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Vertical Alignment Reflection

I learned a lot from this project.  We were able to see how everything was aligned from grade 2 through grade 5.  The concepts were similar throughout, and majority of the projects began with the domain of either Base 10 or Algebraic Thinking.  These started each year at the first quarter because they contain the most fundamental concepts students will need to understand as they move along.  Geometry ended up in the fourth quarter for most of the lesson plans as well because solving geometry problems incorporates all the other domains.  For 5th grade, they can use decimal fractions, fractions, and whole numbers to do geometry.  Other grades focus on addition and subtraction, multiplying whole numbers, and beginning with fractions which are all also incorporated into the domain of geometry.  Students begin measuring in the early years and these skills are applied to solving geometry problems as well. We learned the importance of scaffolding in this class and making sure students under
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Standards & Classroom Change

There are many changes to make in order for students to become proficient in math, understand concepts, and truly be engaged in the subject.  The biggest thing I learned this semester is asking students 'why'.  They always need to be asked why so they can confirm to you their understanding of the concept or where they need more redirection and guidance to explore more.  The SMP and Process Standards allow for students to collaborate with one another and learn from one another.  When they are giving critiques, they can explain why they believe something to be true and students can make reform in their own math education.  They can argue what they believe to be true and why, and support it with different concepts. I also learned that students must constantly be engaged in active learning.  There is no better way to learn than solving problems yourself and searching for what makes a good problem.  Students can become engaged in a problem and use manipulative tools to help them l
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Curriculum Plan Reflection

I learned that the math curriculum, at least for grade 5, is structured in a way that builds so students can constantly be using prior knowledge and understanding of concepts to new ones.  I also learned the wide variety of tasks you can give students.  Some can include modeling; and others do not need to.  Within the tasks you give students, the questions you ask can vary based on the student's level of understanding.  More complex questions that bring in more understanding of the concept can be asked to students who are at a high level of understanding.  Other students may need to work with modeling more and develop a stronger understanding of the concept.  There is a way to incorporate each of the CMP's and Process Standards in a quarter, and especially throughout the year.  One of the biggest things I learned by doing a curriculum plan is that when students are able to critique one another, their own work, and state precisely why, they show their deep understanding of the c
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Reflection on Understanding & Questioning

This semester I learned more about the value of questioning and the different types than ever before.  All the questions we learned how to ask are those of value to gauge the student's understanding of a concept.  Struggling students need to be asked guided questions, all students can be asked questions regarding conceptual understanding, and then students who really get the concept can be asked questions for deep learning.  When students cannot quite answer the questions about conceptual understanding, they can be asked questions for struggling students such as "what do we know?" and "what is the problem asking for us to find?".  When students are showing a solid understanding in the concept, they can be asked questions for deeper learning.  I learned the importance of asking guiding questions, not leading questions.  If you ask students questions to guide them, they will be able to explain their thinking and show their understanding of a concept to you.  If yo
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Errors Reflection

I have learned that errors can either be conceptual misunderstandings or calculation errors.  Most errors depend on what the question is asking and if applicable, what the rubric states.  If there is a rubric and the student fails to meet or exceed what the higher categories are asking but they are able to answer the question, they still may have some errors in their answer.  Errors in calculation may be because the teacher expects students to follow a specific formula or recipe to get an answer so they do not understand the concept.  This is one of the most important lessons I learned this semester.  If students do not understand the concept as a whole, it is likely they will make computation errors when trying to fill out a formula and follow a recipe to get an answer.  Rather, if they understand the concept they will be able to make connections from problem to problem and make the connections to the real-world examples they are given. The first errors we learned were from NAEP.  I
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Journal Summary 3- Bansho: Visually Sequencing Math Ideas

Bansho: Visually Sequencing Math Ideas By: Eloise R.A. Kuehnert, Colleen M. Eddy, Daphyne Miller, Sarah S. Pratt, & Chanika Senawongsa Bansho is a Japanese organizational strategy.  It facilitates multiple problem representations and better classroom communication.  It consists of 3 phases: activating prior knowledge, exploring a problem, and discussing & extending the concept.  The problem situation is written on the left side of the board and they work from left to right.  This allows students to see a running record of ideas that can be connected during whole-class discussion.  The intentional organization of the board focuses students' attention to the problem and helps facilitate meaningful math discourse and learning.  It is also an essential tool for organizing students' thoughts, discover new ideas, and connect to new ideas. Phase 1 of Bansho is activating prior knowledge.  The teacher presents a prompting image along with a problem situation to accompany t
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Assessment Reflection

Assessment comes in different forms.  I learned that assessment and evaluations are different because assessment is measuring what students know and evaluation is how the teacher uses the information from the assessments given.  Assessments must be valid, meaning they are what they say they will be.  Assessments can also be formal or informal.  Formal assessments are planned and given to students intentionally to measure their understanding of a concept.  Informal assessments are unplanned, spontaneous, and can be as simple as observing how students are discussing a concept or ask a question and assess their answer.  Before this class, I knew we had to measure the quality of student work, but we must also consider the quantity of work given and what students put in.  Assessments are either formative or summative.  Formative assessments are given throughout a unit and assess what the students know up to a certain point.  Summative assessments are given at the end of a time frame and the
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