Videos

I watched a few of the videos from Dr. Shafer's students, although I confess that I watched them quickly and didn't catch any mistakes. Writing my own geometric proofs aren't my strength, so when analyzing other's, everything looks good to me. :) But I really liked this method of teaching and assessment of students. When students know that other students will see their work, they seem more motivated to do well. I think that I could use this strategy not only in math, but also in reading and language. Sometime this week or next I would like to try this in my class. I will not incorporate the (very cool) video technology but would like to have students teach a skill to the rest of their class.

Asking the Experts

Ok, my students are really struggling with mixed numbers and improper fractions. So I'm asking the experts--you guys! I'm working with LOW 4th graders and they've been doing pretty well with understanding fractions, but this is really stumping them. We've worked with pattern blocks, fraction bars, and real-life situations. They can understand that numbers like this exist, but they as soon as they see a picture of 2 whole circles and half of another, they label it 5/6. Does anyone have any good manipulatives or lessons that would help with this?

Lesson to Share

Topic-Area and Perimeter
Grade Level-I did with 4th but I think it work for 3rd and 5th too.
Objective-See the difference between area and perimeter and be able to construct rectangles with a given area or perimeter.

My students respond well when there is food involved in a lesson. They pay more attention and behave well because I don't let them eat the food unless they do well. So I used Cheez-its to help students see the square units involved in area. We began by making rectangles of certain dimensions and finding the area and perimeter. This helped them to see how we count inside squares for area and edges for perimeter. I then gave the students a given area and had them construct their own rectangles. We then shared the dimensions of our rectangles and students could see how different perimeters had the same area, and vice versa because I then gave them a perimeter to construct.
This activity really helped my students understand why area is written with square units and perimeter is just regular units. They were also able to see how why we multiply L x W to find area, because they naturally did that when counting their Cheez-its.

March 16th Class

I enjoyed the activities we did on Monday with congruent and similar triangles. I've done the tree height activity in another class and I really like it. I think it's an activity that students would really enjoy and see a relevance for because it's rather difficult to measure the height of a tree with a yardstick. My group worked on the burning tent problem and I think the geometry of it was worthwhile, but the situation was kind of silly. If I were to teach this concept of incoming and outgoing angles needing to be equal, I would probably change the situation to something else like a race for a prize or a miniature golf hole, like we talked about in class.

Chapter Six

I read the Chapter Six article on first and second graders understanding of linear measurement. First of all, thanks Dr. Shafer for giving us an article related to lower elementary. Although I can usually relate the middle/high school articles to my own teaching in some way, it's nice to be able to read something more directly related to the things that I teach. I really liked the article and I think it made some great points. I liked the way that the teacher was continually prodding her students to find out what they were really thinking and she was making mental notes of what to cover in the next lesson. I really liked the way she tied the concept of "half" to birthdays. Having worked with 1st grade in the past, I know how important that "half" mark is to them and they really get what that means. I think it really helped her students to have that concept to relate to. Many students struggle with partioning and fractions in general, and I think it's good that she made her students understand it instead of just brushing it aside and letting the next teacher deal with it. Measurement is such a life skill that students need and I like how she used real world examples like buying wood at Home Depot to help students see the importance for accurate measurements.

Master's Project

I will be creating 1 lesson plan for each grade level (K-5) using Sketchpad. Each lesson will be mainly a demonstration lesson to be used with the projector and possibly SmartBoard because we do not have Sketchpad at our school. Each lesson will include a "Teacher's Guide" for teachers to refer to during the lesson.

ISTEP Concerns

This is an email going around about what we can do with our ISTEP frustrations. If enough teachers voice their opinions, maybe something really can change.

What you can do about I-STEP concerns:

Share your I-STEP concerns (being as specific as possible without violating test security and please do NOT use school computers) with

* State Superintendent Tony Bennett who chairs the State Board of Education tbennett@doe.in.gov ;

* the At Large Member of the State Board of Education David Shane Dshane@LDILTD.com ;

* the State Board of Ed. Member in your Congressional district (You may locate your congressional district at http://nationalatlas.gov/printable/images/pdf/congdist/pagecgd109_in2.pdf )

(Your State Board member's contact information is at the BOTTOM of the page at this link: http://www.doe.in.gov/stateboard/)

* and your legislator. (Locate and e-mail your legislator at http://capwiz.com/nea/in/state/main/?state=IN.)

I-STEP Statewide Meltdown Reported

The term most frequently used to describe student and staff reaction to the new I-STEP tests is "meltdown". The reports
are coming from every corner of the state, from all grades tested, and from students and schools of all descriptions.

The difficulty and apparent non-alignment of the tests with appropriate grades, texts, and student developmental levels has alarmed
teachers, students, parents and administrators. Reports are pouring in of students crying, literally pulling out their hair, refusing to eat,
suffering stomach aches and worse. ISTA has received reports of an unprecedented number of calls to parents to take their children
home because they are physically unable to remain at school.

While more concerns are coming from 4th grade teachers and parents than from any other single grade, complaints are also coming from
those in grades 3 into high school. Among them reportedly -

* even the most advanced students cannot complete the math tests on time;

* tests are covering content not found in some textbooks and not yet taught at this point in the school year (a problem experienced
when I-STEP tests were first conducted in the spring years ago);

* some content, terminology, language, and examples are beyond the grade and developmental level of the students tested. For instance,
the language on some math tests was beyond the grade level of the students, putting accurate assessment of their math skills in question;

* questions are confusing, ambiguous, and sometimes cumulative so that missing any calculation in the a previous question virtually
guarantees the student will miss the follow-up, unnecessarily lowering scores;

* some questions appear to try to trick the students, putting accurate assessment of student knowledge in question;

* multiple standards are included within one question, making it difficult to determine which standard the student didn't understand and
negating diagnostic use of the test results.

Fourth grade teachers have compared last fall's 5th grade test (which tested 4th grade content) to this spring's 4th grade test (which is also
supposed to test 4th grade content), and report that the tests are very dissimilar.

State Board of Ed. members cannot take corrective action unless they know what to correct. If you feel question 1 on day 1 of the 5th grade
math test is flawed, indicate that and describe the flaw as specifically as possible without violating test security rules. Please do not use
school computers or school time to report your concerns.

ISTA will establish a collection site for suggested I-STEP changes and will report that site in future hotlines.

Logo Success

I just had my 4th graders use Logo for the first time and they LOVED it! I gave them a quick overview of the basic commands and then just let them experiment. They worked in pairs, which I think was very helpful, and even my most unmotivated students were totally into this. After they were comfortable moving the turtle around, I challenged them to make a shape. One pair of girls made a square within a couple of minutes. That impressed me! Other groups were eventually able to make a square, rectangle, and some even got really close to making a triangle. Their success with this program makes me wish I had tried it earlier. We are moving onto some Algebra concepts for a couple weeks, but later I will be teaching area and perimeter so I will definitely be using Logo at some point during those lessons.

Slavit Article

I just finished reading the Slavit article and it, again, stresses the importance of exploration of geometric concepts. I remember learning about these properties in high school and I recall that I was told they worked, probably shown a proof that I didn't understand, and required to memorize them. I also remember that I promptly forgot them when the semester was over! I agree with Slavit that triangle similarity should be explored and investigated so that students have a better understanding of the concept. However, it seems to me that the activity would probably not go quite as well in a middle or high school as it did in the college course. Even though the students in the course had probably not worked with triangle similarity since high school, they had done something with it before and would have at least vague recollections of that. These concepts would be brand new to middle or high school students and I think they would struggle with the ideas a little more and perhaps need a bit more direction in exploring the triangles. I do like the idea of using Sketchpad to explore this because it will show the students how side lengths may change but angle measures do not, and that is something that is difficult to do with straws or pencils.

Spring Break

My spring break is March 23-27. I am visiting my best friend in Wisconsin who is due March 3rd with her first baby.

Article Reaction

I fully agree with the article on finding triangle centers. I believe that students often need to have a real world situation in order to understand geometry, as well as most other mathematical skills and concepts. Upper level geometry, in particular, can often lead to the the famous "When I am ever going to use this stuff?" question. By engaging students in problems like the sprinkler and amusement parks question, they can see a real world use of angle and perpendicular bisectors. This motivates students and encourages them to explore the concepts much more than a textbook lesson and worksheet on a skill that seems unnecessary.
I am always trying to think of real world examples to use in my math lessons for elementary students. Some things are obviously easy like addition, subtraction, rounding, and area but other things are more difficult. How do I convince 4th graders that they need to know prime numbers? Other than, "Because you will need that information in middle school!" I think that finding these investigative type of problems is difficult, especially for the elementary level. If anyone knows of a good resource with LOTS of investigative problems for K-5, please let me know.

The Definition of Polygons

My objective today was to teach the definition and properties of a polygon. If I'd chosen to use our textbook (the dusty thing that sits on my shelf) this lesson would've been quite quick because I would have simply read the definition to the students, given them some examples like a square, triangle, and regular pentagon, and assigned them a simplistic worksheet. HOWEVER...I chose to have the students create the definition and properties on their own. I used a "Are/Are Not" chart where the Are side has examples of polygons and the Are Not side has non-examples. I started with a simple triangle and rectangle on the Are side and an open triangle on the Are Not side. As a class (I only have 10) we began discussing what the columns had in common. The students quickly agreed that one property is "closed". I added some more figures, had more discussion, and students came up with "straight lines", "flat," and "3 or more sides." After about a half an hour of discussion on these examples and non-examples, I finally gave the word polygon to the students and discussed that the Are column are called polygons and follow the rules that they created. I then had students draw a figure of their choice in either column and justify their reasoning. They did well with this activity. I'm hopeful that this will be more meaningful to the students and that they will be able to recall the information later in the unit. Heck, I hope they can recall it tomorrow!

Random Thought

Without intending to, I identified 1 of my student's VanHiele level today! We were doing a daily review before my lesson today and one of the questions asked about a square pyramid. I showed the class a square pyramid and asked why it was a pyramid as opposed to a prism or something else. One boy said, "Because it looks like a pyramid!" Internally, I chuckled and thought "Hmm..VanHiele Level 0!"

Technology

As I explored more with Logo this week, I discovered that I had to think more than I thought I would! Many of my predictions were incorrect, and I realized that this program was very useful for making students really consider what they are telling the computer to do. For my 4th graders, I think that Logo will be a little bit difficult for them because they are just starting to learn about angles. I will use it, but probably towards the end of the unit. I will, however, definitely be using Sketchpad as much as possible. I think that it helps students explore a lot of geometrical concepts and the dynamic aspect of it really motivates them. We are fortunate to have a SmartBoard at my school, so I am hoping to bring that in and allow students to work with Sketchpad in that manner.

I'm going to be spending pretty much the whole month of February teaching geometry to my 4th graders. I am excited to be able to use Logo and Sketchpad in my teaching. I am an intervention teacher, meaning I have the lowest 10 4th graders, so I am hoping that these programs will really help motivate the students about geometry. If anyone has any suggestions on lesson ideas or ways to help the students learn all the vocabulary, please let me know. 4th grade is really where students are required to learn ALOT of vocabulary like parallel lines, perpendicular lines, types of angles, types of quadrilaterals, and some polygons like hexagons, pentagons, and octagons.

Math Vocabulary

As I was reading through the information on VanHiele levels, specifically where it mentions vocabulary, a thought popped into my head. I told one of my colleagues (who is also a good friend) to stop using the word diamond when referring to the blue rhombus that is part of a standard set of pattern blocks. (She is a 2nd grade teacher.) I told her if she wasn't going to use rhombus, then she should at least use parallelogram. She disagreed with me at first, saying that 2nd graders don't know the word parallelogram, but I told her that if she taught it to them, they would! I would not expect her 2nd graders to list properties and characteristics of parallelograms, but shouldn't they at least be exposed to the correct terminology? BTW, this teacher did start to use the term parallelogram and commented to me later that most of her students recognize what she is talking about when she uses the term. :)