According to Flores (2009), "researchers have demonstrated that the use of the concrete-representational-abstract (CRA) sequence is effective for teaching mathematics to students who struggle with learning mathematics" (p. 145).

The CRA sequence has three phases:

during the concrete phase

students and the teacher use manipulatives to demonstrate the meaning of a particular math concept

The teacher models the math concept and the students use the manipulatives in the same manner as the teacher

during the representational phase

the teacher and the students use the manipulatives to represent math numbers

in the final phase, the abstract phase

the students do not use manipulatives to solve the math problem,

but instead use a mnemonic or memorization of steps to solve a math problem

In this task, you are going to use a math manipulative to:

practice place-value fluency

represent place values to develop the concept of 10 more, 10 less, 100 more and 100 less

teach place value math concepts using the CRA sequence

1.) Development of Pedagogical Content Knowledge

Develop Pedagogical Content Knowledge

Content Knowledge

knowledge about the actual subject matter that is to be learned or taught^{[1]}

knowledge of the manner in which the subject matter can be changed by the application of technology

Pedagogical Knowledge

knowledge about techniques or methods to be used in the classroom

use of virtual manipulative to teach the math concept of 10 more, 10 less, 100 more and 100 less

knowledge that is involved with lesson plan development and implementation

reading of common core math module

practice procedural fluency— skill in carrying out procedures flexibly, accurately, efficiently, and appropriately (Bransford, Donovan, & others, 2004)

develop conceptual understanding— comprehension of mathematical concepts, operations, and relations (Bransford et al., 2004)

Pedagogical Content Knowledge

knowing how elements of the content can be arranged for better teaching

practice procedural fluency and then develop conceptual understanding

b. Please place this rubric in the dropbox folder you shared with me

I. Imaginary Teaching Scenario: Preparing for the a Math Lesson

This 1st section is a typical narrative any teacher who has to teach the Common Core Learning Standards might be able to tell! It is divided into 2 parts.

1. Imagine this scenario

a. You are a second grade teacher;

b. You have to use the EngageNY curriculum to teach math modules;

c. You want to use a virtual math manipulative to develop the math concept of place value instead of using place value disks;

d. You choose to use a math manipulative developed by Utah State University called Base Blocks

2. Prepare for Your Lesson as a 2nd Grade Teacher

a. You read the Common Core Math Lesson developed for you by the authors of EngageNY

II. Imaginary Teaching Scenario: Teaching the Lesson

This section is one way to teach this lesson by integrating technology.

1. Setting up Technology for Learning -

a. Students grab the laptops from the cart

b. They login to the computer

c. They open a web browser which opens to the school district's web site

(i.) On the district's web site, they click a link to their elementary school teachers' web sites

(A.) On the new web site that opens, the students find Mr. Shively's name and click it

(B.) On the new web site that opens, the teacher directs them to the math section and they click on the math link

(C.) Students find the correct date for today's lesson, they find the fluency section and click on the Base Block Link (which opens in a new tab by design)

(ii.) To eliminate extraneous processing (Moreno & Mayer, 2007), the students setup the Base Block Virtual Manipulative by reducing the number of columns shown from 4 to 3

2. Implement the Fluency Script

a. The teacher reads the revised fluency script to the students

b. The students use the virtual manipulative to represent numbers on the place value chart according to the directions on the script

c. The teacher finishes the script with the students

d. The teacher completes the other fluency script as written on the module

3. Skip the Application Problem because you are not sure how to teach the Read Draw Write Problem Solving Section

4. Concept Development Script

a. The teacher reads the revised concept development script

b. Students use the virtual manipulative to represent numbers on the place value chart

c. The teacher completes the script

d. The teacher completes the rest of the concept development section as written on the module

III. Your Tasks

You will complete teacher tasks and student tasks for this lesson

1. Teacher Tasks for you to do

a. Re-create how I setup the links to the Base Blocks Link

(i.) Create a wikipage on this wikispace

(A.) Procedure for creating a new wikipage

(B.) Name of wikipage: YOUR FIRST NAME + JTerm + 2015 (e.g. Chris JTerm 2015)

(C.)Tag: jTerm2015

(D.) Click Create

(E.) Once your wikipage has been started, type in a few words (they can be made up) and click SAVE. Typing words and saving the wikipage will create the wikipage.

(F.) - Click here - to create your wikipage (link will open in a new tab for your convenience)

(G.) To see if you followed the directions properly, - click here - to see all of the class' wikipages

(H.) If you do not see your wikipage, repeat steps A - D

b. Build what you see, on the image below, on your wikipage

As a teacher, it is important for you to reflect upon teaching

a. On your wikipage, which is here, please post a response to this writing prompt: Use one of the the assumptions below and describe how it IS or IS NOT addressed by the Base Block manipulative

(i.) According to the Cognitive-affective Theory of Learning with Media (CATLM), researchers have made the following assumptions:

(a) humans have separate channels for processing different information modalities (Baddeley 1992);

(b) only a few pieces of information can be actively processed at any one time in working memory within each channel (Sweller 1999);

(c) meaningful learning occurs when the learner spends conscious effort in cognitive processes such as selecting, organizing, and integrating new information with existing knowledge (Mayer and Moreno 2003);

(d) long-term memory consists of a dynamic, evolving structure which holds both, a memory for past experiences and a memory for general domain knowledge (Tulving 1977);

(e) motivational factors mediate learning by increasing or decreasing cognitive engagement (Pintrich 2003);

(f) metacognitive factors mediate learning by regulating cognitive processing and affect (McGuinness 1990); and

(g) differences in learners’ prior knowledge and abilities may affect how much is learned with specific media (Kalyuga et al. 2003; Moreno 2004; Moreno and Durán 2004) (as cited in Moreno & Mayer, 2007, p. 313)

b. On your wikipage, please post a response to this writing prompt: Moreno et al. (2007) wrote,"According to the feedback principle, novice students learn better with explanatory rather than corrective feedback alone. Explanatory feedback (EF) consists of providing a principle-based explanation for why students’ answers are correct or incorrect whereas corrective feedback (CF) consists of only communicating whether students’ answers are correct or incorrect" (p. 318). 1.) What type of feedback is provided by this virtual manipulative? 2.) Based on the feedback you described in question 1, what impact do you think it would have on student learning?

(i.) Use evidence from Moreno et al. (2007) to support your answer - see p. 318 - 319

James Earle Fraser's Sculpture called End of the Trail

You have reached...The End of The Trail. You have examined an Interactive Multimodal Learning Environment which can be used to teach math concepts. You can close this tab and return to the course wikipage.

References

Flores, M. M. (2009). Teaching subtraction with regrouping to students experiencing difficulty in mathematics. Preventing School Failure: Alternative Education for Children and Youth, 53(3), 145–152.

Moreno, R., & Mayer, R. (2007). Interactive multimodal learning environments. Educational Psychology Review, 19(3), 309–326.

## Base Blocks & Place Value

According to Flores (2009), "researchers have demonstrated that the use of the concrete-representational-abstract (CRA) sequence is effective for teaching mathematics to students who struggle with learning mathematics" (p. 145).The CRA sequence has three phases:

phaseconcretephaserepresentationalphaseabstractIn this task, you are going to use a math manipulative to:

10 more,10 less,100 moreand100 less## 1.) Development of Pedagogical Content Knowledge

Develop Pedagogical Content KnowledgeContent Knowledge^{[1]}Technological Content KnowledgePedagogical KnowledgePedagogical Content KnowledgeTechnological KnowledgeTechnological Pedagogical KnowledgeTechnological Pedagogical Content Knowledge## 2.) Method

Read the entire method before you start doing the tasks. Then read and complete each of the 3 sections.## Rubric

## I. Imaginary Teaching Scenario: Preparing for the a Math Lesson

This 1st section is a typical narrative any teacher who has to teach the Common Core Learning Standards might be able to tell! It is divided into 2 parts.Base Blocks? (p. 5.A.4 - 5.A.5)Fluency? (p. 5.A.6)Application Problem? (p. 5.A.6 - 5.A.7)Concept Development? (p. 5.A.8 & 5.A.11 - 12)Problem Set? (p. 5.A.9)Student Debrief? (p. 5.A.13)Exit Ticket? (p. 5.A.14 - 5.A.15)HomeworkRead Draw Write (RDW) Procedureto solve problems## II. Imaginary Teaching Scenario: Teaching the Lesson

This section is one way to teach this lesson by integrating technology.fluency script as written on the moduleother## III. Your Tasks

You will complete teacher tasks and student tasks for this lessonAs a teacher, it is important for you to reflect upon teachingUse one of the the assumptions below and describe how it IS or IS NOT addressed by the Base Block manipulative, researchers have made the following assumptions:Cognitive-affective Theory of Learning with Media (CATLM)Moreno et al. (2007) wrote,"According to the feedback principle, novice students learn better with explanatory rather than corrective feedback alone. Explanatory feedback (EF) consists of providing a principle-based explanation for why students’ answers are correct or incorrect whereas corrective feedback (CF) consists of only communicating whether students’ answers are correct or incorrect" (p. 318). 1.) What type of feedback is provided by this virtual manipulative? 2.) Based on the feedback you described in question 1, what impact do you think it would have on student learning?## References

Flores, M. M. (2009). Teaching subtraction with regrouping to students experiencing difficulty in mathematics.Preventing School Failure: Alternative Education for Children and Youth,53(3), 145–152.Moreno, R., & Mayer, R. (2007). Interactive multimodal learning environments. Educational Psychology Review, 19(3), 309–326.