect students beliefs about math even at the elementary level.  It includes that teachers should teach math enjoyment and effort than pure understanding of concepts.  To read more about teacher's beliefs click on the article below:


http://www.connect.gseis.ucla.edu/pubs/files/TeachersBeliefs.pdf

Taboo Math Game

Taboo Math is a great way to introduce vocabulary concepts that get the students engaged.  When students see the word on the test they now have the ability to relate back the information from the game to the test.

Split the class up into groups of 4-6. Each group gets a set of small cards which each have on them one maths related word. The first thing they have to do is write on each card, under the math related word which is at the top, three words that people will not be allowed to use when describing the top word. For example, if the top word is circumference then three words the team could write underneath could be circle, perimeter and length. The idea is to make the describing of the top word as tricky as possible. The words that they can’t use when describing the top words are called Taboo words.

The sets of cards are then passed onto another group and one person in the group gets 1 minute to describe as many of the top words as possible to their group colleagues without using the taboo words. The teams get a point for each correct word they guess. Each team has a go and the scores added up at the end to identify the winning team. You can do a tie-breaker round if necessary.

There are lots of variations you could do of this game and it does seem to really engage the kids and is an excellent way to revise key vocabulary and assess conceptual knowledge.

You can find a link to the blog here: http://www.greatmathsteachingideas.com/2010/06/17/taboo-words/

Stop Motion

There are many different ways you can create stop motion videos.  Especially in the math class where students demonstrate a video that entails a concept or math problem.

1. http://www.stopmotionpro.com/ is an online software tool where you need a video camera or webcam.  You create a model and then set it into motion.  
2. There are also apps for stop motion on the iPad and iPhone.
1. Stop Motion Recorder  StopMotion Recorder is toy video camera enable you to make stunning stop motion video like claymation.
2. StoMo  Create simple stop-motion animations/movies with this easy-to-use capture utility.
3. Smoovie  Smoovie is the only stop motion app that lets you arrange your content in scenes.

These applications would be great proofs, especially creating proofs without words.  Like the example below finding the area of a circle (formula).  You can have students create projects like these in the classroom over math concepts and ideas.

Algebra with Stamps

I collect stamps from all time periods, older stamps with George Washington as 1 cent stamps.  I even have stamps from Europe that I found in an old box in my father's old store.  Using stamps that I photocopied then cutout is a great way to get students to use algebra hands-on.  Since they are photocopied, each student receives a set of manipulatives they can use.

So if the students run in to a problem 2x=4 they can use manipulatives to either figure out what the missing variable is or use the stamps 2 stamps times x= 4 stamps.  The answer must be 2.

You can also have students add up to postage.  10x+24y=44.  Students guess on what they must use to equal 44.  So x=2 and y=1.

There are many ideas you can use, this blog goes over the last example more in detail: http://mathfour.com/algebra/algebra-with-stamps

Math Maps

Using Google Maps you can create your own scavenger hunt using math maps.  Google Maps gives you the ability to create and share personalized annotated maps of your world.  They are easy to create inside of Google Maps.  Just click on My Places and create a map, you can edit map features, place markers, and create and draw lines.  You can even link them or embed them into a class blog.


View Math Journey in a larger map

Here is the link to one that I created: https://www.google.com/maps/ms?msid=202680541149922653609.0004c2f01baa716e38bab&msa=0&ll=41.287621,-95.961848&spn=0.00163,0.000767

Here is a link to one that another math teacher created: https://maps.google.com/maps/ms?msid=211072539094148567472.0004879310e5c52517689&msa=0&ll=47.857403,-105.622559&spn=8.434745,6.28418

Using this interactive web 2.0 tool in the class is a great way to explore mathematical concepts, especially ones in the real world.  Students can even explore their hometown and make students think out of the box when it comes to problem solving.

Kung Fu Math II

Part one of this blog gives ideas for using physical hand movements to replace mathematical symbols and how this can be used for introducing mathematical vocabulary. We will look at how else this strategy might be used. 

For example, in pairs, children can test each others mathematical knowledge and then link this to inverse operations.

• Child A comes up with a calculation (4x12=)
• Child B then says the answer and creates the inverse operation with their own symbols(48/12=)
• Child A then says the answer(4). 

This would also work well with any inverse equations, especially logarithmic and exponential equations.

This game both gets students to practice speed of their mental answers and allows the teacher to check the understanding of inverse operation. In the classroom, this can often get competitive and children like making the maths quicker and quicker.

Another option for advanced users is to introduce the bracket (one arm pointing up and one down) into the mix and move into groups using a combination of symbols and whiteboards with numbers on. Teachers can introduce equations with brackets in different places to show how they impact on the equation.

As a strategy, Kung Fu Maths gives teachers the opportunity to introduce practical elements to the maths curriculum.Getting children out of their seats doing physical movements which reinforces concepts for many children and, as importantly, is fun.

This blog idea and information came from: http://primary-ideas.blogspot.com/2011/12/kung-fu-maths-ii.html

Play Doh Volume

Keeping students excited and engaged about what they are doing in math class is always a struggle, since most teachers have a variety of learning styles from students such as auditory, visual, and hands-on.  Having students play with Play-doh is the next best thing since it reaches all learners.

Materials:

• Play-doh
• Ruler
• Plastic knife
• Ruler

Instructions:
Many of my students had heard somewhere along the way that volume equaled length times width times height.  So, I started by having them make a rectangular prism out of their Play-Doh.

Once it was made, I had them draw a picture of it in their Geometry Booklets.  Then they measured and recorded the length, width, and height of their prism in centimeters.  Next, I had them cut their prism into 1 centimeter lengths.  They observed that the cross sections were squares.  I had them find the area of this square.  We talked about how many slices they had.  So if their area was 6 centimeters squared and they had four slices how could they find the volume of the box?  They quickly deduced that they needed to multiply the 6 by 4 to arrive at 24 cm cubed.

I repeated this for a cylinder and a triangular prism.  We observed what the cross sections were, found the areas of our cross sections, and then found the volume.  To sum it all up, we talked about how volume of a prism or cylinder is the area of the base (cross-section) times the height (number of slices).

For more information you can follow the link here: http://ispeakmath.wordpress.com/2012/05/28/volume-of-3d-shapes-with-play-doh/

Word Walls

A word wall is most likely unfamiliar to most high school teachers or is something that may have been encountered in an elementary classroom.  As part of a balanced literacy approach, word walls are being used in elementary classrooms as a means of promoting vocabulary growth leading ultimately to improvement in literacy.  There are many reasons, based in research, for the study of vocabulary as an explicit daily activity.  From building prior knowledge to providing contextualized information to simply providing students with high-frequency words that will be encountered in particular units of study, no matter what the justification or rationale, no matter what the grade level and no matter what the subject area, word walls are and extremely effective learning and teaching tools.



As you are thinking about using word walls remember that those for the content area are the vocabulary words you use to help students understand important concepts.  That means your word walls can be the basis for vocabulary games and activities – the more the better.



The purpose of the Mathematics Word Wall is to identify words and phrases that students  need  to  understand  and  use  so  as  to  make  good  progress  in  mathematics.  Mathematical language is crucial to children's development of thinking. If students do not have the vocabulary to talk about math concepts and skills, they cannot make progress in understanding these areas of mathematical knowledge. They need to be familiar with mathematical vocabulary and mathematical terms to understand written and spoken instructions.  

Some links to great sites that have more information and examples of math word walls are below:

http://learningideasgradesk-8.blogspot.com/

http://www.broward.k12.fl.us/PDF/MathWordWall.pdf

http://datadeb.files.wordpress.com/2009/11/001-word-wall-post-for-blog.pdf

http://www.markville.ss.yrdsb.edu.on.ca/mm/oise2005/bestpractice/wordwall.htm

Word Generation

Word Generation is a research-based vocabulary program for middle school students designed to teach words through language arts, math, science, and social studies classes. The program employs several strategies to ensure that students learn words in a variety of contexts.

The program consists of weekly units that each introduces 5 high-utility target words through brief passages outlining controversies currently under debate in this country. The paragraphs are intended to help students join ongoing "national conversations" by sparking active examination and discussion of contemporary issues. The target words are relevant to a range of settings and subject areas. The cross-content focus on a small number of words each week will enable students to understand the variety of ways in which words are related, and the multiple exposures to words will provide ample opportunities for deeper understanding.


Word Generation is designed to provide teachers with opportunities to practice strategies for teaching vocabulary that they can by apply more broadly and easily incorporate into established routines. Teachers across the content areas have told us they recognize their students' problems with vocabulary, but don't always know how best to help them. Word Generation presents teachers with a common language for discussing literacy and comprehension strategies across the curriculum.


You can access the website here: http://wg.serpmedia.org/index.html

Playing Cards in Math

It is possible for a teacher to make the material and activities they use challenging and still have fun in the classroom.  We know that time is one of the biggest obstacles in teaching, so here is a compiled collection of engaging math games for middle school math using only an ordinary deck of playing cards.  Keeping students interested, active, and engaged makes a significant difference in the overall learning experience and I believe that this collection of math games will do just that.

Math card games provide an excellent source of multisensory support, extra repetition, and variety.

Here are few game you can use in your classroom.  You can get all these games below and more here at this website: http://pepnonprofit.org/uploads/2/7/7/2/2772238/acing_math.pdf