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.