Module 13

Annenberg Video Circumference and Diameter

1. Describe Ms. Scrivner's techniques for letting students explore the relationship between
circumference and diameter. What other techniques could you use?

 The children were allowed to look around the classroom for round objects to measure. Using measuring tape, students measured both the circumference and diameter of their object. They then recorded their data and discussed the data as a class. To extend the lesson a bit, you could compare the measurements from two groups  who had measured the same objects.

2. In essence, students in this lesson were learning about the ratio of the circumference to the
diameter. Compare how students in this class are learning with how you learned when you
were in school.
The students in this class were allowed to explore these concepts with a  hands on approach. This is very diffeent from my own experience. When I learned these concepts, I was juts given a formula and a lot of practice problems from the book.

3. How did Ms. Scrivner have students develop ownership in the mathematical task in this
lesson?
Ms. Scrivner allowed the students to develop ownership by allowing them to choose the objects that they wanted to measure.

4. How can student's understanding be assessed with this task?
Observation would be a strong assessment tool for this task. By observing the students during their group work, you would be able to see the way the students measure their objects, if the objects they are measuring are round, and what the students think diameter and circumference is in relation to their object. You could also assess the data that the students recorded.

Annenberg Circles and Pi Module

This module was a great refresher! It has been a while since I have had to use any of these concepts.

Problem B8    When you enlarge a circle so that the radius is twice as long (a scale factor of 2), what do you think happens to the circumference and the area? Do they double? Experiment by enlarging circles with different radii and analyzing the data.

Problem B9 Experiment by enlarging a circle by a scale factor of 3, by a scale factor of 2/3, and by a scale factor of k. Generalize your findings.

For B8, my first thought was that everything would double. After reading the solution I was a bit confused, but the more that I thought about it, the clearer it became. 
For B9 I thought I as definitely understanding the concept better until I got to the fraction and the variable. I think if I practiced this concept a bit more I would be ok, but I honestly feel a but shaky with this concept. 

Textbook Pages 1-26

1. Explain what it means to measure something. Does your explanation work equally well for length, area, weight, volume, and time?

To measure something is to attempt to assess a characteristic of that item using a specialized tool. 

3. Four reasons were offered for using nonstandard units instead of standard units in instructional activities. Which of these seem most important to you, why?

 I think that the most important reason for using non standard units is that it allows very young students to begin thinking about what it means to measure something. Learning to measure objects with nonstandard units, such as hands or feet, allows students to really play around with how to measure and observe variables that effect measurement.

For further consideration….

We have explored so many great topics this semester and I definitely will be incorporating some things that I've learned in my own classroom. I am really glad that we did the children's literature project because it allowed me to see how many rich literature resources there are for many mathematical concepts. After reading the journal articles and watching the videos of  younger students collecting and displaying data, I am confident that if I teach lower elementary I will challenge my students to collect small units of data. I would also expose my students to various types of graphs early on so that they are familiar with how to read and form their own graphs. The biggest take away I got from this class is that students are much more capable than they sometimes get credit for. You should not be afraid to introduce challenging topics. The key is to make the content meaningful.

Module 12

TCM Article – Rulers

I enjoyed this article. I think that the lesson outlined was a great way to introduce different units of measurement. I was very impressed that the students were able to figure out that their rulers are the same size without being told. One point the article made that I did not think about was the difficulty students can have actually using a ruler correctly. Not all the students knew to start at the very end of the ruler (before 1).

Angles Video and Case Studies

One thing that I took away from the case study was that many children focus more on the line segments than the actual angles when they are learning about angles. It was interesting to read the varied understandings that were taking place in one classroom. This held true in the video as well. Many of the students could demonstrate what an angle would look like. They made angles using their arms and imaginary lines. They had difficulty, though, explaining what exact part of their example was the angle.

Annenberg Angles Module

Use two or more polygons to illustrate the angles below, and explain how you would justify that some of the angles are congruent: a.  Vertical angles (the angles formed when two lines intersect; in the figure above, ad, cb, eh, and fg are pairs of vertical angles, and the angle measures in each pair are equal) b.  Corresponding angles (the angles formed when a transversal cuts two parallel lines; in the figure above, ae, bf, cg, and dh are pairs of corresponding angles, and the angle measures in each pair are equal) c.  Alternate interior angles (the angles formed when a transversal cuts two parallel lines; in the figure above, cf and de are pairs of alternate interior angles, and the angle measures in each pair are equal)

Problem B6    Find one or more polygons you can use to see examples of the following angles: a.  Central angles (for regular polygons, the central angle has its vertex at the center of the polygon, and its rays go through any two adjacent vertices) b.  Interior or vertex angles (an angle inside a polygon that lies between two sides) c.  Exterior angles (an angle outside a polygon that lies between one side and the extension of its adjacent side):

I had a little trouble with each of these problems. It has been a while since I have done these kinds of problems so this module was a good refresher. After playing around with the shapes a bit and reading the solutions it became clearer.

TCM Article – How Wedge you Teach?

I could not get this article to load!

Exploring Angles with Pattern Blocks

Green Triangle: For this shape I know that all three angles add up to 180. I also recognize that this is an equilateral triangle so all of the angles are the same. 180/3=60

Blue Rhombus: I can remember that on a rhombus, the opposite angle are congruent so there was going to be two different angles. The smaller of the angles looked similar to the angles in the green triangle so I matched them up and they fit. I know that all the angles of a rhombus add up to 360. Two of the angles are 60 which add up to 120. That would mean that the remaining two angles would be 120 each.

Red Trapezoid: Going in I know that all of the angles would add up to 360. I used the 60 degree angle from the triangle to confirm that the smaller angles were 60 degrees. that would leave the two larger angles to be 120.

Tan Rhombus: I found this shape to be very difficult. I could see that there were two very obtuse angles and two acute. Because it is a quadrilateral, I know that all the angles add to 360. I played around with this for a bit and could not find  a way to get an answer.

Yellow Hexagon:  I know that all of the angles in a hexagon add up to 720 degrees. All of the angles looked to be the same size so I divided 720 by 6 to get 120 for each angle.

Challenge:
By connecting two triangles by their base you get two 120 degree, obtuse, angles.

Combining a triangle and trapezoid created a straight angle.

Combining tow hexagons created a 240 degree angle

I agree with Mai. Using the shapes we have I could not find a way to create an acute angle.

For further discussion

When I think of nonstandard measurements, I immediately think of cooking. You will often times see a pinch/ dash/ splash of a certain ingredient. I have found that these terms are used when it does not matter if there is an exact measure. It is usually an ingredient meant for flavor and left to your preference. You will never see a cake recipe using a non standard measurement on flour, baking power, or baking soda because those ingredients are critical to the cake and must be exact. The example "I'll be there shortly" also falls into this category. It lets the person know that you are probably on the way and will be there soon, but you don't say an exact time. If you were to say "I'll be there in five minutes" but it actually took ten, then it seems like you were late! You use nonstandard measurement when you don't need to be exact.

Module 11

Coordinate Grids 

I explored the websites Billy Bug (1 &2), Stock the Shelf, and Greg's Grid Graphics. I think all three of these websites would be perfect for classroom use. I think that Billy Bug and Stock the Shelf would be a great choice for use in math centers in classrooms with an interactive whiteboard.  They were pretty straight forward and set up for easy turn taking. You could also use these websites in a whole class setting but it would be more difficult to allow every student to have a turn. I think that Greg's Grid Graphics would be more appropriate for whole class instruction. You would still have the opportunity to hear from every student but I feel that it would go more quickly since the teacher could just type the students' answers rather than the student coming forward to manipulate the game.

Miras and Reflections and Kaleidoscopes Article 

I have never used a mira before, I remember being perplexed by that tool when I received my kit at the beginning of the semester. These activities were good practice for me to learn how to properly use the tool. I feel like the only part of the activity that I had significant trouble with the alphabet symmetry. 

Annenberg Measurement Module 

I did not particularly have any questions for this module.The only question that really made me pause was measuring the surface area of the rock with tin foil. I figured that you would measure the flattened foil. It never occurred to me that the foil would have an irregular shape. After the module broke down how to measure an irregular shape, I understood.

Case Studies 

 It was very surprising to see that students struggle with very similar measurement concepts throughout elementary school. The idea that A larger unit of measurement would have a smaller number and that a smaller unit of measurement would result in a larger number seemed to  confuse students for many years. It was interesting to see the younger students begin to question the accuracy of measurements based on techniques used to gather data. This becomes a big focus in the upper grades as they begin using actual measurement tools.

For further discussion

A fellow teacher says that he cannot start to teach any geometry until the students know all the
terms and definitions and that his fifth graders just cannot learn them. What misconceptions
about teaching geometry does this teacher hold? Now that you've had some time to explore the world of geometry, how has your view of the key ideas of geometry that you want your students to work though changed

This teacher seems to be under the impression that geometry is only a series of theorems and complex proofs. In reality, most of his students have probably already begun exploring  geometric concepts. Coming into this course, I also associated geometry with more complex concepts such as the Pythagorean Theorem. I felt that geometric concepts would not be introduced until closer to middle school aged. Throughout the modules I have been reminded that through use of manipulatives, students can begin to understand geometric concepts such as symmetry, reflections, and spatial reasoning.

Module 10

Annenberg Symmetry Module

This module was so strange to me. While I was reading the definitions, it all felt terribly abstract and I had to re-read explanations multiple times. When I looked at the actual examples and problems, however, I knew how to solve them. 

Problem A3

For each figure, reflect the figure over the line shown using perpendicular bisectors. Check your work with a Mira.

Printable PDF of figures

For these types of problems is there a way to ensure a more accurate reflection? While I was solving the problem, I knew to reflect the shapes across the line but I felt like I was missing an important step. 

Pentomino Activities

I tried the pentomino activity on the Scholastic website. I decided to start on the easy mode as a warm up. I think I must have a different definition of easy! I filled up the square pretty quickly until I was left with three lone spaces which could not be filled by any of the remaining shapes. I reached this dead end three more times before I finally solved the puzzle. At that point I was simultaneously happy and still a little annoyed so I did not go for the medium mode!



Pentomino Narrow Passage

My passage ended up being 15 spaces long and closed on both ends, It took me a few tries to find a way to fit all of the pieces together without having wide areas in the passage.

Tessellating T-shirts Article

I really enjoyed this article. I always like the idea of integrating Art into Math activities, I like that the teacher gave students the option of creating their own shape to use in their activity. I think that will allow students to make a deeper connection to the assignment. Tessellate means repeating a shape over and over again.
When I think of tessellation, I immediately think of moroccan tiles and patterns.

I also thought of a naturally occurring tessellation: honeycombs

Tangram Discoveries

 Which polygon has the greatest perimeter? …the least perimeter? How do you know?
I think that the trapezoid had the greatest perimeter and the square had the smallest.

Which polygon has the greatest area? …the least area? How do you know?
I think that all of the polygons had the same area because I could build each polygon using the same three triangles.

For Further Discussion
Many cultures use beautiful patterns and tessellations in their art and clothing designs. These artifacts could be a great way to connect Math and Social Studies. You could challenge students to come up with their own shape-centric patterns to use in their own stylized artwork.

Module 8

Quick Images Video 

I found the video this week very interesting. It really highlighted the way that everybody thinks of things differently. Most of the children connected the shape with a real life object such as a boat or banana. My first thought was that it was a picture of the shape, crescent. I always remember what a crescent looks like because I think of a crescent moon. I thought it was really interesting that one of the students said that she remembered the shape because it was part of a circle. I have never thought of a crescent as part of a circle, but it really is.

Case Studies- Shapes and Geometric Definitions 

The case studies outlined students' responses to seeing familiar shapes in unfamiliar positions and proportions. In Andre's case, she presented students with an array of triangles. All of the students agreed that the oddly shaped ones looked like triangles, but could not decide whether they were "real" triangles. The kids had become so accustomed to seeing a triangle depicted as an equilateral triangle that it did not feel comfortable to classify different triangles as being the same shape.

Annenberg Polygons Module

Problem A2
How many polygons can you find in the following figure? Problem A3    How many polygons can you find in the following figure?

The kindergarten class that I am assigned to this semester recently began exploring shapes. Just last week I was working with some students during their Math centers and told them "I bet I can make a square out of 2 triangles." They seemed skeptical but watched me intently. They all immediately modeled what I had just done with the triangles. I challenged them to create other shapes using the manipulatives. When I came upon these series of questions I felt it was very simple. 4 triangles and a rectangle. When I read the solution I was shocked to see so many other combinations. I went back to look at the figure again and began to see more chapes jump out that I missed the first time.

For further discussion

I have never really noticed before, but my home is filled with rectangles. Tables, doors, windows, picture frames, the television, tiles, and even this computer is composed of rectangles. Most of the circles in my home are located in the kitchen. Plates, bowls, pots, pans, and a large wall clock. I went on a hunt through the house for triangular objects but, other than a few decorative patterns, I found none.

Module 6

Annenberg Probability Module 

Problem A3    What is a random event? Give an example of something that happens randomly and something that does not. When I read the solution to this question I began to feel the same confusion that has followed me through many years of working with statistics. The solution mentioned that some things are just random while others require skill. I understand that. The example they used as a random event is what card would show up on top of a freshly shuffled deck. Where I get confused is would that actually be random? You would always have a 1 in 42 chance of drawing a specific card. SO it isn't as if the probability of pulling any one card is randomly changing. Am I just over thinking this? Problem B2    Suppose you toss a fair coin three times, and the coin comes up as heads all three times. What is the probability that the fourth toss will be tails?

This question made me laugh a little bit. Logically, I know that in a coin toss, there will always be a 50/50 chance of heads or tails. It is easy to forget this in the heat of the moment, though. I know that my odds are still 50/50 but there is this nagging feeling in your mind that the next toss HAS to have this certain outcome.

A Whale of a Tale article

Create your own probability line chart that displays events that are impossible, certain, likely, or
unlikely to happen. You should have a minimum of 2 events for each area

Dice Toss 

• Based on the data, the class concluded that 7 was the most likely outcome. Some of the students did have some preconceptions, though. For example, some students thought that 12 would be unlikely because it is more difficult to roll a 6. I think that this would be a difficult concept to get out of their heads. Like I explained earlier with the coin toss, even though you know that there is an equal chance of either outcome, it is so easy to get caught up in the results. You could toss a coin 4 times and get 4 heads in a row, but that doesn't affect the probability that you could land on tails next even though you may feel otherwise. 
• I do not think that they were too young. They were able to clearly answer their teacher's questions and even expressed their surprise at some of the results. 
• The teacher asked the students to roll 36 times because it would allow the students to collect a large amount of data to be able to see the trends. One advantage to this is that the results would be more accurate. One disadvantage is that this would take up a lot of time in class. Also the large amount of data  might be overwhelming. 

Module 5

Box an Whisker Plots

1. What are some differences in the data that you can observe? 

Our class has a larger range than the German class. The German class has a larger population but their range is smaller. 

2. What does the median for each class tell us about the data?

The median for the German class is approximately 55. This means that half of the German class threw out less than around 55 pounds of trash and the other half threw out more than 55 pounds. The median for our class is 83. This means that about half of the class threw out less that 83 pounds of trash and half threw out more than 83 pounds. 

Common Core

First Impressions:

• My first thought when exploring the standards was that there are A LOT. It is a bit overwhelming, imagining how to fit in all of these standards throughout the school year.
• The second thing that I noticed was how the standards progressed as they advanced in grade level.

How do the concepts progress through the grades?

As you move through the grades, you revisit the same concept but you delve deeper into the content.

How do the concepts change and increase in rigor and complexity for the students?

Each year, students build upon the concepts that were covered in the previous year. For example, in kindergarten students are expected to master addition up to sums of 20. By the end of second grade they are expected to add to sums of 100.

Does the Common Core Standards align with what NCTM states students should be able to know 

and do within the different grade level bands?

For the most part, the Common Core Standards align with NCTM Standards.

Give examples of which standards align as well as examples of what is missing from the Common 

Core but is emphasized in the NCTM standards and vice versa.

I focused on the earlier grade levels since I am assigned to a kindergarten classroom this semester. I thought that the concepts all aligned pretty well. I noticed that one major difference is that NCTM stresses connecting materials to the students and the every day lives. This is not mentioned in the Common Core Standards.

Module 3

Lost Teeth Video 

I think that the teacher asked the students about the range in order to get them to think critically about the different populations that they gathered their data from. Would it make sense for younger grades to have a wide range of tooth loss? Why or why not? etc. I think that the students showed pretty good insight in regards to the range. One of the students mentioned that he lost teeth before he even entered kindergarten. He was able to draw upon his own experienced to explain the variation in ranges.

I think that the students did a great job analyzing the data. They investigated how their predictions differed from their actual results and discussed the differences. I was impressed by their discussion about how the range is constantly subject to change. This was clear when one girl lost an additional tooth during the project, changing the range for that population.  

Annenberg

I thought this module was very informative because these are skills that I have not used in a very long time.

Problem A5  

Since the goal is to estimate when a minute has elapsed, it makes sense to consider how close the estimates are to the correct response, which is 60 seconds.

a.	How many people's estimates were more than five seconds away from one minute? That is, how many of the responses were less than 55 seconds or greater than 65 seconds?
b.	How many estimates were within five seconds of one minute?
c.	How many estimates were more than 10 seconds away from one minute?
d.	How many estimates were within 10 seconds of one minute?

This question tripped me up, at first. I had to reread section A a few times before it clicked. I decided to include this in the blog because, to me, it was a reminder of how important the phrasing of the question is for students' understanding.

Problem B2    Using only the histogram and grouped frequency table, give two descriptive statements that provide an answer to this question.

I included this question because of a little sense of hesitation that I had. I instantly made the observation of the range, and that most of the data was within 10 seconds of 1 minute. However, I felt unsure whether these were sufficiently descriptive enough. When I read the solution to this problem, it was clear that my observations were valid descriptions. I think this uncertainty would also be shared by students who are new to interpreting data and graphs.

Stem-and-Leaf Plots Article

My take away from this week's articles is similar to the article we read last week. I was very impressed at how quickly the students seemed to pick up the concept of the stem and leaf plots. I think the concept of using the stem and leaf plots as a tool to teach 10's and 1's place value is a really great idea! I can definitely see myself incorporating this approach in my own classroom.

Questions

What kinds of graphs can be used for data that can be put into categories?

Bar graphs are a great way to present categorized data. Pie charts also come to mind. 

What is the difference between a bar graph and a histogram?

A bar graph gives you an exact value for the data while a histogram give you an approximate range.

Module 2

Annenberg:

QUESTION B1: Using the data above, answer this question: How many raisins are in a half-ounce box of Brand X raisins? Answer the question in whatever manner seems the most descriptive.

The first thing that I did for this question was plug the data into the chart. This let me see all of the numbers. The first thing that I noticed was that 28 was the most common number of raisins in each box. I was going to stop there since that is the mode, but out of curiosity, I wanted to know if the median would give the same number. I lined the numbers up and, again, I got 28! So I concluded that a box of raisins would have 28 raisins on average.

Problem B3

Does Problem B2's data strongly suggest that the next box will have 28 raisins? Does it prove that the next box will have 28 raisins? If so, why? If not, would there be a way to prove, statistically, that the next box must have 28 raisins? I was a little confused by this question. Initially I would say that, yes, there will be 28 raisins in the next box. The past 17  boxes all had exactly 28 raisins. It seems very likely that the next box would also contain 28. Other than showing the data supporting that claim, I'm not sure how you could prove that this is true.

Median

I actually made a mistake when I first plotted my data! I confused a line plot with a line graph so I had to go back and do it again!

Kindergarten Data:

Mode: 0

Median: 0

1st Grade Data

Mode:7

Median: 5.5

2nd Grade Data

Mode: 8

Median:8

 3rd Grade Data

Mode: 9

Median: ? (I'm not sure how to find the median when there are unknowns)

Just from glancing at the four line plots we can tell that at least one student in each grade has lost at least 1 tooth. As the grade level rises, so does the number of teeth lost. In the Kindergarten class, there were more people who had not lost any teeth than there were people who had lost teeth. In the 2nd and 3rd grade classes everyone had lost at least 2 teeth.

If only the mode for each class was given, we would know the most common number of teeth that each class had lost. If we only knew the mode, we would have no idea about the outliers. For example, the mode for 3rd grade is 9 teeth, yet there is also a student who lost 19 teeth! If I thought that most of the class had lost 9 teeth I would never consider that someone had lost as many as 19.

Only having the median would not really give you a clear picture of the data unless you also knew  the range. When you know the range you know that the class has lost anywhere from x-y many teeth. The median gives you an idea of what the average number lost was.  for 2nd grade you would know that they had lost between 2-13 teeth. On average they lost around 8. You would not know, however, that most of the class had lost 8 or more teeth. 

I Scream

The opening statement was a bit surprising. I don't really think about 4 year-olds gathering and representing data! The kindergarten lesson in the article seemed like it would be a bit ambitious for students to do independently. I think the teacher did a great job letting the students take the lead. They all seems very excited and motivated which I think makes a big impact. The point of the lesson was to let the students individually practice these graphing and data skills that they have been exposed to in a full class setting.  I like that the teacher allowed students to pick their preferred style of graph. Though the data was not the most accurate, all of the students represented their data successfully.

Module 1

Categorical Data

Before I looked at the actual data, I tried to think of the 3 most likely categories of people that someone would want to talk to. I came up with a politician, a celebrity, and a religious icon. My categories were pretty accurate but it was clear that I would need to add a few more.

Bar Graph of Data

Pie Chart of Data

It was surprisingly difficult to come up with groups to completely classify the data. I feel like many of the people who were mentioned could fit into multiple categories. For example, you could argue that all of the politicians are also celebrities. Many of the celebrities and the religious figures were also humanitarians. I tried to classify each of them to what I would consider to be their primary categorization. There were a few people listed who are fictional. I did not consider this possibility when I was initially brainstorming categories.

After looking at the data already provided, it could be interesting to ask what exactly it is that people would want to talk to the people about. For example, I said that I would want to talk to Steve Irwin, who I classified as a celebrity. I would not want to talk to him about life as a celebrity but about his conservation efforts.  

ARTICLE

My own introduction to statistics and data was very different from the lessons described in the article. My experience was much more structured and less interactive. The data used always came from the book or a worksheet. I also do not remember the questions going as deep as they seem to be in the analytic step.  I found that extra content to be very interesting! After the initial sorting, distribution and analysis of the data they plotted, questions were asked that could change different variables of the chart. It may not really pertain to the original problem but it encourages students to think critically.

How Many Pockets

I really enjoyed this video. It is one thing to read about a lesson, but I think it is really helpful to see it happening. I liked the way that the student's were arranged in a circle. This allowed all of the students to have comfortable visibility of the board, the teacher, and their peers all at once. The teacher did a great job of never out right giving the students the answers. Instead she lets the students talk it out themselves. At one point a student said "5 is bigger." You could tell that she had the right idea she was just having trouble articulating it. Instead of telling her she was wrong and rewording the answer, the teacher allowed another student to add on to the answer. Overall I think this was a very successful lesson. 

Annenberg

1.What do you think of when you hear the word statistics?

   I immediately think of averages and percentages

2.Think of a general question that could be answered with statistics. Now think carefully
about the four components of the statistical process. How could you carry out each step in
order to answer your question? 

  Would people rather speak to a well known man or woman?

First you would have to survey the class asking them what well known person would they most like to have a conversation with. Once the survey is done you can sort their replies into two categories, male and female. Knowing the amount of responses that were female and the overall number of responses you can easily solve this problem. 

3. What type of shoe is the most common for 3rd graders?
The sample would have to consist of both male and female students and students of diverse racial/ethnic backgrounds. It should also be reasonably sized. An example of a sample that would not be representative would be 5 girl students from a class of 30, intended to represent the 3rd grade as a whole.

Practice

While I was grocery shopping this weekend I decided to put my categorization skills to the test. I settled on two different types of categorization and they actually yielded similar results!

 The first way that I categorized people were by shoe type. I made 4 categories: sneakers, flip flops, sandals, and other (heels, loafers, etc).
I found that the women who were wearing flip flops and sneakers were more likely to have children with them. In contrast the women wearing other shoes were typically without children. This classification did not seem to affect men.

I then classified people by hair style. I made 4 categories: up-do, long hair, short hair, and unusually colored hair. I found that people with the longer hair and unusually colored hair were younger. People with short hair and up-do's tended to have children with them. Again, men were fairly unaffected by these categorizations.

Introduction

Hello everyone! My name is Sarah. I am a senior (FINALLY!!!!!!!!!) in the UNCW Elementary Education program. I live out in Richlands with my husband David and our dachshund Tokyo.

David and I are high school sweethearts. We have been married for 3 years and are loving every second.

This is us from 14-20

 David is in the Navy so we have had the opportunity to move around a bit. We lived in Rhode Island for a few years and we have been in North Carolina for a year. We both love to travel so, for the most part, the experience has been awesome. The only downside to moving around is you never graduate!!! I transferred to the University of Rhode Island as a junior and had to go back and retake so many gen. ed. classes that I was not able to get through all of my major classes before we had to move again. I then transferred to UNCW and had to retake classes to meet this university's requirements as well. I can see the light at the end of the tunnel and am so pumped to finally be able to start my career. I love to be outdoors and can't wait to move back to the mountains or somewhere with good hiking! I am an introvert so I enjoy being a homebody.

MATH

I feel like this is an accurate portrayal of my early Math experiences:

 I didn't really start to do well in Math until high school and I have never come to appreciate it. I do know that it is a necessary skill and I hope that I will be able to foster positive attitudes towards Math in my future classroom.

• Math is... a necessary evil  :)
• When it comes to learning Mathematics, I feel... that practice makes perfect. I wish it did not take me so long to realize that home work is actually very beneficial! When I finally went from being bad at Math to OK, I would go home and put off my Math homework because I dreaded it. I would end up rushing through and just writing in answers to get it done. When I finally did start to actually sit down and do my Math homework, I found it surprising how much easier Math class became. 
• When it comes to teaching Mathematics, I feel... I am a believer in mnemonic devices and other tricks! To this day I still run through Please Excuse My Dear Aunt Sally and the little song my Geometry teacher taught us so we wouldn't confuse circumference and area of a circle. I feel like my "aha" moment for Math came in high school. I know that there were formulas in my life before my first Algebra class, but the way they were taught never made it click for me. I know that formulas aren't necessarily "tricks" but that is how my Algebra teacher explained them. "You want to find this? Well this formula finds that! You literally just plug in this number and this number into the formula. Then you have your answer. That is literally all you have to do" I feel like it gave me a clear template that I could build off of. 
• Elementary Mathematics should be... encouraging! I feel like the most devastating thing that can happen in Math is the development of a negative attitude. That negative association follows you for life!
• Being good at Mathematics means... being a critical thinker. Something that I learned way too late in my academic life is that there are many ways to solve a problem. Someone who is good in Mathematics can see a problem and apply a concept even if it isn't the concept that is being discussed. 
• Good teachers should encourage their students to apply critical thinking. They should expose them to frequent opportunities to build these skills. They should be encouraging and supportive and constantly challenging their students to go farther. 

Who would you talk to?

If I could pick someone to sit down and talk to I would choose Steve Irwin. His programs were a major part of my childhood and I feel like he shaped a lot of my personality growing up (for better or worse). Growing up in the middle of no where, I spent a lot of time outdoors playing in the woods and surrounded by animals. My parents used to get so mad at me because our yard quickly became a hot spot for stray cats because I would sneak bowls of cat food outside. They eventually accepted what was happening and bought a big bowl to keep on the back porch. This led to other visitors such as raccoons and opossums which, much to my parents' dismay, I would also try to touch and feed. My husband and I visited Mexico last year and he told me that we could never live anywhere with a lot of wild life because I wanted to touch everything! The joke is on him though because I got to pet a coati!

I was constantly getting in trouble for bringing frogs, lizards, and turtles into the house. Since most of the cats that hung around the house were fairly feral and because I was the only one in my family interested/patient enough to earn their trust, every summer when the cats had kittens, it was my job to find the litters and to make sure they were comfortable around people so we could find them homes. In high school I was active with our county animal shelter and fostered a lot of cats and dogs. I can not wait to not be a renter anymore so that I can start fostering again!

I really admire Steve Irwin because of the immense impact he had on wild life conservation across the globe.
Most of all, it was clear by listening to him talk for 2 seconds that he genuinely loved animals and he believed in his cause. He did so much good in the short time he had and he left a powerful legacy that is continuing his work. It has always been on my bucket list to visit the Australia Zoo (the zoo that his father started as a reptile conservatory) and I only wish I could had met him as well.