Preparing for PARCC - Blog Series Part XI

Preparing for PARCC

Building Comfort with the 

PARCC Math Equation Editors

This post is part of our blog series on PARCC. In this series, we offer tips and strategies you can use to ensure that your students perform at their very best on the PARCC tests.

Imagine you are a student taking the PARCC Summative Assessment for Math online. As you click, drag and drop, and make other answer selections, you encounter an item with a large text box that has selections that look much like calculator functions. Perhaps, it is a calculator (it is not). You have encountered one of the PARCC Equation Editors. If this is your first encounter with the editor, it may appear as a “BIG SCARY BOX.”

Many software programs provide equation editors that are useful for creating math expressions and equations. Most equation editors provide symbols for the mathematical operations (+, -, *, ÷). Other symbols are provided such as <, π, . Equation editors are not universal in design; each software program can have a unique editor. Because many students are beginners with keyboarding skills, they may have little to no experience with equation editors.

The PARCC online assessments are delivered on the TestNav8 software program and have unique equation editors.

The Basic Equation Editor is provided as the answer box with an item that requires the student to construct the math answer. The Basic Equation Editor is provided because the answer may require the use of special functions. For example, an item may have this instruction: “Enter only the fraction.” It is not possible to enter fractions in a simple text box using a standard keyboard on the TestNav8 software program. However the Basic Equation Editor has a special fraction function. Here is a screenshot of the Basic Equation Editor for various grade bands:

Notice how the functions are different for each grade band.

The Open Equation Editor is provided as the answer box for items that require the student to enter words and math. PARCC Type II and Type III items with hand-scored responses will include the Open Equation Editor. Here is a screenshot of the Open Equation Editor for each grade band:

PARCC has provided both equation editors at all grade bands for practice. On the PARCC Pearson.com website, select the “Test Preparations” drop-down menu. Then select “Tutorials.”

On the right-hand side of the page, there is a menu of selections for the Equation Editors:

The Equation Editor Guide is a PDF on how to use the editors to create responses. A separate guide is provided for each grade band.

Select the “Practice with the Equation Editor” drop-down menu for online practice with equation editors. Here are some suggestions for providing students with a practice experience:

• Allow students to practice entering sample answers. Create a document of sample math answers that make use of the various functions on the Basic Equation Editor. For example, for grade 3:

                     

• Allow students to respond on paper to a sample PARCC Type II or Type III practice item. Ask the student to enter the response in the Open Equation Editor online.
• Continue with practice experiences online using the PARCC practice tests. The equation editors are provided with the items, as needed. 
• Provide a poster of the editors in the classroom or a small printed image of the editors for each student to reference as needed. This allows the editors to be reviewed frequently. Students can identify the function keys that are needed to create specific answers. As a result, the functions are familiar and visible each day in the classroom, not just when practicing on the PARCC website.
• Use a screenshot of the editors on classroom paper items as the answer box. Ask the students to circle any functions they used in their responses.

The Equation Editor Tutorials provide helpful hints and practice. It highlights various features and operational techniques for entering responses.

Students have varying abilities with keyboarding. The same is true with the equation editors. Each student’s learning curve is unique. Experience with the online editors is necessary to build familiarity with the tool and ease of use. Building a level of comfort will allow students to be more confident with online assessment and to focus more on the content of the assessment items, instead of the software platform. There is no reason why the equation editor should be the “BIG SCARY BOX.”

Standards Solution and Inspired Instruction offer 540 PARCC lesson plans, online PARCC-like assessments with technology-enhanced items, PARCC workshops, and PARCC demonstration lessons. Please contact Judy Cataldi for more information. 

Judy.cataldi@standardssolution.com or call 908-223-7202.

Standards Solution Holding, LLC is not owned by or affiliated in any fashion with PARCC, Inc.

Preparing for PARCC - Blog Series Part X

Preparing for PARCC

 Gaining a Greater Understanding 

of 

PARCC’s Type I Math Items

This post is part of our blog series on PARCC. In this series, we offer tips and strategies you can use to ensure that your students perform at their very best on the PARCC tests.

When I was a classroom teacher, I often asked myself, “What can I do to provide my students with an authentic summative assessment-like experience that will enhance their learning and not interrupt the instruction?” For me, the answer was to understand the design of released summative assessment items and to incorporate similar items in the classroom.

PARCC has shown itself to be transparent. They’ve disclosed the summative assessment structure and focus, evidence statements, and released items from the 2014-2015 PBA and EOY assessments, and provided testing tutorials, practice tests, and other support materials. According to the PARCC Claims Structure (Grades 3-8, HS), more than 50% of the total points on the 2015-2016 summative assessment in math are from Type I items (Sub-Claims A and B). Making sure your students understand Type I items is essential to their success.

What Are PARCC Type I Items?

Type I Tasks assess concepts, skills, and procedures:

• Balance of conceptual understanding, fluency, and application
• Can involve any or all mathematical practice standards
• Machine-scored, including innovative, computer-based formats
• Sub-claims A and B, including fluencies

What Do Type I Items Look Like?

Before PARCC, most state summative assessments included mainly multiple choice and short-constructed response items that were used to measure concepts, skills, and procedures. The level of rigor was limited. In some previous assessments, the lack of quality distractors and/or the effective implementation of simple testing strategies could allow students to score well, but the scores were not a true reflection of the students’ understanding of the concepts. With the new styles of PARCC summative assessment items and the design of high quality distractors, the level of rigor is increased. Students need a deep level of understanding of the math concepts, and they need to apply reasoning and other critical thinking skills. There are two categories of PARCC items:

Constructed Response: The student constructs the answer. This could be a single number, an expression, equation or inequality, and/or a completed mathematical model.

Here’s an example of a PARCC machine-scored Type I item in which the student constructs the answer:

Selected Response: A selection of possible responses are provided; the student selects the correct response(s). There are at least seven different styles of these technology-enhanced items. Some of these styles include: Drag and Drop, Multiple Select, Multiple Choice, Drop-Down Menus, Sort by Category, Reorder the selections. 

Here’s an example of a PARCC machine-scored Type I in which the student selects the answer:

The best way to see the PARCC Type I items is to access the website: http://parcc.pearson.com/

In the menu, select Test Preparation. You will find tutorials and practice tests. I highly recommend engaging in the Student On-line Tutorial  for your grade band. Descriptions of the styles of items and sample items are provided. Also, I highly recommend taking the on-line EOY practice test  for the grade/course you teach. As you engage with the practice items, ask yourself, “What features within the items will be challenging for my students?” 

Consider these features:

• Imbedded Vocabulary
• “Teachers should use strategies for involving students in reading, writing, speaking, and listening as necessary to meet the mathematics standards — for example, to understand the meanings of specialized vocabulary, symbols, units and expressions to support students in attending to precision (MP.6)…”  
• Details in Directions
• Each item has its own specific directions that describe how to record the answer.  Students should highlight directions. Refer to: How to Respond to PARCC Math Items “Direction Detective”  blog.
• Technology Skills
• Notice the technology skills needed to provide the response.
• Design of Distractors
• When identifying distractors, consider how a student may solve the problem incorrectly. This incorrect response is usually one of the distractors. Notice that the distractors are not obvious; this increases the rigor.

Consider the features in this PARCC sample item:

What content is measured by the PARCC Type I Items?

PARCC has disclosed the Evidence Statements  used by the assessment designers.

“Evidence Statements describe the knowledge and skills that an assessment item or a task elicits from students. These are aligned directly to the Common Core State Standards, and highlight their advances especially around the coherent nature of the standards.” 

Evidence Statements include information on "Clarifications, Limits and Emphasis," related "Mathematical Practices" and "Calculator Designations." 

When examining the document, notice the first column on the left side of the table. It identifies the PARCC Sub-Claim. Type I items are Sub-Claims A and B.

A great way to connect the Evidence Statements to the practice test items is to:

• Print the answer key to the practice test. It provides the Evidence Statement Key aligned to the items. 
• Find the matching key in the Evidence Statement Table.
• Review the assessment item. 

This comparison will allow you to gain insights on how a standard is being measured on the summative assessment.

Standards Solution and Inspired Instruction offer 540 PARCC lesson plans, online PARCC-like assessments with technology-enhanced items, PARCC workshops, and PARCC demonstration lessons. Please contact Judy Cataldi for more information. 

Judy.cataldi@standardssolution.com or call 908-223-7202.

Standards Solution Holding, LLC is not owned by or affiliated in any fashion with PARCC, Inc.

Preparing for PARCC - Blog Series Part VI

Preparing for PARCC

How to Respond to PARCC Math Items 

“Direction Detective”

This post is part of our blog series on PARCC. In this series, we offer tips and strategies you can use to ensure that your students perform at their very best on the PARCC tests.

Rigor in the PARCC Assessment

I asked students, “How does the new assessment compare to the previous assessment?” The most common response was “the new questions are challenging.”

I asked for more details about how they are challenging. “Thinking more” was the phrase many students used to describe the increased rigor and use of higher-level critical-thinking skills.

Here is how Common Core describes “rigor”: “The standards will include high-level cognitive demands by asking students to demonstrate deep conceptual understanding through the application of content knowledge and skills to new situations.” - http://www.corestandards.org/assets/Criteria.pdf

Increased rigor in the assessment is not just part of the question design and how PARCC measures understanding. It’s also part of how the student is required to provide their answers. Advancements in assessment delivery via technology contribute to this rigor. Consider the critical thinking needed to consider all the possible ways to express a number verses identifying just one way to express a number:

Features to Emphasize in the PARCC Assessment Items

The PARCC assessment features new technology-enhanced items in two categories:

Constructed Response: The student constructs the answer. This could be a single number, an expression, equation or inequality, a completed mathematical model, or a combination of words and math.

Selected Response: A selection of possible responses are provided; the student selects the correct response(s). There are at least seven different styles of these items, including: Drag and Drop, Multiple Select, Multiple Choice, Drop-Down Menus, Sort by Category, Reorder the selections.

A PARCC assessment item is more than a standard math question. Each item has specific directions that describe how the student should provide the answer. Here is a short list of the various directions provided with PARCC practice items:

• Drag and drop the fractions and operation symbols.
• You may select more than one box for each figure.
• Select the correct symbol from each drop down menu.
• Enter your answer in the space provided.
• Which explanation about the figures is correct?
• Enter only your fraction.
• Choose three statements that correctly describe….
• Select all that apply.

Because each assessment item has its own unique directions, students need to become a

How to Become a Direction Detective:

• When practicing with the PARCC Practice Test online, students need to use the electronic highlighter to decipher and to draw attention to the specific directions given with each item.
• When students practice math in the classroom, students should use a highlighter to decipher the directions for any task. Allow the student to do this independently and then check for understanding by asking the student to state the directions in his or her own words.
• Incorporate similar styles of questions and accompanying directions in the tasks used in the classroom. If the direction sentences are commonplace, they become familiar.
• Ask students to recognize what error(s) can occur when the directions are ignored.

Standards Solution and Inspired Instruction offer 540 PARCC lesson plans, online PARCC-like assessments with technology-enhanced items, PARCC workshops, and PARCC demonstration lessons. Please contact Judy Cataldi for more information. 

Judy.cataldi@standardssolution.com or call 908-223-7202

Standards Solution Holding, LLC is not owned by or affiliated in any fashion with PARCC, Inc.

Preparing for PARCC - Blog Series Part IV

Preparing for PARCC

Aligning Mathematics Instructional Practices

This post is part of our blog series on PARCC. In this series, we offer tips and strategies you can use to ensure that your students perform at their very best on the PARCC tests.

Regardless of how you feel about PARCC, or any standardized test, I think that in PARCC states we can all agree, at this moment it is necessary to prepare our students for the experience. And to be honest, I don’t think that preparing for PARCC is a waste of instruction time. PARCC is a test that evaluates students’ progress toward college and career readiness. It is a test of our students’ competence regarding the Common Core State Standards. Therefore, when we are preparing students for PARCC we are applying and practicing the Common Core. That is what we are supposed to do.

But what does a fully aligned mathematics classroom look like?

“The PARCC assessments are aligned to the Common Core State Standards (CCSS) and were created to measure students' ability to apply their knowledge of concepts rather than memorizing facts.” (NJDOE)

The mathematics PARCC assessments require students to:

• Solve problems using mathematical reasoning
• Be able to model mathematical principles 

Mathematical Reasoning

What Is Mathematical Reasoning?

According to G.W. Martin, et al., “Reasoning can be thought of as the process of drawing conclusions on the basis of evidence or stated assumptions…Sense making can be defined as developing an understanding of a situation, context, or concept by connecting it with existing knowledge.” (Martin, G.W. and Kasmer, L. “Reasoning and Sense” Mathematics Teacher Dec. 2009/Jan. 2010).

The ability to reason is essential to understanding mathematics. Teachers should use effective questioning techniques to promote their students’ reasoning abilities. Students need opportunities to respond to effective questions that require critical thinking, and to share ideas and clarify their understanding. When students are able to connect mathematical ideas, they develop a deeper and lasting understanding of mathematics. The process of reasoning has three stages: conjecture, generalization, and justification.

The Process of Reasoning

• Conjecturing: developing statements that are tentatively thought to be true but are not known to be true
• Generalizing: extending the reasoning beyond the scope of the original problem
• Justification: a logical argument based on already-understood ideas

Types of Reasoning Tasks

• Proof and Justification Tasks: Students are asked to use reasoning to provide an argument for why a proposition is true or is not true.
• Example: the student draws a comparison between two fractions and provides proof that the comparison is true, using a mathematical model.
• Critiquing Tasks: Flawed reasoning is presented and students are asked to correct and improve it. Example: the student reviews an answer created by a fictitious student and must identify and explain possible flaw(s) in the reasoning, correct the answer, and provide an explanation supporting the correct reasoning and answer.
• Mathematical Investigations: Students are presented with a problem and invited to formulate conjectures and prove one of their conjectures.
• Example: the student tests an idea, such as, “Is it always true that when two fractions are multiplied, the product is less than the two fractions?”

Modeling in Mathematics

Concrete models and pictorial models can be used to demonstrate the meaning of a mathematical idea and/or communicate the application of mathematics to solve a real-world problem.

“Students can develop a conceptual understanding of mathematics through modeling, following a progression of representations: concrete, pictorial, and abstract.” (Strategies for Successful Learning, Vol. 6, No. 2, January 2013)

Concrete representation is often demonstrated with manipulatives. Pictorial representation can be various drawings, such as graphs, number lines, object drawings, Ten Frames, and visual fraction models. Abstract representation is the use of numbers, letters and symbols to represent the mathematics.

Consider these examples of the three types of representation:

“There are three times as many cats as dogs; there are 15 dogs. How many cats are there?”

In the Common Core State Standards, each grade level addresses distinct operations and number relationships. 

Here is a list of the distinct operations and/or number relationships for grades 2 through 6:

• Grade 2: addition and subtraction
• Grade 3: multiplication and division
• Grade 4–6: fractions and ratios 

The operations and number relationships are developed sequentially, to allow students to visualize and solve increasingly complex problems. Solving for an unknown quantity at the concrete and pictorial stages aids in the transition to the abstract.

Mathematical Methods and Representations within the Standards

Many of the Common Core Standards for Mathematics are very specific about which methods and representations need to be used to develop understanding of the mathematical concept(s).

To demonstrate this, let’s examine a grade 4 Standard:

4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

The main concept is multi-digit multiplication; the specific digits are provided. The methods are place value strategies and properties of operations (commutative, associative, distributive). The representations are equations, rectangular arrays, and area models. The standard states the specificity clearly; the expectation is that classroom instruction would include the specificity as stated. What could this look like?

An example of an equation that demonstrates place value and properties of operations:

3 x 27 = 3 (20 + 7)

A rectangular array can be demonstrated using a manipulative, such as tiles or base-ten blocks, with a place-value mat.

An example of an array model:

Conclusion:

The PARCC assessment is closely aligned to the Common Core State Standards. When considering classroom instruction and the students’ demonstration of understanding, the specificity of the Standards cannot be ignored. Since the students are expected to reason mathematically and use modeling to represent mathematics on the PARCC assessment, they need opportunities to communicate reasoning and provide modeling in classroom tasks.

It is our sincerest wish that you find value in these ideas and resources and begin to integrate the concepts that students will experience on PARCC. Please let us know if we can help you make your classroom or school more fully aligned with the Common Core and PARCC.

Standards Solution and Inspired Instruction offers 540 PARCC lesson plans, online PARCC-like assessments with technology-enhanced items, PARCC workshops, and PARCC demonstration lessons. Please contact Judy Cataldi for more information: 

Judy.cataldi@standardssolution.com or call 908-223-7202

Standards Solution Holding, LLC is not owned by or affiliated in any fashion with PARCC, Inc.