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1) Establish mathematics goals to focus learning 

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1) Establish mathematics goals to focus learning 

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In every mathematical classroom it is important to establish mathematic goals for students to achieve during the lesson. I created a 3D shapes lesson for a kindergarten classroom. My first goal or objective for the lesson is students will circle the matching object that looks like each 3D shape. Students will achieve this objective by answering all four questions on the worksheet. This allows them to look at real life objects and compare them back to the 3D shape. Next goal for the lesson is students will be classifying and analyzing four real life objects and understanding the difference between each 3D object. They can also relate back to the 3D shape on the worksheet to help them. The assessment of this goal is allowing students to be hands on and working in groups classifying and analyziing real life objects. After each group will have a chance to explain their reasoning for classifying each 3D shape. They can use their previous knowledge from the worksheet and video to their explainations.

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2) Implement tasks that promote reasoning and problem solving

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2) Implement tasks that promote reasoning and problem solving

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Throughout this semester we learned the importance of promoting reasoning and problem solving. I Notice, I Wonder is an example of implementing problem solving skills within the classroom. A way I could implement this in my classroom is display a problem scenario on the board and ask students "What do you notice about the each worm?" I would give time for students to raise their hands and write down all student suggestions. If students have a hard time saying their ideas to the class. I can have students do a turn and talk so students feel more comfortable sharing what they notice about the worms. After students shared what they noticed, ask them, "What do you wonder about each worm?" I will again provide time for students to think and share their answers to class or have them turn and talk. I can also ask if students need any clarification on what other students are noticing or wondering before solving the problem. At the end of this process students should understanding what the visual or story problem is saying and work independently on carrying out each step to solving the problem. If students still don't understand how to solve the problem. I could implement an activity to help them work toward the steps. One activity could be acting out the problem while looking at what they noticed and wonder in the problem. This could help students see a different visual of the problem and they could better understand the notice and wonder ideas.

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3) Build procedural fluency from conceptual understanding

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3) Build procedural fluency from conceptual understanding

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Throughout this semester we worked on a foundation of conceptual understanding so students, over time, become skillful with using procedures. In order for students to understand place value of 10s and ones. They need to begin with developing a conceptual understanding of grouping with base-ten models. This will help students begin understanding the position of each number. Base-ten models play a key role in developing that idea of "a ten" as both a single entity and as a set of 10 units. This model is not meant to show the concept but allows students to construct a conceptual understanding that "tens make one relationship." Beginning the model in kindergarten will allow students to eventually become skillful at using this procedure to understand place value in order to solve any type of problem. A model I want to implement my classroom are unifix cubes. This allows students to make groups of tens out of the single cube. It will begin to introduce the language of "tens." For example I could have students make groups of tens and group of ones. This early process is vital because students need to understand the difference between grouping tens and ones. Eventually once they understand the language I could start having students count with base-ten models. I would give students a number such as "62" and they would use base ten blocks to show the number I gave them. This is a great model for teaching place value. As a future math teacher I will implement base ten models as a foundational skill when I teach place value.

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4) Support productive struggle in learning mathematics

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4) Support productive struggle in learning mathematics

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During my practicum, the students had limited exposure to mathematics. When they did work on math they just did worksheets out of their Math Go books. Below is an example of a lesson that students go through daily. This does not represent a productive struggle because students are being instructed what to do based on the directions the teacher is giving them. A productive struggle allows students to make mistakes but lets them grow and learn from them. This does not show me that students are being challenged or allowing them to make mistakes in order to learn and grow from them. One way I could turn this lesson of comparing heights into a productive struggle is having students find two objects to compare. Then they could practice measuring the objects in order to compare and see which object is taller. This allows students to be hand-ons and productively struggle finding objects to compare. Students may also have questions like, "How do I use a ruler?, What do the lines mean on the ruler? or How do I find out which object is taller?" When students are asking questions it is a sign these students are having a productive struggle. As a future teacher it is important to incorporate productive struggle into my classroom because children need to struggle in order to learn. When a child is not struggle they are not learning.