# data[].attributes.body
"Effective teaching of mathematics establishes clear goals for the

mathematics that students are learning, situates goals within learning progressions, and uses the goals to guide

instructional decisions."

# data[].attributes.headline
Artifact- Community Based Lesson Plan Standards, Objectives, Assessment

# data[].attributes.subject
Artifact- Community Based Lesson Plan Standards, Objectives, Assessment

# data[].attributes.body
This artifact is an example of establishing mathematical goals to focus learning. Standards are the foundation for what you teach so that your students are learning the material they need to be learning. In my lesson plan, my standard was "Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems¹ using information presented in a bar graph." After finding the standards, you must ask yourself "What do I want my students to know?" This is how you create your objectives. My objectives for this lesson were "Student’s should be able to answer simple put-together, take-apart, and compare problems using information presented on a bar graph worksheet.

Student’s should be able to create a bar graph to represent data with up to four categories when given a graphing worksheet." The objectives aligned with my standards. Lastly, it is important that you understand whether or not your students met your objectives at the end of your lesson. This is done though formal and informal methods of assessment. During the whole group aspect of the lesson, I observed students and checked for understanding using thumbs up or thumbs down. During independent work, I observed to see if they were able to complete the worksheet correctly or if they were struggling to understand the topic. At the end of the lesson, the students completed an exit slip explaining what they learned during the lesson and rated how well they understood the lesson on a scale of 1-3.

# data[].attributes.body
"Effective teaching of mathematics engages students

in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry

points and varied solution strategies."

# data[].attributes.body
"Effective teaching of mathematics engages students in making

connections among mathematical representations to deepen understanding of mathematics concepts and procedures

and as tools for problem solving."

# data[].attributes.body
"Effective teaching of mathematics facilitates discourse among

students to build shared understanding of mathematical ideas by analyzing and comparing student approaches

and arguments."

# data[].attributes.body
"Effective teaching of mathematics uses purposeful questions to assess and advance

students’ reasoning and sense making about important mathematical ideas and relationships."

# data[].attributes.body
"Effective teaching of mathematics builds fluency

with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using

procedures flexibly as they solve contextual and mathematical problems."

# data[].attributes.body
"Effective teaching of mathematics consistently provides

students, individually and collectively, with opportunities and supports to engage in productive struggle as they grapple

with mathematical ideas and relationships."

# data[].attributes.body
"Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and

extend learning."

# data[].attributes.attachment_link.description
Create a new document and edit with others at the same time -- from your computer, phone or tablet. Get stuff done with or without an internet connection. Use Docs to edit Word files. Free from Google.

# data[].attributes.body
This artifact is an example of how to incorporate meaningful mathematical discourse into your classroom. During this lesson, a small group of students and myself worked together on a measurement worksheet. Following each question on the worksheet, we had a discussion about that problem. This discussion was facilitated through the use of number talks, which are discussion about how a student solves a problem. Student's were able to share their thoughts and ideas about how they solved a problem. Some of the talk moves I used included re-voicing, repeating, adding on and reasoning. Whenever a student shared an idea, I made sure to re-voice what the student was explaining so that they knew I valued and understood their thoughts. During this discussion I asked other students to repeat what their peer said in their own words. Math discussions can be very meaningful because it is a way for students to share, listen, respond to their peers thoughts in agreement or disagreement. It is also a great way for teachers to better understand their students thoughts and how they learn.

# data[].attributes.headline
Article- Interactive Stem Productive Struggle Research Article

# data[].attributes.subject
Article- Interactive Stem Productive Struggle Research Article

# data[].attributes.body
This article explains the importance of productive struggle and what teachers can do to incorporate it in their classroom. Productive struggle is when students are given a task that challenges them, but they are able to persevere through the task by becoming mindful about the strategy they are using. They learn to understanding if a strategy is productive or unproductive. It is often viewed problematic when student's struggle when doing mathematics, but this struggle can be productive and positive. As teachers, it is important that we support this productive struggle by providing challenges that are appropriate and encourages perseverance.

# data[].attributes.headline
Artifact- Assessment of student thinking interview and observation

# data[].attributes.subject
Artifact- Assessment of student thinking interview and observation

# data[].attributes.body
During my observation, the teacher used evidence of her student's thinking to adjust instruction in ways that extend and support their learning. Her students had been learning measurement for 2-3 days. Throughout each lesson the teacher asked critical thinking questions throughout each lesson. She also observed the students during their independent work to see if there were students who struggled to understand the topic. Based on these observations, see knew what she needed to adjust the next day. During this lesson, she knew that her students were understanding what they had learned the past two days about measurement very well. It almost seemed too easy for them. Therefore, the teacher moved on from measuring in inches to comparing and contrasting inches, centimeters, feet and yards.

# data[].attributes.headline
Artifact- Assessment of student thinking and observation

# data[].attributes.subject
Artifact- Assessment of student thinking and observation

# data[].attributes.body
After observing my cooperating teacher teach a lesson on measurement, I pulled a student aside to complete a worksheet similar to what the students completed together during whole group instruction. During this interview, I asked purposeful questions to assess and advance the students' reasoning about important math concepts. Some of the purposeful questions I asked included:

"Why did you use feet to measure your desk?"

"How would you measure the width and length of an object?"

"Yes, to measure width we would measure longways, but what is a better term for something that is longways? What about up and down" (horizontal vs. vertical)

"Why were your answers for centimeters bigger than your answers for inches?"

"What is something in our room, not on our worksheet, that we could measure in yards?"

# data[].attributes.headline
Artifact-Intentional Talk by Kazemi & Hintz, pg. 22

# data[].attributes.subject
Artifact-Intentional Talk by Kazemi & Hintz, pg. 22

# data[].attributes.body
On page 22 of the Intentional Talk book, the author explains that while planning for an open strategy discussion in your classroom, it is important that you pick problems that can be solved in more than one way. In other words, there are multiple entry points and varied solution strategies. During an open strategy mathematics discussion, students listen for and contribute different ways to solve the same problem. This discussion can build the students collection of strategies.

# data[].attributes.headline
Artifact-Using Number Talks to Build Procedual Fluency Article by Anne Berger

# data[].attributes.subject
Artifact-Using Number Talks to Build Procedual Fluency Article by Anne Berger

# data[].attributes.attachment_link.title
Using Number Talks to Build Procedural Fluency through Conceptual Understanding | (Maranda) Berger | Ohio Journal of School Mathematics

# data[].attributes.attachment_link.description
Using Number Talks to Build Procedural Fluency through Conceptual Understanding

# data[].attributes.body
This is a great article that ties together what we have learned about number talks and procedural fluency. This article explains that procedural fluency can be strengthen through the use of number talks. During number talks, students are encouraged to make sense of mathematics, use multiple representations to deepen their understanding, and make connections amongst different strategies in order to develop more efficient and flexible thinking. As students share their thoughts during a number talk, they are presented with thoughts from their peers. Once these different strategies are presented, the students can make connections between the strategies and adjust their own thinking. "By providing students with the opportunity to engage in Number Talks, teachers facilitate discourse among students about their thinking, help students build connections among strategies, and present students with opportunities to put their knowledge into practice as they solve problems." (

# data[].attributes.body
A., B., & Maranda. (n.d.). Using Number Talks to Build Procedural Fluency through Conceptual Understanding. Retrieved from https://library.osu.edu/ojs/index.php/OJSM/article/view/5666

Pasquale, M. (n.d.). Productive Struggle in Mathematics - Interactive STEM. Retrieved April/May, 2018, from http://www.bing.com/cr?IG=9FB0EAE3AC954AD5A44638A2F1055E2B&CID=2F6BAC1BD24E6E431A43A7FED31E6F92&rd=1&h=A5te7nFuje767_RorHaeeeKtTumJRYCycQdr7X0_WUQ&v=1&r=http://interactivestem.org/wp-content/uploads/2015/08/EDC-RPC-Brief-Productive-Struggle.pdf&p=DevEx.LB.1,5068.1

Kazemi, E., & Hintz, A. (2014). Intentional talk: How to structure and lead productive mathematical discussions. Portland, ME: Stenhouse.

# data[].attributes.body
This chapter talks about creating discussions where students can compare and make connections between strategies For example, a teacher could create a compare and connect discussion about two strategies she/he feels is important for her students to understand. Strategy one could be counting on by ones on fingers or a number line. Strategy two could be splitting up the 5 into 3 and 2 and combine 7 with 3 to make 10, and then add 2. This example is found on page 42 of our Intentional Talk textbook. Then, the teacher thinks about what connections are important for her students to notice. In this case, she wants them to understand that you can start with 7 and count on the five one by one. Or they can break up the five into chunks that allow us to easily make tens. This is an important mathematical idea because she wants her students to understand that breaking up the second number into chunks that easily make tens makes counting the total more efficient. This idea of using and connecting mathematical representations is important for students because you want them to see which strategies are more efficient and how those strategies