Math Methods: Interview

For my interview, I contacted Stephanie Hentze at Stephens Middle School due to the fact that this is the school where I completed my practicum. Her and I spoke via email about the following questions. (She stated that another Willamette student had also contacted her about these questions, so she copied her answers from when she spoke with the other student- Just a heads up!)

How does the CMP curriculum align with the NCTM standards?

 I am not familiar enough with the Common Core standards to address how
 CMP aligns.  The work I/we do are closely tied to the state standards for
 this year.  I know the district and CMP are working to create supplemental
 units and adjust the material to match the new standards more closely.

 I am told that the practices component of the common core standards (the
 justification/ explanation/ exploration/ inquiry part) lines up pretty well
 with NCTM, and that is what the CMP is designed to do - get students
 working with and exploring concepts to discover rules and patterns, and
 then explain what they find and how they know it's correct.

How does one address the needs of students of varying needs on a daily basis so that they can reach grade level and experience success in the inquiry to investigation philosophy of the CMP?

Sometimes I assign different homework to different students based on
 their level of competency of the basics.  Last week, one group did a
 worksheet about coordinate points and the others answered questions from
 the book that had them extend the work with coordinates.  Including a
 review of each topic before beginning the exploration is critical.  Pulling
 small groups to re-teach is a good strategy when the class dynamics allow
 for groups to stay on task without constant supervision.  I have found that
 sometimes students who are low in the basics (division, multiplication,
 etc.) do better than expected when they are placed in a challenging
 curriculum.  It's a different type of work, and it's great when students
 find they can be successful in something difficult (or even just on
 grade-level).

What is the role of homework (and accountability) in the CMP?

 I can't speak for all of CMP, but in my classes, homework is an
 important part of the learning process.  It is viewed as practice - as
 opportunities to try and to struggle and to ask for clarification.  The
 goal, of course, is for the homework to help students understand better.

 Because it's practice, homework is weighted as a small percent of the
 total grade.  There is a movement to have homework worth 0% of the grade
 and have the grade solely reflect their test scores.

What are some classroom management techniques that ensure all students are actively engaged?

 Some management strategies:

 set up roles:  I have a captain, pirate, scout, and wizard.  (Not every
 activity needs to be a group activity!)
 posters: have each member write in a different color
 all students need to share something from their group results
 roll a dice to see who shares - make sure everyone in your group is ready!
 exit quizzes - short questions at the end of class.  answer on a slip of
 paper and turn in as you leave.
 partner quizzes - work in teams of 2 on a quiz, but you only get to ask
 the teacher 1 question.
 talk about and wait for 100% attention before direct instruction
 have students' desks set up in pairs for work at the board, and teach them
 to quickly turn desks into 4s for groupwork.

Math Methods: C.M.P.

The Connected Mathematics Project (CMP) appears to me to be a problem-based learning style, otherwise called “Inquiry Based.” I believe that CMP is inquiry based due to the nature at which material is presented. For Inquiry based, as mirrored in CMP, there is a problem presented, hypothesizes are created, and solutions/conclusions are determined by gathering and displaying data in a safe environment.  This challenges the typical, more traditional methods, because it has students actively learning and being a part of the process, rather than simply receiving direct instruction from which they are told to repeat and memorize.  This is a very unique, yet important way to consider teaching. I believe that this inquiry based learning would especially be beneficial within a mathematics environment simply because it can be a difficult subject to figure out and students should have the ability to go through this discovery and learning process with other classmates within the classroom. By having to try to figure out how to solve problems together, rather than simply being told to memorize, the students would be more likely to remember and use the knowledge they are obtaining. 

Math Methods: Standards

Standards, standards, everywhere! Standards are the meat and potatoes from which we must teach when we are working within the public school systems. These standards, however, vary from grade level to grade level, and differ among content areas. For math, the most important to follow are the Common Core standards (basically the “National” standards). These standards are what we use to develop our lesson plans and objectives, and are what is tested.      

While developing these plans, however, it is important to note that you do not have to teach every single part of the standard in every lesson. Rather, a standard can be broken a part and scaffolded upon over the course of a unit. Also, while teaching these standards, it is important to give your students a heads up as to what they will be learning. This can be done by placing a student friendly (an measurable) learning target on the board. This can help keep students focused as well as keep them focuses on the objective for the day.

Teaching Mathematics: Musings on New Practices

It is interesting to look at the way in which people approach math and the teaching of said subject. I find that people are often repelled at the idea of 'math' when I am discussing it with them and they are even more surprised when I state that I enjoy it and advocate for better practices in the teaching of math.

Why does there have to be such feelings? Most of this, I have found, stems from people having a bad experience growing up. This bad experience may have been from a teacher, from a particular topic/area (ie. fractions), or through the person having a lack of confidence due to some struggles that they may have encountered. I believe that a lot of these things could be turned around through changing the way at which well all view the teaching of math as both students and teachers alike.

Through investigating and reflecting on the practice of teaching of math, I have come to the belief that there are a lot of changes teachers could be making to help make their classroom more successful.  Some articles that have lead me to this belief are as follows:

Math is Not Linear

This is wonderful Prezi presentation arguing against the traditional ways at which math is taught. The presentation offers a clearly researched and honest viewpoint that offers solutions to some of the issues we have while teaching math, or that students claim to have while learning math. It addresses the facts that math is not linear, but rather a more complicated process. We should, as educators, be giving our students more reasoning as to what and why we are teaching concepts rather than because it "is the next chapter in the book," or "because you will need this for a class later." We should also for challenges and exploration to occur rather than filing all of our students along through a damaged system.

A Better Way to Teach

Along with that presentation, this article on "A Better Way to Teach" discusses that we need to change the way we are teaching so as to give our students more confidence in the classroom.  It is important to offer our students opportunities in mathematics to succeed so they do not become discouraged A successful way to do this is through scaffolding the material. By taking small steps and breaking a larger concept up into mini steps can allow for more students to follow along and learn. This will instill confidence in the students and aid in getting rid of their math anxiety! It was also discussed that it can be helpful to separate math problems from math and simply relate the concepts to real world situations.

Flipped Classroom

Lastly, this article discusses using a flipped classroom technique. This technique works by creating a podcast or a video of the lecture you would normally give your students.  The catch is, however, that the podcast or video is watched at home, rather than in the classroom. The watching of the podcast would be the "homework." Then, in the classroom you give the students the actual "work" to accomplish together. This allows for students to share, work, and collaborate with one another rather than having them hit bumps or struggle on their own at home (as typically happens per the traditional methods of sending the students home to work alone on their homework problems). I believe that the author of this article drove this concept when he stated that:

Maybe "homework" no longer means that "work you do at home," but "the work" you do IN CLASS that drives the concepts "home."

Note: Another KEY book to look up is The Talent Code by Daniel Coyle. This book offers another look into how we should be viewing our classroom instruction, or rather, how to better any talent in general. This summary discusses how there are some key points that we miss when we are approaching the art of creating new skills. We focus too much on the idea that practice makes perfect, without considering the other parts that come into play. The author talks about how master coaching, ignition, and deep practice are the major ingredients at which talent develops.

Closures and Anticipatory Sets

So you may be thinking, "Why should I have an anticipatory set? What is the importance of a closure? Who needs them?" Right? Wrong.

Both of these are fundamental for an effective lesson! Think of them like the wrapper paper and bow to a present. You need to start out by laying out your wrapper paper (your anticipatory set) then you place the gift in the middle (your lesson) and wrap it up. At the end you make the gift even more put together by putting ribbons or a bow on it (your closure). It is as simple as that!

Your anticipatory set serves as the "attention-getter" for your lesson and occurs at the beginning of your class period or lesson. This can be as simple as a warmup activity, a short video clip, or a fun mini demonstration. This should take less than 10 minutes (ideally more around 5 or less). It is to get your students thinking about what you are going to be teaching. At some point during the beginning of the class (I typically would do this prior to the anticipatory set), I also find that it is very important to address what the learning target/objectives are for the day so that the students know what they will be learning. This can help add routine and structure to the classroom as well.

Your closure is very important because it ties everything together at the end of your lesson. This, like the anticipatory stem should not take very long. When you are doing a closure activity you are having the students reflect on what they just learned. It helps to get some feedback from your students as to what they learned by having them perform their knowledge in an informal or formal quick and simple assessment. This can be as easy as writing a journal entry summary or completing an exit slip. Personally, I always find that readdressing the learning target/objective at the end of the class really helps keep me on track as well as let's my students visualize exactly what they had accomplished for the day (so they can take more responsibility for their learning, as well).

While I am familiar with the practice and use of anticipatory sets and closures form other courses, I looked up a website to help those that may not be as familiar. This can also simply serve as a jumping off point for those who merely want ideas (even if you are already familiar with them)! There are also some great youtube videos for Math Anticipatory sets (Just be sure that youtube is not blocked at your school).

Math Anticipatory Sets (Reviewed by Math Teachers)

Practicum- Sharing a Lesson

I started teaching in my practicum this week and absolutely love it! I was placed in an 8th grade Health classroom and am currently teaching their Nutrition unit.

The lesson objective: Students will be able to identify at least 2 components of energy drinks, and how they affect health, and determine at least 1 alternative choice.

For the main bulk of the unit, I had a hands on activity for the students to participate in. There was a table located at the front of the room from which had a variety of different caffeinated beverages on it. I performed an activity from which the students got to play a "game show" and have a few students come to the front of the room to try to organize the beverages from the least caffeinated to the most caffeinated. The other students would "call out" to try to help their classmates.  We then discussed why we organized the drinks the way that we did then took a peak at the answers and continued the discussion Afterwards we did the same thing but organized the drinks in order of sugar content. We also placed a bag full of sugar cubes representing the amount that was in that drink in front of the corresponding drink.  After this occurred, we discussed the caffeine and the sugar within the drinks and what other alternative choices we could have that wouldn't have the negative side affects. They completed an exit slip at the end of class that stated:

Energy drinks have high levels/amounts of both ___________&_____________. A healthy alternative to these could be ________________.

During the activity I was able to assess my student by asking critical thinking questions and seeing how they responded. I did some thumbs up/down questions as well as some think/pair/share activities.  The exit slip at the end of class way a great way for me to measure how the students performed as well.  From this I was able to see that the majority of my students did learn something from the lesson. I have been able to revisit and build upon this knowledge over the course of the week and look forward to assessing them tomorrow on our weekly mini quiz to see how much they still remember.

After reflecting on this lesson, however, I think that I would have had a set of cards (with a picture of the drinks) at each table so that the table groups that weren't at the front of the class could organize the drinks as well. I think that by having cards with the pictures, or even by having a small set of drinks for each table group, that I would be able to hold all of the table groups accountable.  Another idea that I had was to make it a competition between the table groups or even one half of the class against another. I think that this would help by keeping all of the students engaged.

Appropriate Use of Technology

What mathematics does it teach or reinforce? Is this effective?

This teaches several of the standards from the NCTM Standards, as well as rotantional symmetry. If it engaged the students to follow along, it could also teach students to draw triangles and some of the properties of them as well (Standard 7.G.2). It also teaches towards the 7.G.5 Standard in which it shows how to use supplementary, complimentary, and adjacent angles in a multi-step problem. I think that this is an effective way to do this because it allows students to work at their own pace. They can really see what is going on and pause whenever they need too.


Does the technology offer something that offer tools would not?


I think that the technology does offer children another outlet for learning. While I believe that hands on learning would be just as effective in any normal occasion, I think that children that require more time to process information would definitely benefit from using Kahn's academy. The program allows for you to start and stop at anytime, thus allowing you more time to try to solve the problem or to take notes. I also think that it is helpful because students (with computer access) could do it at home.

Are there other effective ways to teach or reinforce this same content?


I do! I think that the Kahn academy offers a great way for people that are simply audio or visual learners to process information at a slower pace, where as a more hands on technique would be better for those who prefer a more hands on approach. For example, I know that I do not process information very well online or using computer. I seem to get overwhelmed, cannot understand what is happening, or simply tune out. When I am in a classroom, or learning in-person from someone (seminars, etc), I learn a lot more. I learn better when I can take a liter hands on approach. I believe that the same could be true for our students. They are all different and have different learning styles, this should be no different. I would not use the Kahn videos for my geometry lesson exclusively, but I do think they would be great for an added tool to help aid my students.


If you were to teach this same lesson, what might you change about the delivery or example(s)?


I would definitely use some more hands on techniques (having them cut out triangles, build them using blocks draw them, etc). I believe that it is important to teach to all of the learning styles, and by providing not only a lecture, some visuals, and some hands on activities, I think that I would be better able to suit the needs of all of my students. I also think that by doing this we are able to reinforce the lesson for the students that may almost be there but aren't quite yet. Even if you are simply doing the video, demonstrate cutting out the triangles so that the children can follow along, perhaps? Maybe simply show more items? Just some thoughts.

New Tech Standards and Requirements

The 3 Technological Standards and Requirements that stood out to me the most were:

• Creativity and Innovation
  
• Communication and Collaboration
  
• Critical Thinking, Problem Solving and Decision Making
  

I believe that these really reached me due to the automatic ideas that flooded my brain on how to incorporate them into the classroom.

Every class, despite the grade, needs to be creative and innovative. From kindergarten to high school, from college to the "real world" we are constantly finding new discoveries and ways to accomplish tasks or express ourselves. As we approach a new age, we are confronted more and more with the ever changing ideals of technology...and the classroom should definitely represent and demonstrate such. I think that it would be easy to allow our students to do this! They could create projects using different online tools such as Prezi or Screenr, or even have the ability to discovery other ways to accomplish tasks in a different way.

Along with this, technology allows for a better way not only for us to create, but for us to collaborate and communicate with one another. As a teacher, technology allows us to have a better opportunity to keep in contact with the parents of our students through email, blogs, or even classroom websites.  Students can also use technology to work together and keep in contact with one another. This can be done simply through group forums, or through the wonderful tools Google supplies (ie. Google Reader, Google Presentation, Google Docs, etc). By using these the students can work together on projects at their own speeds at the same time, on the same documents!

Lastly, I believe that technology really allows for students to use and develop their critical thinking and decision making skills. Using technology makes us have to problem solve and figure out new ways to try things. It is amazing how much we have to use problem solving skills in order to figure out how to accomplish tasks using technology. By doing this, and allowing our students to do this, we are at the highest level of Bloom's taxonomy. It is also important because technology is evolving at such a rapid exponential rate that we need to provide our students with the knowledge on how to use it as a tool and to have the skills to grow and change with it.

On a side note: It is important to note that some teachers think that using technology is not appropriate or even feasible to use in their classroom due to only having "one computer" in the classroom. I think that this is merely a minor bump in the road! Yes, each student having their own computer or access to such would be ideal, but one computer is just fine! Even setting aside time to check out the carted laptops, or going to the computer lab could be helpful. Don't simply write-off the idea of using technology simply because you hit a block in the road. Use your own problem solving skills and figure out great ways to solve the "issue." Technology is here and is not going away. We need to do whatever we can as educators to equip our students with basic knowledge and skills in order to prepare them to be learners in this new society.

This allows us to be creative ourselves and engage our students...don't be scared, but excited!

Think of all of the "normal" ways you would typically accomplish a classroom task.

Now, think to yourself: 

What could I add or alter in order to make this assignment or activity more exciting using technology?

For myself I must admit that I am enthusiastically trying to incorporate these technologies with my 8th grade Health lesson for my Practicum. I think that I could do a variety of activities with regards to food tracking and food group advertising using the array of technological applications that we have become familiarized with. There are SO many ideas that you could do...how could you ever get bored?

The sky really is the limit in cloud computing!

Warm-Ups in Math Education

I think that warm ups are not only important to implement into the classroom, but that they are critical!

My personal philosophy of teaching centers around the principles of scaffolding, engagement, and excitement. I think that the use of warm up in a math class, or any class for that matter, accomplishes all of these things.

I believe that students learn better when they are able to use and be reminded of the skills they learned from the previous day in order for them to be built upon on that current lesson. I also believe that the use of warm up enables a certain "routine" for the students to become familiar with. They are able to arrive in class and begin working, and ask any questions from the previous lesson that they may still have regarding the information before moving on. This is also extremely valuable from a teaching perspective because it allows for the instructor to do an informal assessment on whether or not their students understand the material before moving on and not realizing they don't understand until the unit exam, for example.

Analyzing Student Data in a Spreadsheet

Performing the computations on this set of student data was relatively easy once I got the hang of using the Google Spreadsheet program. I think that the program is an extremely valuable tool to use as a classroom teacher in order to both organize and analyze student data quickly.

By being able to calculate and graphically organize student data quickly, I believe that we will better to be able to serve our students. We can quickly tailor our lessons and get feedback on how our students are performing.

The data for this set of students, for example, shows that while they were initially falling below the average of 192, that they were still showing growth from tests 6-10. This growth can be seen in the following data and charts:

I chose to demonstrate this in two different charts because while the line graph shows the student growth progression over time across the tests, it was difficult to see each individual student. The bar graph provides for a clearer analysis of each students' progression across tests.

As a teacher, I think I would take note of the students progress over time. While they are not totally mastering the concepts, it is obvious that they are improving. My expectations might have to differ between the varying students and their needs. I might have to do break out sessions or change my teaching style if this many students are not meeting my criteria.

I would also want to know more information regarding this data. Are the tests on the same material or content area? How much time has elapsed? Do the same students perform below average on everything or just this content area? I would also want to compare the averages of the first set of tests (Tests 1-5)with the averages of the second set of tests (6-10) to see what the progression was.

By gathering more information on these tests I believe that I could form a more accurate opinion an analysis of the students performance on these tests.

The entire set of data can be found here:
Entire Collection of Student Data and Charts

Google Docs Group Project

Google Reader is a great tool for teachers and students alike to use. It provides for users with a way to organize a plethora of information with regards to any sort of subscription that you may have. This is extremely helpful when you are trying to follow several blogs at once, or if you are interested in a particular subject that has a subscription option (magazines, newspapers, etc).

I was absent when the group's were assigned for this assignment, but was able to quickly catch up with my group due to the ease of Google Reader! It was nice because I was not only able to get feedback from my teammates as to what Google Reader was, but I was actually able to quickly go into and actually use and research the program and place my input! While they had most of the key points already noted, I was able to figure it out and provide a reflection on why I like it an think it is a useful tool.

For more detailed information, please take a look at our Google Reader document!

The Multi-Media Project

On today's edition of "What Types of Awesome Technology Can Be Used in the Classroom" I bring to you the fabulous Ustream! This was my first time trying to use the program so bare with the mad skills, or lack there of, demonstrated in the video to follow.

But first! A word from our sponsor...or rather, an explanation of the program itself.

Ustream is an internet based program that allows for videos to be made in "live" time by simply using your laptop. Note: The laptop used must have a webcam and a microphone. Fear not, however, most laptops come with that built in these days! Thank you computer programmers and developers!

The program Ustream is very simple and easy to use...so to those of you who are saying to yourself "But Amanda, I am horrible at using technology, I do not think that this is applicable to me." Then I say to you "Ha! You CAN do it! Now turn that frown upside down and get to it, fool!" It is as easy as setting up an account and clicking a few buttons (basically the same procedure you would use to create and email account, or any account on most websites).

Tip! When you begin to use Ustream to create videos, make sure the you press "Record Now" to begin your recording and not "Broadcast Now." Broadcasting does not begin your recording, and thus if you try to create your post to use for later, nothing will record but it will (as the title suggests) simply broadcast you to the world. Now how's that for entertainment?

Ahh, and now for your viewing pleasure, a tour of the GSE and my first time trying using Ustream.

Note: I apologize for the weird look on my face and the use of the word "lovely" way too many times.

Now, welcome to the GSE...


Video streaming by Ustream
Now that I have tortured enlightened you with my technological talents, let's discuss how this can be used in the classroom!

There are many applications that this tool could be useful for. Some could include:

• Teachers using it to record their classroom

• Teachers/Students recording their progress for Classroom/Individual Blogs

• Students performing group projects

• Student monologues/reflections

• using it as a literacy tool so the students can hear themselves read

There are many more ways that this could be applied to teaching that I have not listed...so get to creating!

Favorite Web 2.0 Tools

Team viewer is an amazing tool that provides easy access for computers to connect with one another anywhere in the world. This is a fun and unique way for people to connect remotely onto another's computer.

I think that this would be a fabulous tool for teachers and students to use for several reasons.
Students, for example, could use it to work together on partner projects. It could also be great to use for presentations!

I also really like it because I tend to have a lot of problems with my computer and my friends have to try to "talk me through" the issues. With Team Viewer, they could get on my computer remotely and fix the issues as though they were sitting with me at the computer!

Take a look for yourself:
www.teamviewer.com/