# data[].attributes.headline
Support productive struggle in learning mathematics  

# data[].attributes.subject
Support productive struggle in learning mathematics  

# data[].attributes.body
Artifact that supports principle: One example of productive struggle could be during a number talk. During number talks students may give you multiple different answers but would not know the steps they took to reach their answer.
Rationale that justifies why the artifact was included: Struggling in math is not always a negative, but can help with understanding. Teachers should be able to promote productive struggle in the classroom by using this term during guided math groups and then creating a whole class discussion. Number talks can display to the teacher if students can thoroughly explain how they answered the problem, if students do not know the problem at all, or know the answer but cannot recall the steps in how they got there.

# data[].attributes.headline
Build procedural fluency from conceptual understanding

# data[].attributes.subject
Build procedural fluency from conceptual understanding

# data[].attributes.body
Artifact that supports principle: Examples include, Counting, measurement process, manipulatives by being able to show and connect place value and number relationships, word problems (circle what they need to know and underline what they need to find). Being able to build a model of the relationships by using base ten blocks. During my experience I was able to teach a math lesson about measuring. I put out multiple measuring tools for students to use. students used all different types of tools to measure objects. Each student measured lengths and object in their own way!

Rationale that justifies why the artifact was included: Be able to have students know how to go through problems, instructions, and assignments in their own way. Encourage students to solve problems in more than one way and explore other ways answers are found. The teacher should be able to offer enough information and strategies for the students to build off of the knowledge they already have. This will give students the opportunity to do work independently. Students need to be able to experience integrating ideas and procedures by building on familiar concepts. During the lesson, students were given materials and help to connect the outside community with more than one way to measure an object.

# data[].attributes.body
Artifact that supports principle:  The artifact I have chosen is, what works best and why. What works best and why helps students to problem solve together, and continue into deeper thinking during course work. Being able to discuss problem solving strategies and answers as a whole class will help students ponder upon strategies. Once discussion begins, students start to collaborate and bounce off of each other’s answers and ideas.
Rationale that justifies why the artifact was included:
Posing purposeful questions will help students to see reasoning and connections about mathematical ideas. Encouraging students to explain and reflect on their thinking will help the teacher and peers understand reasoning behind why they chose that strategy and how they produced an answer. The teacher wants the child to use the best strategies possible when answering problems. What works best and why help students to think freely and say their thoughts out loud so the teacher can help gear the childs focus to another strategy that would be more beneficial. However, students need to understand that there is more than one way to solve a problem.

# data[].attributes.body
Artifact that supports principle:  one artifact could be, the teacher leads a math discussion with the whole class. While that is taking place, the teacher is asking multiple questions to keep students engaged and listening. Then the teacher will have students share answers, thoughts, and reasoning with others. The teacher could use discourse in small-group or whole class. The students will be listening and be able to build conversation by using mathematical examples to agree or disagree with another students reasoning to a problem.

Rationale that justifies why the artifact was included:

Mathematical discourse amongst a classroom helps students to learn more about math and reasoning. Giving students the opportunity to talk to other peers, respond to arguments and discussions to build discourse in the classroom. Discourse will build thinking and for students to understand explanations and strategies used by their peers.
https://www.bing.com/videos/search?q=math+discourse&&view=detail&mid=4D8852AA7E999C969C754D8852AA7E999C969C75&FORM=VRDGAR

# data[].attributes.headline
Use and connect mathematical representations

# data[].attributes.subject
Use and connect mathematical representations

# data[].attributes.body
Artifact that supports principle: Giving diagrams to help with problem situations or giving students the ability to draw diagrams or other representations to help justify their answers. Children may use drawing to help them understand math problems such as “6-5=x” the student might draw 6 circles and then cross out 5 to see how many are left. Giving students a manipulative, diagram, or graph can represent concepts or ideas. An example of using representation would be- (I.E: 1 hundred dollars + 40 dollars + 2 dollars = 132 Dollars. The student could draw out one 100-dollar bill, four 10 dollar bills, and two 2 dollar bills). This could help model how much money is in total. Representations will help the student make sense of their answer and to help with difficulty in a problem.

Rationale that justifies why the artifact was included: The teacher may promote children to use drawings to help them understand the problem and to explain their answers. Asking students to create drawings or to use other visuals will help them justify their answers.

# data[].attributes.headline
Implement task that promote reasoning and problem solving

# data[].attributes.subject
Implement task that promote reasoning and problem solving

# data[].attributes.body
Artifact that supports principle:  In my first-grade classroom, problem solving was our toughest area for children to grasp. However, the students did not realize they problem solve every day inside and outside the math period. Students primarily focused on problem solving with word problems that would challenge them and prepare them for the next grade level. Prior to word problems, students were asked to create their own problem and then solve with detailed answer.

Rationale that justifies why the artifact was included: Teachers are able to use tasks to encourage students to learn and to continue building new knowledge through continuous problem solving. Teachers can model problem solving by doing an example and then giving students problems to do on their own. If students struggle with problem solving, have students work in groups to collaborate and find multiple solutions. Letting students know it is okay to not have a quick solution but to talk out their reasoning for better understanding.
https://www.bing.com/videos/search?q=promote+reasoning+and+problem+solving&&view=detail&mid=8450BC7AE89F15EFFFAA8450BC7AE89F15EFFFAA&FORM=VRDGAR

# data[].attributes.headline
Establish Mathematics goals to focus learning

# data[].attributes.subject
Establish Mathematics goals to focus learning

# data[].attributes.body
Artifact that supports principle: Engaging students in math discussions that have a clear purpose. Goals must be related to course work presented through the year and in the classroom. Using the students learning goals can be individualized based on abilities or set for the entire class. These goals can help students stay focused on their progress through the math course or assignments given.
Rationale that justifies why the artifact was included: Establishing goals for students is important because it shows the teacher and students the result from lessons or coursework. Being able to discuss with students the purpose of mathematical goals will help them connect work to their present and previous learning.