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====**Hello...My name is Miriam Martinez and I am a senior at UTEP. My major is EC-6 BED Generalist and I am graduating May 2012. I am doing my internship at Desert Hills Elementary in Clint. My first semester I was assigned 3rd grade and this semester I was assigned to first grade. My experience with math has been alot of emotions mixed **==== ====**together. I was very good in elementary and middle school. I would always get the highest point average and my work would always be posted outside in the hallway. This changed when I scored into algebra in the six grade. I got a teacher that was very unexperienced and had no class management skills so the students would talk and not do what was assigned.In UTEP I also had those kind of professors. I had alot of bad experiences with algebra and have had several tutors. I am very optimistic that one day I will get the intelligence that I once had and will be able to help ****y future students. ****know that this Math class will help me alot. So far the class provides a very positive learning environment for those of us that need help in math. The professor seems super cool and relaxed. I am doing alot of math with students in first grade and I know this class will prepare me to provide my future students with good learning skills and with the positive attitude that all students need in order to learn math. **====

Jan 24, 2012 Summary: In my Math BED 4310 class we learned about the 12 different theories on how people learn. These theories are Constructivism,Behaviorism, Piaget's Developmental Theory, Neurosciece, Brain-Based __Learning__, Learning Styles, Multiple Intelligences, Right Brain/Left Brain Thinking, communities of Practices, Control Theory, Observational Learning, Vygotsky and Social Cognition. The Professor assigned us into groups of 3 and we had to draw our learning Theory on a paper without using any letters or numbers. We also had to create a song with lyrics that identified our Theory. We went around group by group guessing by looking at the drawings which Theories they had. We did an excellent job because we got them right. It was a challenge my group to draw the theories because we are not great artist so I we did our best and drew a man with a big head so the brain could fit in it. We got Brain-Based Learning so we drew the three instructional techniques which are associated with the brain-based learning. Which are 1. Orchestraed immersion 2. Relaxed alertness 3. Active processing. On creating the lyrics and song I think we did an awesome job!! We used the tinkle little star tune and created our own lyrics using Brain-Based Learning Theories functions. Reflection: I found all the activities we did in class extremely important and very creative. I think that as a future teacher this prepares me on knowing the different learning syles and different functions that the brain has. I also like the fact the we can use this activies of drawing and singing with our __students__.The activities we did in class used the four learning domains that are very important in learning comprehension. They are listening, speaking, reading, and writing. We read our song, listened to our classmates, we wrote our lyrics, and we spoke to each other in order to organize our ideas. The activities are also very helpful in engaging our LEP students and they help students interact with each other and learn by scaffolding. The theories are excellent in providing me knowledge as a future teacher in understanding how each of my student will learn and react to different activities or circumstances that we might face in our classroom. I have studied some of the learning theories by Piaget, Vygotsky, and Gardner and have found them fascinating. I think that Gardner's Theory of Multiple Intelligence is the one of the theories that I will always apply in my classroom. I am doing my second intership and I have become aware that every child has a different style of learning. Some are Visual others are Intrapersonal and go on. I already know each learning style that the children in my classroom have and I always try to accomodate the activities they are doing with their learning style. I found the activies and assigned reading we did in class very educational and helpful in preparing me and reminding me that everyone has a different personality and way of learnign and I have to respect that and work with it.

1/31/12 ====Summary :Today in class the professor went over classroom management and Bloom's Taxonomy. She gave us different scenarios and assigned us to a group to discuss what we would do as teacher to solve the problem. My group got scenario #2 which consisted of 3 students always disrupting the class and not letting other students participate. After discussing the problem and going over the handouts we came up with the conclusion that a teacher should always set the rules and establish discipline from day one!!!! If the students see that their are no rules to follow and the can get away with doing it with no consequences then they will never stop. Obviously they have been doing this because they are doing it constantly. From day one a teacher should go over the rules and make sure to enforce them. It is not fa ==== ====ir for the students that really want to learn. The check yourself approch should be used in this case this strategy involves telling the students to check what they are doing and correct their actions. The classroom rules should be posted so the and in the rules their should be the rules that students must respect other classmates and the teacher. The teacher can not allow this to continue anymore and she should call the parents and let them know so the students know that actions will be taken. The professor gave us many scenarios that actually happen in real classroom. The scenarios really made us think what we would do if we were faced with this situation. Another topic we talked about in class was Bloom's Taxonomy which is the process of using higher order thinking and applying it to activities. I think it is and excellent way of applying knowledge, comprehnesion, application, analysis, synthesis, and evaluation. This help so much in cognitive development and students can also do hands-on activities by applying their knowledge by constructing. Excellent topics to prepare us for our future jobs!!!! ==== ====Reflection: I really appreciate what professor Joyce is doing for us. She is preparing us with scenarios that we will deal with in a daily basis. Now that I am doing my internship I have encountered with many or these scenarios. I think that many of the students are facing so many issues now that were did not exciste before and that is what is creating many problems. Bulling is a very serious problem. Students pick on each other about who has the coolest games, sneakers, and clothe. Violence is seen everywhere and students want to imitate that. How can we help the students become better persons and create peace instead of violence. I think that talking to them and letting them know that we understand what their problem might be and always letting them know that they can count on us as teachers can help them alot. ====

Feb14,2012 Summary: Today in class three groups presented. The group that presented chapter 8 did a very good job. They went over the objectives and benefits that math provides for children in pre-k. The activities were age appropriate and fun for children that are learning the concept of numbers. Group ch. 9 also did an awesome job. They covered addition and subtration for children in pre-k. They also had very age appropriate math activities that would really grab the childrens attention. Ch 10 group went over alot of strategies that we can use in our future classroom that engage children and motivates them to want to learn math. Reflection: I really think that the group presentation helped me. All of the information that they gave us is very useful to all future teachers. Math is a subject that alot of students fear and that alot of teachers feel insecure when teaching it. I liked the info that group 8 gave us about age and how they learn math. It might seem as through small children dont get the concept of numbers. But they do, they are startintg to get the idea. If you show them alot of cents and one dollar bill and ask them which is more they will say that the cents. Its because children think that more objects means that its value is more. This is our opportunity as future teachers to make our lessons fun and have activities that allow interaction. I also like the idea of having math songs for children. The monkey song has rhyme and repetition and this benefits students in phonics and also in comprehension.They are not only memorizing the song but they are thinking of how many monkeys are doing what. It also creates a positive feeling for those children that might not like math. A song allows for interaction with the teacher and classmates, they are having fun while learning math and this idea sticks to their head. So whenever they think about math they will think of a positive memory. The games that we played were awesome for children to play in class. I think that the teacher should have a play center with all kind of games so that children that are done with their work can go to the center and play. I went to school in California. I remember all sort of fun stuff that the teacher had for us. We had alot of games and every class had a pet. We had a snake so it was fun seen a snake and getting to pet her. I noticed that in Texas there is alot of concentration in assessments. I dont see alot of games in the classes that I have observed. There might be a misconception that maybe games do not provide learning. I think it is the opposite, games provide alot of cognitive benefits. Children have to think of tricks, memorize, act fast, in order to win. There is alot of competion so students have to act quick. The three learning domains are applied in games: Cognitive, Affective, and psychomotor skills are developed. Students think, they win or lose this provides affection, and use game pieces as manupulatives. I feel more comfortable with math with all the strategies that I am learning from my classmates and professor. I also think that professor Joyce has a beautiful attitude when it comes to approaching math. She makes it seems very relaxed and that is the kind of attitude that every teacher should have so that students can feel comfortable and not panic when they hear the word math.

Review Questions Ch.8 1. The four types of relationships that children should develop with numbers 1 through 10 are:
 * 1) Patterned sets: children can learn to recognize sets of objects in patterned arrangements and tell how many without counting.
 * 2) One and two more, one and two less: the two-more-than and two-less-than relationships involve more than just the ability to count on two or count back two.
 * 3) Anchors or " benchmarks" of 5 an d10: It is very useful to develop relationships for the numbers 1 to 10 to the important anchors of 5 to 10.
 * 4) Part-part-whole relationships: To conceptualize a number as being made up of two or more parts is the most important relationship that can be developed about numbers. Examples: Patterened Sets: Use the activity Dot Plate Flash for the students. This activity consists of holding up a dot plate for only 1 to 3 seconds. Then ask the students how many dots they saw and how did the pattern look like. This activity provides good reflective thinking for the students. One and two more, one and two less: Use the activity " Make a Two-More-Than Set." Give students six dot cards. Their task will be to construct a set of counters that is two more than the set shown on the card. Then, spread out eight to ten dot cards and ask students to find another card for each that is two less than the card. Anchors or " benchmarks" of 5 to 10: An example I would use in my future class would be "Ten-Frame Flash." This activity seems fun and very useful in learning in understanding the relationship between number 5 and 10. Flash 10 frame cards to the class and see how fast the children tell how many dots are shown. The students thas to say 10 facts. Part-Part whole relationships: I would definetely provide my students with Scott Foresman's eTools software. It is very important that children have access to technology and learn from it. Technology helps children visualize the concept of numbers and helps them understand by exploring the part-part-whole and missing numbers. 2. The benefits of developing a "think-addition" approach for substraction are that children are encouraged to think about the hidden part" What goes with the part I see to make the whole?" In the ' think addition" the child is likely to think in terms of ' 6 and what makes 9" or "what goes with 6 to make 9 ?" they use the " think-addition mentallity and get used to using the same thought pattern instead of the " count what's left" mentallity which doesnt help much.

Feb 28,2012 Summary: Today in class we had three presentations. Group presenting chapter 11,12,and 13 presented. All three groups did an awesome job. Each group outlined the important information. They also included alot of strategies that we can use in our future class. Reflection: I think that the groups that presented did an excellent job in using manipulatives and visuals in their math activities. Group chapter 11 which presented Whole Number Place Value did activities that I do with my students in first grade. We so alot of those activities in Calender Math. Using straws to represent the Hundreds is very fun and the kids really enjoy it. The Bingo game, flashcards, and Who has? Place Value are fun and practical games that we can incorporate in our future classroom. We should reward the children allowing them to play math games. I mean they get bored with the same stuff. Group 2 presented Chapter- Strategies for Whole Number Computation. This group did an excellent job!! I really liked all the strategies they shared with us. I also liked the activites. The activities made us think!!! It was not just playing games but really developing strategies that help us gain knowlege. Lattice Multiplication is very useful for students that are learning multiplications. If I had now this way of multipling trust me that I would have enjoyed math and because it would have been an easy task when it came to multipling. Also I would have taught my brain different ways of multiplying not just the traditional way. I think this is what schools lack in math. They just stick to the same old games and strategies. The brain is not challenged to think outside of the box and therefore we only think in the traditional way. The multiplication chart is also very important and I think that we should always have our students work on them. It challenges them to multiply fast and become competitive with other students. The Problem Solving Board used the four learning domains. I think this activity should be done as a whole class discussion because it gives students the opportunity to think and discuss and use their own judgement. SuperKids Math Worksheet is also very helpful for our visual students because they can draw their tens and ones in one side and do the traditional math. The last Goup Chapter 13. Using Computation Estimate also had great activities. Estimating gives the student an estimate of what the answer will. Students become very good at estimating and rounding when they are giving the appropriate activities and also if the teacher gives good instruction. Everything we covered in class was very useful in giving me ideas for my future class. I think that the more we challenge our students in math the better they will do in knowing their strategies.

Review #2 Chapter 12. 1. What are the differences between invented stategies and the traditional algothrithms for whole-number computation? Give an example of each difference. The differences between invented strategies and the traditional algorithms are: invented strategies are number oriented rather than digit oriented. An example would be thinking of number 40 and 30 as 4 +3. Also invented strategies are left-handed rather than right-handed. An example would be 20 x 40is 800 instead of the traditional algothrithms which begin on the right. Finally, invented strategies are flexible rather than "one right way." It means to change with the numbers involved in order to make the computation easier. In traditional algorithms teachers need to introduce and explain them and help students understand why they work. Children pick up the traditional algorithms from family members, older siblings, and teachers. Children will use algorithms according to their cultural difference. Chapter 13 What are five general principles you need to keep in mind as you work with children to develop their estimation skills? Give an example for each principle. 1. Use Real Examples of Estimation. Discuss with the students situations in which computational estimation are used in real life. An example would be dealing with money and budgets. 2. Use the Language of Estimation. Words and phrases such as about, close, just, about, a little more or less. This are words that give the students a mental idea of how near they are getting to the answer. 3. Use context to help with Estimates. Focus on the first digits to calculate the answer. An example would be to first round the number then multiply the first digit of the numbers you are multiplying. 4. Accept a Range of Estimates. Estimation depends on the strategy used and the kind of adjustments in the numbers that might be made. Students make different estimates. For example for the problem 27 x 325, on student might use 20x 300, another student might use 25 x 300. 5. Focus on Flexible Methods, Not Answers. Discuss strategies because it will help students understand that there is no " right" estimate. For example 438 x 62 would be 450 x 60. March 20,2012 Summary: Today in class we had 3 presentations from chapter 14,15,and 16. This chapter are a bit more for upper grades so the chapters that presented gave us important information that we can use in our future classrooms. Excellent chapters that teach us the best ways on how to teach students in a way that the information can be applied in their daily life.

Reflection: I presented on Tuesday my group and me had to teach algebra chapter 14. I'm not going to lie the thought of teaching algebra freaked my out, but at the same time I wanted to learn how to teach students this important subject so that they don't go through all that I went through. My group and I selected very educational activities and we were taking a risk because the groups that presented before all had targeted 1st grade and pre-k. We thought that the activities might seem boring to them because we wanted to make them think and practice just like they do in a regular 5th grade class. I came up with the decision of practicing Mountain Math with them since this an everyday activity that prepares them for the STARR. Some elementaries schools dedicate at least 1 hour and 30 minutes with math. All this is aims for the students to pass the STARR Exam. I took the exact math problems used in an elementary school because the teacher was very kind and lend me her material. Some of my classmates were confused because they thought that the equal sign meant that the problem had to equal the same as the other. I had to explain to them that it meant that they had to find the value of the number in the problem. This is a hint of were the children get confused, so we have to make sure that as they work on math we walk around to get an idea of how they are working the problem and if they are having problems go over the algebraic rules and algebraic thinking. This is what happened in my case. I was very smart in 7th grade always made the A honor roll in Math, in the test I scored in Algebra. Only 3 of us in the whole 7th grade class's scored into algebra. When I got to 8th grade and the first day I walked into the algebra class I knew it was going to be a disaster. The teacher had zero classroom management so she would talk over the students and I couldnt understand the words that she was saying. I stayed in that class for one month until sadly I decided to go to the counslers so I could go back to regular math. They did place me in regular math but to my disgrace with the same teacher. I failed in algebra and didnt understand regular math all because of the teacher. So a student that had excellent mathematical knowledge and loved math went to a student that was confused and not interested in the subject. I definetly do not want any of my future students to go through this. Well going back to the subject, we also had other activities that made them think algebraically. Some were algebraic expressions, Jeopardy for fun and learning, and finding the slopes. Chapter 15 presented developing fractions and they also did a good job. I liked the pizza fraction games. It allows the students to learn in a hands-on while allowing them to use a real life situation because children each pizza almost every weekend. <span style="background-color: #00fffd; color: #000000; font-family: 'Lucida Console',Monaco,monospace;">Chapter 16 Developing stategies for Fraction Computation did an excellent job. I really think that the graphic organizer is an excellent strategy for the students so that they know that there are several ways to compute a fraction. It also allows them to think out of the box and not be afraid and stick to the same traditional old fashion way of working out problems. I really loved the presentations because I presented and because we spiced up the class by using activities that stimulated a regular 5th grade class.

<span style="background-color: #00fffd; color: #000000; font-family: 'Lucida Console',Monaco,monospace;">Questions #3 <span style="background-color: #00fffd; color: #000000; font-family: 'Lucida Console',Monaco,monospace;">Chapter 14. What are the five different representations of functions? What are the important ideas students should understand about these representations and about the connections among them? <span style="background-color: #00fffd; color: #000000; font-family: 'Lucida Console',Monaco,monospace;">The five different forms are <span style="background-color: #00fffd; color: #000000; font-family: 'Lucida Console',Monaco,monospace;">1. Generalization from arithmetic and from patterns in all of mathematics.It is the process of creating generalizations from number and arithmetics begins as early as kindergarten and continues as students learn about all aspects of number and computation, including basic facts and meanings of the operation. An example would be in Addition when students explore addition families and in the process learn how to decompose and recompose numbers. <span style="background-color: #00fffd; color: #000000; font-family: 'Lucida Console',Monaco,monospace;">2. Meaningful use of symbols. Symbols represent real events and should be seen as useful tools for solving important problems that aid in decision making. It is important that students understand, see, and symbolize the relationship in our number system.Ideas inicially and informally developed through arithmatics, are generalized and expressed symbolically, powerful relationships are available for working with other numbers in a generalized manner.This exactly the problem that my classmates faced during mountain math. They didnt quite understand that the equal sign meant to solve for the number. <span style="background-color: #00fffd; color: #000000; font-family: 'Lucida Console',Monaco,monospace;">3. Studey of structure in the number system. It is important for the students that they learn basic facts and strategies for computation. For example, the commutative or order property for both addition and multiplication reduces substantially the number of facts necessary to learn. Also students have to examine these structures or properties explicitly and express them in general terms without reference to specific numbers. <span style="background-color: #00fffd; color: #000000; font-family: 'Lucida Console',Monaco,monospace;">4. Study of patterns and functions.This is very important because learning to search for patterns and how to describe, translate, and extend them is part of doing mathematics and thinking algebraically. Students must recognize that the color pattern "blue, blue, red, blue, blue, red," is the same in form as " clap, clap,step, clap, clap, step."This recognition lays the foundation for the idea that two very different situations can have the same mathematical features. <span style="background-color: #00fffd; color: #000000; font-family: 'Lucida Console',Monaco,monospace;">5. Process of mathematical modeling, integrating the first four list items. It is the equation or mathematical model, that allow us to find values that cannot be observed in the real phenomenon. Sometimes a model is provided and the important task is for students to understand and use the formula. <span style="background-color: #00fffd; color: #000000; font-family: 'Lucida Console',Monaco,monospace;">The five different representations of functions require students to use algebraic thinking when solving problems and allows them to explore strategies that make them think outside the box.

<span style="background-color: #00fffd; color: #000000; font-family: 'Lucida Console',Monaco,monospace;">Chapter 15- 2. List three equivalent fractions for2/3. How did you generate this list of fractions? How could you prove that they are equivalent using an area model, a length model, and a set model? What are some teaching points to keep in mind when helping students develop understanding of equivalent fractions? If you start with 2/3, you can multiply the top and bottom numbers by 2, and that will give you 4/6 so they are equivalent. Another way is if you have a square and cut it into 3 parts and you shade 2, that would be 2/3. Also if you cut all 3 parts in half, that would be 4 parts shaded and 6 parts in all. That's 4/6 it would be equivalent to 2/3. You can also simplify 4/6 and get 2/3. I generated this list of fractions by paying attention to the presentation in class and the activities that they gave us. Also ch 15. does and excellent job in explaining different strategies. I have also learned how to work with fractions on my own and have learned a lot of strategies that I have developed with time. You can prove that they are equivalent by using a Length Model because students can visually see and work out the problem they can work out the fraction by using rods as whole or parts and use folding paper strips to form the fraction. This is an excellent strategie that help the student work out the problem and also check if their answer is equivalent. Some teaching points to keep in mind when helping students develop understanding of equivalent fractions is that Equivalence is a central idea for which students must have sound understanding and skill. Connecting Visuals with the procedure and not rushing the algorithms too soon. <span style="background-color: #00fffd; color: #000000; font-family: 'Lucida Console',Monaco,monospace;">Chapter 16. 3. Briefly explain and give an example of each of the four guidelines you should keep in mind as you help students develop computational strategies for fractions.Which of these guidelines will be the easiest and which will be the hardest for you to implement and why The four guidelines to keep in mind are the following <span style="background-color: #00fffd; color: #000000; font-family: 'Lucida Console',Monaco,monospace;">1. Begin with simple contextual tasks.Using contextual problems and letting students develop their own methods of computation with fractions. What you want is a context for both the meaning of the operation and the fractions involved.

<span style="background-color: #00fffd; color: #000000; font-family: 'Lucida Console',Monaco,monospace;">2. Connect the meaning of fraction computation with whole number computation. Ex. 2 1/2 x 3/4 we as teachers should ask " What does 2x3 mean? Follow this with " What might 2x 3 1/2 mean? slowly moving to a fraction times a fraction. <span style="background-color: #00fffd; color: #000000; font-family: 'Lucida Console',Monaco,monospace;">3. Let estimation and informal methods play a big role in the development of strategies. Ex. " Should 2 1/2 x 1/4 be more or less than 1? More or less than 2?" Estimation keeps the focus on the meanings of the numbers and the operations, encourages reflective thinking, and helps build informal number sense with fractions. <span style="background-color: #00fffd; color: #000000; font-family: 'Lucida Console',Monaco,monospace;">4. Explore each of the operations using models. Have students defend their solutions using the models, including simple student drawings. Sometimes students don't get the idea by pencil and paper, some students work at best when they visualize the problem. Ex. a student can draw a pie or pizza to work out fractions. Excellent strategy that helps them visualize and use objects that they can apply in their daily lifes. <span style="background-color: #00fffd; color: #000000; font-family: 'Lucida Console',Monaco,monospace;">I think the easiest guideline for me to implement would be Explore each of the operations using models.It is simple but very effective. It really helps out the visual students and ELL students get the concept of the problem. I would have a great time working with my students problems were they can draw but at the same time they are learning. The hardest but one of the most important guidelines would be Let estimation and informal methods play a big role in the development of strategies. Getting the students to get the idea would be the hard part to implement in my class. But I like to take risks and get my students to use alot of cognitive skills and all the benefits that this guideline provides is very helpful to my students. It encourages reflective thinking, and helps build informal number sense with fraction. This will what students need to become excellent in math!!! March 27, 2012 Summary: Chapter 17,18, and 19. Today in class three groups presented. Chapter 17 did a great job. They had great activities for their future students and also great information for us to help us in our future lessons. Four activities they presented were computer game converting decimal, convertion chart, skillswise, and what is the answer. Ch. 18 group did a very good job! They explained Ratios, Types of Porportional Reasoning, Equivalent Ratios,and Different Rations. Their activities consisted of M&M Ration Sheet, Minibasketball, Technology-Ratio Game, and Receipe ingredient activity. Ch. 19 Developing Measurement Concepts did an awesome job. They did their activities for 1st grade. They explained using small units to measure and the 3 steps. Types of Attributes for example measuring using straw. Also teaching Technology making comparisons, using models of units, Developing benchmarks. Activities consisted of Measure by using cubes, What is the area, How much does it weight? and the clock activity. Reflection: I think that the 3 groups did an awesome job. I think that the activities were excellent and age appropriate. The activity which I think was the best was the ingredient activity. I would have like if the group would have taken some measuring cups so that the students can get the idea by actually looking at the amount. At first it seemed hard but as one of my team mates explained it to me, I got the idea. This activity really makes the students use their mental skills to come up with the amount. Th is also helps the students in their prior knowledge because every student has played kitchen or they have helped their parents with some kind of receipe. My nephew used to bake cookies when he was 3 years old. Of coarse we did all the measurements and he only mixed the ingredients, but he thought that he had done everything. In an actua class I would have taken the ingredients and the students could have done the actual receipe and eaten it. I think this motivates them more because they know that they will eat the actual product so they will be careful as to do everything correct. This also motivates them in their self esteem. They will feel proud of their product. It's kind of like self worth. Another activity which I thought was very useful for the students was the post it. What is the area? we had to fill in the shape with post its. This activity provides the students with another strategy as how to measure by not using the same old traditional ruler. It is simple and fun and I bet I could be able to accomodate it in my future class. The Volume: How much does it weight activity is a daily activity that we do in class with the first graders. This good that they work out this kind of problems because it gives them the problem plus the image and at last they can comprehend on their own and draw an object that they think will be larger than all of the objects in the paper. The drawing will surprise you..My first reaction to the drawing was, How can a 6 year old understand? but they do they know alot of stuff that we assume they don't. Excellent presentations that gave me alot of activities to use in my future class. Now I don't feel as nervous because I have information and activities to back me up!!!!!!! Review Questions #4 Chapter 17. 1. When introducing percents to students, what are some important ideas you want them to realize about the relationship among fractions, decimals, and percents? There are at least 3 ways to help students see the connection between fractions and decimals. First, the teacher can use familiar fraction concepts and models to explore rational numbers that are easily represented by decimals: example. tenths, hundredths, and thousandths. Second. Teachers can help them see how the base-ten system can be extended to include numbers less than 1 as well as large numbers. Third, teachers can help children use models to make meaningful translations between fractions and decimals. 2. Chapter 19. 2. Why should students make an estimate before making a measurement? What are some ways to ask children for estimates that avoid the expectation that they must come up with an actual number? Give an example for each why? There are four good reasons why students should estimate before making measurements. The four reasons are 1. Estimation helps students focus on the attribute being measured and the measuring process. 2. Estimation provides intrinsic motivation to measurement activities. 3. When standard units are used, estimation helps develop familiarity with the unit. 4. The use of benchmark to make an estimate promotes multiplicative reasoning. Some whats to ask children for estimation that avoid the expectation that they must come up with an actual number is asking them " Think how you would estimate the area of your desk using cards, straws or post its." Children will come up with smaller units to try to measure exactly. You can ask the same question for length and have them measure with Giant footprints, Measuring ropes, Plastic straws, and short units. With this strategy students will develop an understanding of measuring using units. Chapter 20. 1. A common activity is to give children pattern blocks, Tangrams, or other tiles to construct shapes. Identify the van Hiele level of geometric thought emphasized in these types of activities. Why are these types of activities valuable for children? van Hiele is a five-level hierarchy of ways of understanding spatial ideas. Each of the five levels describes the thinking processes used in geometric contexts. Level O: Visualization-The object of thought at level 0 are shapes and what they " look like." Students at level 0 recognize and name figures based on the global visual characteristics of the figure. Ex. a squared is defined by a level 0 student as a square " because it looks like a square." Appearance dominate at this level and they can overpower properties of shape. The product of thought at level 0 are classes or groupings of shapes that seem to be "alike." This types of activities are valuable for children because they can observe, feel, build, take apart, or work with in some manner. The goal is to explore how shapes are alike and different and to use the ideas to create classes of shapes both physically and mentally. Level 1: Analysis- The object of thought at level 1 are classes of shapes rather than individual shapes. Students at the analysis level are able to consider all shapes within a class rather than a single shape on their desk. This activities are valuable for students children because by focusing on a class of shapes, students are able to think about what makes a rectangle a rectagle ex. four sides, opposite sides parallel, opposite sides same length, four right angles, congruent diagnals, etc. The product of thought at level 1 are the properties of shapes. Level 2: Informal Deduction- The object of thought at level 2 are the properties of shapes. Students are able to develop relationships between and among geometric objects. Ex. " If all four angles are right angles, the shape must be a rectangle. The products of thought at level 2 are relationships among properties of geometric objects. With the activity minimal defining lists students are able to create a collection of new relationships that exist between and among properties.  Level 3: Deduction-The objects of thought at level 3 are relationships among properties of geometric objects. This activity is valuable for students because they are able to examine more than just the properties of shapes. Their earlier thinking has produced conjectures concerning relationships among properties. Students at this level are able to work with abstract statements about geometric properties and make conclusions based more on logic than intuition.  Level 4: Rigor- The objects of thought at level 4 are deductive axiomatic systems for geometry. At the highest level of the van Hiele hierarchy, the objects of attention are axiomatic systems themselves, not just the deductions within a system. At this level there is appreciation of the distinctions and relationships between different axiomatic systems. Chapter 21 Question 2. Technology makes it easy to compute statistics and create graphs of all types. What is the value of using technology for these purpose? Chapter 21 did an excellent job in explaining about technology and graphs. The purpose of using technology in computing statistics and creating graphs is so that students can have a visual image of the mathematical problem they are computing. Statisticis is numbers in context, called data. Statistics is about variables and cases, distribution and variation, purposeful design or studies, and the role of randomness in the design of studies and the interpretation of results. In statistics the context is essential to analyzing and interpreting the data. Students must be able to interpret the data they gather in graphs Technology helps students create many different kinds of graphs that they can use in class, asignments, and projects. Students are using graphs from 1st grade until they graduate even after they graduate from college alot of careers use and depend on graphs. What technology does in creating graphs is preparing the students for the future, it is also helping them visualize and use an abstract part of their brain they will help them view the data and relate it with the outcome. Chapter 22 Question 3. Describe the difference between experimental probability and theoretical probability. Will these ever be the same? Which is the " Correct" probability? The difference is that experimental probability is the relative frequency of outcomes from experiments that can be used as an estimate of the probability of an event. The larger the number of trials the better the estimate will be. The results for a small number of trials may be quite different from those experienced in the long run. The exact probability can be determined by an analysis of the event itself. A probability determined in this manner is called a theoretical probability. No they will not be the same. One is based on experiments and the other on analysis of the event itself. The correct probability is "theoretical probability because it is based on analysis. 4/17/12 Summary: Today in class chapters 20,21,22 presented. The three groups did an awesome job. Chapter 20 Geometric Thinking and Geometric Concepts explained the concept of Prism and Pyramids, Faces, Edges, Vertex, and Symmetry. The activities consisted of What Am I? Constructing 3D Figures, Identifing faces, vertex, and edges,, 5 Symmetry Figures also marshmallow figures. What I liked about the presentatin was the activity were we had to construct the shape , name the figure and count the sides. Ch. 21 group did Developing concepts of Data Analysis. They explained alot of classification, graphical representation, circle graph, pie chart, line plot, histogram, scatter plots. I love their activities because we got to graph alot of things. The best activity was green eggs and ham. The last chapter 22 exploring concepts of probability also did an excellent job. The activities were hands on and so fun. I loved the activity of buck and water. Reflection- I think the three groups did an excellent job in providing us with hands on, visuals, and also making us use our comprehension in each activity. Eventhough the activities were for 5th grade the groups made sure to provide their future students with activities that they would enjoy.I had already done a lesson on Geometric shapes for my 1st grade class. It was the day my UTEP observer would go evaluate me. My lesson was excellent. I choose math as the subject that I wanted my observer to go evaluate me because the students already knew the concept of shapes. We always talk about shapes in Calendar Math and I make sure to know their level of comprehension by letting them tell me what shapes we see in the world. I get alot of different answers by them. For example a television, stop sign, a party hat, a beach ball, a clock, pizza, and a wheel. This to me proves that they get the idea and they connect it to their daily lifes. I also think that is very important that we start our students with geometry in their early years of school. Remember that geometry follows us all the way through college. It is better that the students grab geometry now so when they get to college they wont have any trouble and feel confident about it.

5 /1/12 Summary: Today we had a pot lock in class. Reflection: Today we presented our final project in class to two other classmates. The project consisted of the math interdisciplinary unit and the evaluations that our teachers gave us on the lesson. We also evaluated professor Joyce. lesson that I teached in my first grade class was about Presidents Week. All the subjects connected in a way that I planed excellent lessons that the students would develop comprehension on each lesson and also be able to apply their previous knowledge and new learnings. I also taught a geometry lesson for my students. I planned this lesson for a whole we and made sure to use manipulative, visuals, and alot of hands on practice. What I mean is that I would make the students show me what a face, vertices, and edges was with their table. I also think that modeling for them helps them alot. I think that that is the best lesson I have taught as an intern, and I really mean it. I got to experience what the teachers do on a daily basis. I got evaluated with very good comments and the best part of all was the great satisfaction I felt. Knowing that math is not my strong subject and being able to prove to myself that I was capable to teaching this subject and also getting my first UTEP evaluation for it was amazing!!! I owe this to Professor Joyce. The first time I walked into her class I felt butterflies. I get nervious when I her the would math. But after listening to everything she said and all the confidence she gave us, I felt relieved. Professor Joyce has created a class with a very positive learning environment. She is kind and has a very positive energy. If only all the math professors could be like her. I want to thank her for giving me the opportunity to prove to myself that I could do it!!! I also want to thank her for all the tips and advice she has giving us as future teachers. Everything that she has taught me I will take with me and apply it on my future class. Thank you for your kindness and thank you for having faith and confidence in us. Thank you a million times!!!!!!