Welcome to the Standards Solution blog! Here we’ll share our experiences, challenges, and insights in the age of the Common Core.

We’d love to hear about your experiences with the CCSS and PARCC assessments, too. Please feel free to leave comments. Thank you for reading and sharing.

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: 


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



Nov 20, 2015
BY Standards Solution

I am thankful for….


When I was five years old, my mother took me to the local public school to enroll me in kindergarten. She told me we walked out of that big public school and I looked at her and said, "I'm not going to make any friends here." My sympathetic mother took me across the street and up the block to the small Lutheran school. A two-story brick building with red doors that, according to my mother, smelled like an old basement.

I had to be tested first, so the kindergarten teacher, Mrs. Babcock, came downstairs to get me and took me up to her classroom. I don't remember what happened up there, but my mother says I came downstairs holding Mrs. Babcock's hand and smiling. I had found my school.

I went to Eltingville Lutheran from kindergarten through eighth grade and graduated as valedictorian on June 26, 1996. I am grateful for my time there, as it was there that I discovered my love of learning and realized that I wanted to be a teacher (in kindergarten!). I remember all of my teachers, all of their different personalities, all of the fun events, like the Thanksgiving Day Feast, Father-Daughter dances, bake sales (where Mrs. Green, my third grade teacher, came in with a roll of quarters and gave students who forgot their money fifty cents each, enough to buy two treats), all the plays, the poetry recital, my middle school teachers asking me to tutor the other kids in Spanish and math. I remember how all the teachers knew every student and their parents and how we could tell they truly cared about us. While I went on to get a bachelor of science in elementary education, it was at Eltingville Lutheran School on Staten Island that I discovered what it means to be a teacher. I will be forever grateful for all the teachers and friends that I met there and for everything I learned there. I believe I am the person I am today in part because of Eltingville.

Judy Cataldi

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When I think about education, there are so many things I am thankful for: my parents, who were educators themselves, the many teachers I had over the years who shaped me into who I am today, and the students I had in my classroom, who taught me as much as I taught them.

Today, though, I am thankful for the enthusiasm and commitment of young teachers! My daughter Hailey, a fourth grader, has a young and new-to-the-classroom teacher for math this year. In the short time since the school year began, Hailey has benefited from this teacher’s enthusiasm and commitment to education in so many ways. Math is not one of Hailey’s favorite subjects, but since this teacher is young and enthusiastic, Hailey connects with her more, making math a little more tolerable. I can tell this teacher truly cares about Hailey’s success. She has been instrumental in helping Hailey stay organized. She has provided extra support and even extra credit opportunities for Hailey when needed. And she has maintained an excellent level of communication with me, letting me know not only her concerns about Hailey’s progress, but also Hailey’s successes in the classroom.

My hope for this teacher is that her enthusiasm and commitment to education do not fade over the years, but only continue to blossom. Students benefit from teachers of all ages, who love what they do and demonstrate it through their actions with students and parents.
Jennifer Caldwell

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In seventh grade I tried out for the school basketball team. I was tall, fast, and possibly the worst player that ever tried getting a ball to go through a hoop. On the day when the team lineup was announced, I was sitting in English class preparing for a writing conference with Ms. Smith. Over the loudspeaker the coach called those who tried out down to the gymnasium. I didn’t make it. When I returned to class it was my turn to meet with Ms. Smith about my latest essay. She asked me if I made the team. I mumbled a plaintive “no.” Calmly, she said, “That’s all right.” And then she pointed her pen toward my paper, looked at me, and nodded, as if to say, “But you have this.”

At the time, though I perceived her gesture, I’m not sure that I fully appreciated what Ms. Smith had done. Years later I realized that her tacit encouragement, just a simple glance and nod, was possibly the most formative experience of my writing life.
Jim Ambrosky

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A great teacher can make all the difference in a child’s life, and the child can make a difference in the teacher’s as well. My daughter has grown very attached to quite a few of her teachers. She often visits them and thanks them for showing her strategies that she now applies in her daily learning. One teacher in particular had every student in class make a book of all the lessons they did. Every day, she had them tape that day’s lesson into a composition book. Grace was not a fan of this—the tape needed to be applied in a very specific way. Grace didn’t see how the book served a purpose. After all, she’s in eight grade and knows everything. So this book became a Bible for this class with all its notes very neatly organized. It made studying much easier as every lesson was in one spot. Grace still had difficulty admitting it was helpful. Now three years later my youngest son, Billy, has the same teacher. One time, he was complaining to Grace about having to make the book. I overheard Grace telling Billy that she now finds the book very helpful, she used it to do her summer math packet and that she applies the concept to other studies as well.

Alice Maxton

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I grew up in a rural area of southwestern PA and had learning disabilities that weren’t diagnosed until I was in sixth grade, which by then I had learned on my own how to compensate for. In high school I was told by my guidance counselor that I wasn’t smart enough to get into college! I earned an associate's degree with a B+ average from art school, and am now back for my bachelor's in fine art with a current 4.0 GPA at the Art Institute of Pittsburgh. 

I am thankful that my daughter has teachers who are more open to the fact that she might have dyslexia. I had noticed signs early on when she was spending time with me when I was a stay-at-home mom. Many people are upset with the No Child Left Behind, PARCC testing, and other programs. If it wasn't for these programs for the last four years my daughter wouldn't have had school supplies, backpacks, school lunches, preschool or even her first year of kindergarten with caring teachers who cried when she relocated. The world of education is ours if we just embrace it. My principals in both elementary and high school made me understand that we should never take for granted access to a free education. I have passed that along to my daughter who has loved going to school every day since she was three.

Jennifer L. Stevens

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As a new mom, I realized dropping your child off at daycare is no easy feat. I had a bad case of the “mommy guilts.” In the beginning most days my daughter would have a death grip on me as the daycare teacher would gently try to pry her off me, saying, “It’s okay. Mommy has to go to work.” Then I would walk down the hall, which seemed to get longer and longer with the echoing of my daughter’s cries of “Mommy.” It is the ultimate walk of shame. I felt terrible…

After that, all day at work I felt anxious…is she still crying, is she upset, is she sad…

But I guess that is par for the course in the daycare world because the teachers at my daughter’s daycare always find clever ways to make that morning goodbye a good experience and fill her day with activities and learning.

My separation anxiety in those first few months was eased by those wonderful teachers. Now when I drop my daughter off, she runs to the window to watch mommy’s car pull away, and when I pick her up, she runs into my arms, showing me a picture she colored or telling me about what she did that day. I might still secretly wish that I could spend all day with her, but knowing she’s being nurtured and comforted makes my day a whole lot better. I can’t thank the teachers at my daughter’s daycare enough for giving her a warm, safe, learning environment and making her mommy feel a few less “guilts.”
Michaela Szidloski

Preparing for PARCC - Blog Series Part III

Preparing for PARCC
Using PARCC Writing Rubrics to Inform Instruction – Part 2
Creating a Corrective Instruction Plan

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.

Last year, PARCC posted their writing rubrics for the Prose-Constructed Response (PCR) and then revised them this past July.

In the first post, we discussed how instructors can score their students’ essays by creating item-specific guides. And we stressed that the only reason we assess students is to identify their strengths and needs, which in turn enables us to provide corrective instruction. In this post, we’ll show you how to analyze students’ needs and create a corrective instruction plan to address these needs.

Analyzing Student Results
      Use the Analyzing Student Essays form and identify your students’ needs.
      Based upon your analysis, what is your class’s greatest need in relationship to constructing an on-demand LAT or RST?
      Which students performed exceptionally well? What was special about their essays?
      Which students displayed the greatest needs? What are their needs and how will you provide corrective instruction?

Consider Your Classes’ Needs
What did you discover when you reviewed your classes’ essays?  Below are some common needs:
      Students answered the prompt, but wrote an open-ended question response instead of an essay.
      Students did not write an introductory paragraph with a thesis statement.
      Students’ essays lacked structure and organization.
      Students did not respond to all parts of the PCR prompt.
      Students provided evidence but did not link it to the reasons, topic sentences, and/or major claim.
      Students did not finish in time.

Create a Corrective Instruction Plan
Use the Corrective Instruction Plan in this section. Based upon your findings, what activities will you implement to address each class’s greatest needs?  Moreover, what is your plan for providing assistance to individual students? Click on the links to access suggested activities.
                           Deconstructing Essays
·                          Honing Understanding of Evidence
·                          Creating Advanced Arguments
·                          Creating Rubrics
·                          Selecting Literature
·                          Constructing PCRs
  
In this two-part blog, Using PARCC Rubrics, we learned:
·                         How to create item-specific guides
·                         How to score our students’ LAT and RST essays
·                         How to analyze our students’ results
·                         How to provide corrective instruction to address student needs

If you have any questions or comments about this content, please feel free to contact this blog’s author, Victoria Pagonis at victoria.pagonis@standardssolution.com.  She will be happy to help you make preparing for PARCC a meaningful learning experience.

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.  


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


Preparing for PARCC - - Blog Series Part II

Preparing for PARCC
Using PARCC Writing Rubrics 
to Inform Instruction – Part 1
Scoring Student Essays



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.

Last year, PARCC posted their writing rubrics for the Prose-Constructed Response (PCR) and then revised them this past July. However, since each writing task is unique and the rubrics are generic, to make good use of these rubrics you must create item-specific guides that qualify the range of student responses.

You can create item-specific guides to score your students’ on-demand writing samples. These guides will give you an idea of which writing skills you should focus on to help students improve their writing.

First, we need a thorough understanding of PARCC’s generic rubrics, and then we must identify the item-specific information related to each prompt. There are three components to PARCC’s generic rubric: Reading Comprehension – Comprehension of Key Ideas and Details; Writing – Written Expression; and Writing – Knowledge of Language and Conventions. Below is a list of student expectations for each category.

Reading Comprehension
     •     Students must include evidence of understanding, including direct references and inferences.
     •     Students need to link perspective (“analysis”) to specific evidence.

Written Expression
      Students must respond to all parts of the prompt.
      Students must develop a claim or topic with reasons and textual evidence.
      Students must write in the specified discipline (narrative, essay, etc.).
      Students must write in a style and organization effective for the conventions of the discipline.

Written Conventions
      Students must demonstrate command of the conventions of standard English.
      Students need to write enough so that scorers can properly assess their command of standard English conventions.

The first step in creating the task-specific rubric is to survey your students’ essays. Task-specific rubrics are constructed using student responses and by identifying expected conditions for each category of the generic rubric. Use Standards Solution’s Item-Specific Considerations to set the expectations for each category.

Now that you have considered every element of the rubric, return to your students’ essays and use the rubric and your item specific guide to identify strengths and areas of need.

Scoring LATs and RSTs
For responses to the Literary Analysis Task and Research Simulation Task, three dimensions are scored for a total of 19 points (15 for grade 3).
      Reading: worth up to 4 points
      Written Expression: worth up to 12 points*
      Knowledge of Language and Conventions: worth up to 3 points

*When determining the score for Written Expression, the scorer first determines the holistic score (4, 3, 2, 1, 0) based on which score point best describes that paper. Then that score (4, 3, 2, 1, 0) is multiplied by three. This means that only certain scores can be represented (12, 9, 6, 3, 0). This is true for both rubrics.

The Scoring Process
      Use the rubric and your item specific guide to review each essay.
      Score Reading Comprehension.
      Consider the elements to Written Expression and score accordingly:
      Did the student write an essay that addresses all parts of the prompt?
      Did the student provide a claim with reasons and evidence?
      Was the student’s essay organized and effective for the given genre?
      Remember to consider the holistic nature of the essay when selecting point values for Written Expression and remember to multiply by three.
      For the Writing – Knowledge of Language and Conventions category, points should only be deducted when the errors impede meaning.

Remember, the purpose of evaluating our students is to help them improve their abilities. In our next post, we’ll describe how to analyze your students’ needs and provide corrective instruction.

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. 


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


Preparing for PARCC - Blog Series Part I

A Six-Step Process for Completing the LATs and RSTs


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.



In this article, we’ll explain our six-step process for responding to the Prose-Constructed Response (PCR) prompt on PARCC’s Literary Analysis Tasks and Research Simulation Tasks. Students who follow these steps will have a great advantage on tackling the essay questions in these tasks.

These steps are meant to be followed after the student has read the prompt and texts at least once.

Step 1: Consider the Prompt
           
Too many educators assume that students read a prompt and just know what it’s asking them to do. But PARCC’s writing prompts can be startlingly easy to misread if one isn’t careful. Students should be taught how to analyze the prompts and then state in their own words what the prompt is requiring of them.

For an example, read the PARCC prompt below. A student may read it and think that she is only identifying the authors’ arguments. However, what she’s really being asked to do is analyze the strength of the arguments.  

Step 2: Rewrite the Prompt as a Thesis Statement

Once the student understands what the prompt is asking her to write about, she is then ready to make a claim in the form of a thesis statement. A thesis statement can be constructed following a simple formula: Restate the main idea of the prompt and then state your position. In the example below, I restate the crux of the prompt and state my position:

Step 3: Gather Evidence

Next, the student has to gather evidence to support her position from—and only from—the text, not from personal experience or from life at large. The box below displays quotations that the student gathered as possible evidence. She won’t use all of it, but she wants to gather enough so that she has enough to choose from. Because the prompt requires the student to evaluate the strengths of the arguments in each text, the student should collect all the evidence that mentions Earhart’s bravery or demonstrates it by describing her actions. Based on the evidence collected, a student may notice that her original thesis needs to be modified.  

Step 4: Organize the Evidence and Construct the Outline

This step is most often the hardest. Writing a clear and organized essay is relatively straightforward when you have a good quality outline. Organizing your argument and evidence into a coherent whole is where the greatest challenge lies.

The outline should address each of the three major sections of an essay: the introduction, the body, and the conclusion.

Here’s a useful way to organize each body paragraph:
A. Topic Sentence
B. Support
C. Explanation
D. Support
E. Explanation
F. Summary
G. Transition

With this order, the student ensures that she introduces the topic of each paragraph, offers enough support (textual evidence) for her thesis, and justifies the use of each individual piece of evidence. Ideas for transitions and summaries can be jotted down too, but they can also be left for the writing stage, when it will be easier to articulate them once the ideas for the body paragraph are expressed.

Here is a sample with two body paragraphs. The student should aim for specificity and simplicity. Sophisticated language is best left for the revision stage.

Step 5: Write the Essay

Once students understand the format of PARCC’s LATs and RSTs, the majority of classroom instruction should focus on improving the quality of students’ writing. Instruction should begin with the requirements of the task, followed by Steps 1 to 4 above. Once students have mastered the essay construct, instructors can assist students to write strong transitions between paragraphs, to make better word choices, and to write conclusions that leave the reader thinking.

Step 6: Revise, Edit and Proofread

The last step should be taught using explicit directions. Instructors often tell students to revise and edit their essays but don’t explain what or how students should do so. One method that worked well for my students when I was a teacher was to give them an editing checklist, catered to the specific prompt the students were writing from. After students finish their drafts, direct them to go down the list and confirm that they have each item or add the items they don’t have.


Conclusion
Equipped with this six-step process, students will be able to craft clear and organized essays for the PARCC RST and LAT. Practice this process several times throughout the year, so that by testing time your students are clear on what steps they should take to complete the Prose-Constructed Response.

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.