Extra Credit - Alpine School District Math Investigations

What is Investigations Math?
Investigations Math is a program that involves hands-on, standards based learning to help students understand "how" to solve a math problem and not just know the steps involved to achieve the answer.

Some key features of the program include:
* Using manipulative's to help the students understand how to solve the problem.
* The students can each take a different methods to achieve the correct answer. Each path could be different as long as it ended with the correct answer.
* The students have opportunities to share with each other the steps they took to achieve the answer and demonstrate to each other the process of achieving that answer instead of just the giving the answer to the problem.

What were the arguments for and against its use?
This was a very controversial program in the Alpine School District. Orem Elementary was one of the pilot schools that used this program before it went to the rest of the school district. I interviewed a teacher that was teaching at Orem Elementary during this pilot program and my information came from her experience.

Some of the arguments FOR Investigations Math include:
1. The students would be able to understand the process of achieving the answer and would know how to apply it into their everyday lives (instead of just learning the FOIL method, they would learn why they need to use this method and how to apply it to their lives.)
2. Instead of having timed tests where students just spit out an answer that they have memorized (like multiplications for example), they would find ways to understand the process of how that answer is achieved.
3. Students share their strategies and teach each other. It's not just teacher directed, they learn from their peers. The students share their strategies of how they came up with the answer and demonstrate for the class their path. This helps the students understand that there is more than one way to complete the problem. The students don't just perform a procedure but they understand the problem and how to come up with the answer.

Some of the arguments AGAINST Investigations Math include:
1. Parents didn't like their children to come up with the "method" of answering the problem on their own. They wanted their children to be taught the method and have step-by-step procedures taught and followed by their children.
2. Parents didn't like the freedom that it offered their children. They didn't think that their children were being taught math formulas and procedures by the teachers.
3. The parents didn't like that the major focus wasn't drill-timed tests.
4. Parents didn't think their child was learning as quickly using this method. They felt that using so many manipulative's slowed their children's mathematical progress.
5. Parents didn't understand how the program worked and just thought that their child was "playing" instead of actively learning with the manipulative's they were using.
6. State standardized tests weren't up to speed with the new program so the student's received lower tests the first few years. While this was expected, the parents didn't like that.

What were the results of its use in Alpine?
Because of all the controversy and opposition from the parents, Alpine School Districts decided not to make Investigations Math the district wide program that they wanted everyone to use. Instead, they gave each school an option to choose between three different math programs. Each school decision was made by a combined panel of teachers and parents through a math preview night. At Orem Elementary, the parents and teachers were given samples of each of these programs that they could research at this preview to help them make their decisions. Because the different publishers only provided small samples for the preview, the parents selected a program other than Investigations Math that had more materials that could be reviewed at the meeting (the McMillan Program at Orem Elementary). The program selected by the parents had more workbooks, worksheets and physical objects where they could see their child learning in a physical timed matter.

The Alpine School District has adopted the BALANCED MATH APPROACH instead. This method is a combination of the teachers instructing the step-by-step directions for the different mathematical methods while still providing manipulative's for the students to learn with. By balancing both of these programs, the student will have the methods needed and still be able to use manipulative's and hands-on techniques to fully understand how to apply it into their lives.

What is your opinion?
I believe that with the BALANCED MATH APPROACH, the students will be better able to grasp the concepts that the teacher is teaching and still be able to find a way to apply it into their lives. I don't think that the parents gave the original program a chance and that they didn't give the teachers enough credit to know that their children would still be learning the different methods to complete the problems. It is my opinion that for the lower grades, that Investigations Math is the best method possible to help reinforce the skills being taught and really teach the students different ways to apply this into their lives.

Chapter # 6 - Learning and Cognitive Processes

WHAT?
A Model of Human Memory:
When new information is learned it is imput into the SENSORY REGISTER. If the learner didn't notice it, it will be lost forever and they will not have access to it. If they pay attention to it, the information will be moved to the WORKING/SHORT-TERM MEMORY. Three disadvantages of the working/short-term memory are:
1. It has a limited capacity
2. Information doesn't last long here.
3. It is fragile.
After the information has been in the working/short-term memory, if it goes unused, it will become lost. However, if the learner is able to encode it, there is an indepth processing that takes place and the information is moved to the LONG-TERM MEMORY. Three advantages of the long-term memory are:
1. This memory will last forever (unless there is an illness or injury that takes place).
2. It has unlimited capacity.
3. The brain is very organized and moves information to an organized place where it can later be retrieved.
However, if information in the long-term memory is not used or neglected, it could become lost or deminished over time.

SO WHAT?
As teachers, we need to help our students have stimuli they will have a desire to learn more about. They need to "notice" what we are teaching and "pay attention" to it so that this information will move to their working/short-term memory. After they pay attention to this information, we need to provide indepth processing through different memorization techniques, activities and learning experiences that will help this information move into their long-term memory, where it will last forever and they will be able to recall what we have presented for extended periods of time.

NOW WHAT?
I learn best through mnemonic strategies, chunking, rehearsing and other memorization techniques. I know that the more stimuli I have with a topic, the better able I am to move this information into my long-term memory. As a teacher, I want to help my students learn these skills so that they will be able to remember what information I have presented and become better learners. By understanding the Model of Human Memory and the different memorization techniques listed in this chapter, I will be able to help my students become better learners and I will also become a better learner in the process.

Chapter #3 - Erickson's Model of Psychological Development

WHAT?
In chapter 3 I learned about the 8 stages of Psychological Development by Eric Erickson.
1 - Infancy - Trust v. Mistrust
2 - Toddler - Autonomy v. Shame and Doubt
3 - Preschool - Initiative v. Guilt
4 - Elementary - Industry v. Inferiority
5 - Adolescence - Identity v. Role Confusion
6 - Young Adult - Intimacy v. Isolation
7 - Middle Years - Generativity v. Stagnation
8 - Retirement - Integrity v. Despair

It was so nice to be taught a memorization method to help me remember each of these stages. It really helped me be able to understand each stage better and find a way to remember this information for the test. By learning this memorization technique, it will also help me remember this information beyond the testing period and be able to move this information into my long-term memory better.

SO WHAT?
It was good to learn about each of these stages and find out what the greatest psychological challenges are for each stage of development. It was especially helpful to have examples of each stage to help me better understand these stages.
It is important as an educator to understand each of these stages and know what challenges our students will be facing so that we can help our students excel and feel good about their abilities as students.

NOW WHAT?
Since I want to teach Kindergarten, my students could be between two different stages of development (Initiative v. Guilt & Industry v. Inferiority). I need to provide opportunities for my students to take initiative and give them the support for their efforts to help them make appropriate choices as they develop initiative. I also need to help my students to feel self-confidence and encourage them and help praise them as they begin to demonstrate industry.

Piaget's Stages of Cognitive Development v.s. Vygotsky's Theory

WHAT?
This week we learned about Piaget's Stages of Cognitive Development v.s. Vygotsky's Theory.

In Piaget's Stages of Cognitive Development, he defines four different stages of cognitive development:

1 - Sensorimotor Stage: (birth to age 2) During this stage, schemes are based largely on behaviors and perceptions and what is in their immediate view. They also develop an understanding of cause and effect during this stage.

2 - Preoperational Stage: (age 2 until 6 or 7) During this stage, children can think about objects and events beyond their immediate view. However, they lack the ability to reason in logical adult like ways.

3 - Concrete Operations Stage: (age 6 or 7 to age 11 or 12) During this stage, children begin to reason in an adult like logic but this is limited to concrete reality. They begin to display deductive reasoning and can draw logical inferences from information that they are given.

4 - Formal Operations Stage: (age 11 or 12 through adulthood) During the Formal Operations Stage, logical reasoning processes can be applied to concrete and abstract ideas

Vygotsky's theories outlines several different aspects to consider:

- Guided Participation: Vygotsky's believes that adults play an important part of children's learning process.

- Peer Interactions: In addition to the important role of adults, peer interaction also plays a key role in the learning process. Both peer and adult interaction are very important to Vygotsky's.

- Socio-Cultural Learning: The cultural environment a child is raised in has a great impact on the child's ability to learn and know different things.

- Importance of play: Vygotsky's believed that children learn so much during play. They need to be given opportunities for play to be able to help them develop and grow.

- Zone of Proximal Development (ZPD): Vygotsky's defines this as "the range of tasks that a learner can perform with the help and guidance of others but cannot yet perform independently."

- Scaffolding: A support mechanism that provides a guidance for the learner until they are strong enough to support the learning on their own. As the structure gains stability the scaffolding is gradually removed.

SO WHAT?
It's important to understand about both Piaget and Vygotsky's because educators need to know the stages of development and what influences contribute to their students learning. We need to know what to expect at each age of development and what we can do as educators to provide the scaffolding needed to provide the best learning experience possible and develop age appropiate lessons.

NOW WHAT?
I believe that it's important to use both Piaget's and Vygotsky's theories in my teaching. Not only do I need to understand the stages of cognitive development that Piaget outlined, but I need to realize that the cultural background and adult interactions outlined by Vygotsky also play a critical part of the child's learning process.

"Rainman" - Kim Peek

I really enjoyed hearing Kim Peek and his father speak on Monday. I found it very interesting to learn more about Kim and his ability to remember and recall information and how his brain functions. It was a great experience to see the love that his father has for him and the relationship that they have with each other. I thought it was fun to see how the two of them work together and the kinds of conversations that they have. At times I felt like a fly on the wall watching them talk about the events of the week and the upcoming surgery of his brother. How cute that he was concerned about being able to visit his brother while in the hospital.

When Kim would lose interest in what his father was saying, he would walk away and blurt out unrealated comments. It was cute to see his father remind him to be quiet and not speak out. His father said that Kim needs help with many of the basic life skills such as showering, shaving, getting dressed and feeding himself. Yet, his knowledge and ability to remember information far outweights that of an adult. When the audience had the opportunity to ask him questions, Kim wouldn't just give them the answer they were looking for, he would also give them all the background information about their question. It was interesting to hear his thoughts about the many different subjects and the information that he would share about it.

I feel bad that Kim wasn't able to have his first MRI until his 30's and that he has been so misunderstood throughout his life. It wasn't until the movie "The Rainman" came out in the 80's that he started to be more understood and appreciated by the general public. I'm so glad that he is able to go out and let people get to know more about him and gain an appreciation for him and others with the same condition. I especially loved his message that "everyone is special". I'm so glad that we were able to attend. The brain is an amazing organ and we still have a lot of research to be able to understand it more and more.

Chapter # 2 - The Human Brain - Cognitive and Linguistic Development

What?
The human brain is a complex organ that is essential for living. Each part of the brain serves an important function in cognitive and linguistic development. There are many studies and theories that help us understand the human brain. Two different researchers listed in this chapter have given us some valuable insight on human development. Jean Piaget believed that children develop cognitively through assimilation and accommodation in 4 different stages (sensorimotor, preoperational, concrete operations & formal operational). He believed that each stage builds on the accomplishments of any preceding stage. Lev Vygotsky believed that adults in the child's life foster the child's cognitive development and that their background and experiences contribute to their cognitive and linguistic development.

So What?
By knowing about the different theories conducted by researchers such as Piaget and Vygotsky, educators are able to provide learning experiences that not only help the child develop according to what stage the child is in, but will also be able to provide and understand the importance of a child's background and the important role that adults can provide in their cognitive and linguistic development. Also, by understanding the human brain and it's functions, we will be able to provide a variety of learning experiences that will help the child be able to develop both cognitively and linguistically.

Now What?
Now that I've been introduced to the human brain, it's functions and some of the researchers who have dedicated their lives to studying human development, I need to apply what I've learned in my teaching and lesson planning. As a teacher of young children, I need to understand that their brains are still developing and that each child comes to class with their own background knowledge (schema) and that I can help provide experiences in my lessons that will build upon their stage of cognitive development and provide learning experiences that will be appropriate and engaging to their development and learning. I also need to study and understand each stage of development outlined by Piaget to understand the children's learning abilities and provide appropriate lessons where the child will succeed.