Darby Brenkman ETE 339

Manipulative Activities  When students are using manipulatives, it is important that teachers question them in ways to monitor their understanding. Teachers questions should guide students from manipulative to abstract thinking. Teachers can assess students understanding and growth through students answers to these questions. They can also assess the students ability to move away from the manipulatives after a certain period of time. When students are working in groups, students may be given roles to make sure each student is accountable for their learning. Students should rotate roles, so that each student gets to experience and practice with each role. When students are working in groups, teachers may individually question students or allow students to build off of each others answers.  Students problem solving skills are improving when using manipulatives, because you are giving them something to physically move around and work with. Anything you can make visible will help

Classroom Changes to Deepen Math Learning In the past ten years, the way mathematics is taught in schools has changed drastically. When I was in school, teachers taught the most basic way to solve a problem. Many times this included a standard algorithm or formula. I was expected to memorize facts, but was not always taught the rationale behind them.  In today's classrooms, we focus on teaching the meaning behind mathematics rather than asking students to memorize facts and equations. Many times we use manipulatives to teach the concepts of addition, subtraction, multiplication, and division. These manipulatives give a visual and concrete description of what is going on in each of these types of problems.  In today's classrooms, we encourage students to be problem solvers. This can mean that students are discovering math concepts on their own by making connections to things that they already know. Making connections in mathematics is a major push in classrooms now.

Learning Center Reflection Creating my Learning Center I created my learning centers for a first grade classroom. I did this, because my novice teaching placement was in a first grade classroom and my student teaching placement will also be in a first grade classroom. I thought creating my centers for this grade would be the most beneficial for me. I focused on the topic of place value. I chose this topic based off of my learning segment topic. I did my best to create three interactive activities that students would enjoy. In first grade, math should be fun! I created a place value chart practice, a manipulative representation, and a place value game. I think creating these learning centers was a great assignment, because it is something I can use in my placements and possibly in my future classroom. Other Learning Centers Participating in the learning centers of other was a great opportunity. Other students were extremely creative. I got many ideas o

Calculation Error Reflection During class, we looked at many examples of students making common errors in mathematics. I think this was an important thing to do, because it is something each one of us will see in the classroom. Errors are common, but they are something that can be learned from. Students tend to make common errors. It is important that teachers are aware of what these errors are and are able to recognize them in student work. If teachers are aware of common errors, they may help students avoid making these through their instruction. Obviously we did not have time to cover all common errors made by students in class, but the ones we did cover gave me a good idea of why we need to be aware of these errors.  Many of the errors we covered were related to the operations (addition, subtraction, multiplication, and division). Some of the errors we looked at were easy to recognize and others took much more time to recognize. Some students struggled with the concepts of

Technology in Math Class We have used many different types of technologies in this class throughout the semester. At the beginning of the semester, we started each class with a SmartBoard presentation. We each presented a different skill/tool that the SmartBoard has. This was AMAZING! I loved this, because I know it is something I will be able to use in my future classroom. Some of the tools were more applicable to math in the classroom than others, but it was great learning all these different tools. There are so many different things that can be done on the SmartBoard that I was not aware of.  Within multiple assignments, we created videos displaying an infographic and speaking about the topic. This was a good way to wrap up and bring together the concepts of each assignment. I also believe that this is something I could use in a future classroom. A video students create could be an alternative assessment form.  We used multiple softwares to create infographics, comics,

Understanding & Questioning in Mathematics During the learning segment assignment (and other class activities and assignments), we created multiple types of questions. The three main types of questions are: Gathering and Probing Questions (Assessing Questions)  Gathering and probing questions are asked to help struggling students. These questions prompt students to dig deeper and think in more depth when working on problems.  Making Math Visible Questions (Advancing Questions) Making math visible questions are asked to gauge students' conceptual understanding.  Questions that encourage reflection and justification  These questions encourage students to think about what they did to solve a problem and why they took those steps. These question types will be asked in different situations. Asking questions in mathematics is extremely important. Questioning is a tool that teachers can use to determine what their students know. Teachers also use question

Curriculum Grade Level 6th Grade Creating this year-long curriculum grade level plan was extremely beneficial. I think I learned a lot from this assignment. I knew there were many standards that need to be covered throughout the course of a year, but I was not aware that these standards are split into domains at each grade level. It was very helpful to use the chart and break down the domains and standards into quarters and semesters. It was very beneficial to plan activities and projects that align to each quarter and semester. This gave me an idea of how to begin planning a year-long curriculum in my future classroom. After watching the videos from the other groups, I realized how much the domains aligned across grade level. I discussed this more in my curriculum alignment blog. It was very beneficial to see how the domains and standards line up in the elementary grades. Part of this assignment was very frustrating, but overall I think the assignment is very helpful and is som

CCSSM Content Domain Vertical Alignment Analysis Fractions & Operations & Measurement (algebra & functions are included) As students go from grade level to grade level, they build on the information they previously learned. Even if the domain is not continued in the next grades curriculum, students will need the skills. For example, counting is mastered in kindergarten and therefore; that domain is not continued into first through sixth grade. That does not mean students at these grade levels do not use counting skills to complete tasks within their grade level domains. Although some domains do not carry over the grade levels, many do. For example, the measurement and data domain was included across grades one through five. This domain was built upon throughout the grades. Many grades will review previous content from the same domain, using standards from the previous school year. For example, in sixth grade, measurement and data will be reviewed before covering

Assessment Activity Reflection Evaluation of project: I think this project was a good way to explore the different types of assessments that can be used for mathematics. Typical forms of assessments seem repetitive and sometimes don't seem to display the students knowledge as well as other forms of assessment. I liked that each group focused on one assessment type and then shared that information with the class.  Reflection on academic language and assessment questions from class: I enjoy that this class assesses us in different ways. I think many of our classes assed with homework, tests, and quizzes. It is nice to have a change of pace when it comes to assessments. I also like that the class gives examples of the assessments we learn about.  Learning from my groups topic (journals, learning logs): I love the idea of assessing students with journals and learning logs, because they show the student's growth over time. They are a less stressful way of assessment for

Chapter 10: Pulling it All Together This chapter is a summary of the entire textbook, pulling all the concepts together. The eight mathematical teaching practices are connected to teaching mathematical content. When all eight practices are used together, the environment will be supportive of student learning. Once you have a classroom/mathematical framework created, it is important to create meaningful lessons that support the students through their learning. Instruction must be equitable, meaning it must support all students in the class. It is also important to focus on next steps. This is how you will help students progress after a lesson or unit, based on their performance. Overall, the goal is to create a classroom that helps students succeed in mathematics. Implications for teaching: In my classroom, I would like to give students all the materials they need to succeed in mathematics. I want to make sure that I make my lessons and teaching strategies helpful for all student

Double impact: Mathematics and executive function This article discusses  the goal of "double impact." This goal is to develop students mathematical proficiencies and executive  function skills at the same time. Executive function skills allow children to consider and change their own thinking. These are extremely important skills for children to have. The three categories of executive  function skills are inhibitory control, working memory, and attention shifting and cognitive flexibility. Inhibitory control is the idea that students need to stop to think about what they are doing before they instinctively solve a problem (possibly in the wrong way). Working memory means thats students have the capability to hold and process information they have read or learned. Cognitive flexibility is the capability of students to adjust their thinking and strategies to certain situations. All of these things can be adjusted or scaffolded to meet the levels and needs of