Preassessments for Differentiation

Pre-assessment Differentiation in Teaching First Grade Math

In a first grade classroom, 22 students were given a  pre-assement at the beginning of the second week of school in order to determine where they fell in their understanding of Math concept standards.  According to the California C.O.R.E. standards, by the time students enter into the first grade they should already have a solid understanding of the following math concepts:

1. Students use numbers, including written numerals, to represent quantities and to solve quantitative problems, such as counting objects in a set; counting out a given number of objects; comparing sets or numerals; and modeling simple joining and separating situations with sets of objects, or eventually with equations such as 5 + 2 = 7 and 7 – 2 = 5. (Kindergarten students should see addition and subtraction equations, and student writing of equations in kindergarten is encouraged, but it is not required.) Students choose, combine, and apply effective strategies for answering quantitative questions, including quickly recognizing the cardinalities of small sets of objects, counting and producing sets of given sizes, counting the number of objects in combined sets, or counting the number of objects that remain in a set after some are taken away. 

(2) Students describe their physical world using geometric ideas (e.g., shape, orientation, spatial relations) and vocabulary. They identify, name, and describe basic two-dimensional shapes, such as squares, triangles, circles, rectangles, and hexagons, presented in a variety of ways (e.g., with different sizes and orientations), as well as three-dimensional shapes such as cubes, cones, cylinders, and spheres. They use basic shapes and spatial reasoning to model objects in their environment and to construct more complex shapes.

- California Common Core State Standards 2013

I presented students with a baseline preassessment in order to gauge the following skills: addition and subtraction with double digit numbers, writing numbers 1 -25, and filling out a number chart 1 - 120.  After students completed the First Grade Math Preassessment, I was able to gauge their knowledge and understanding in accordance with the above CORE standards and the following results were presented:

1. 5 students answered the most questions correctly, including the most difficult of the pre-assessment questions.
2. 12 of the students demonstrated having some knowledge of Math Common Core Standards, but need to develop higher order thinking skills
3.  5 students appear to have limited knowledge of Math Common Core Standards.  Three of those students show signs that they are struggling with language and are at different reading levels, and 2 students show little to no comprehension of the Math Common Core Standards and therefore need to be tested further for special needs

Based off of the information gathered on student performance provided by the results of the pre-assessment, students will be placed into the following 3 groups and both their instructional lesson time as well as their further assessments will be tailored to meet their academic needs.  Students will all begin working on the Math concepts of addition and subtraction and place value of numbers.

Tier 3: Above Grade Level

Differentiated Instruction:

The 5 students who displayed having a firm grasp on California Common Core Math Standards and who were able to answer the most questions correctly, including the most difficult of the pre-assessment questions, will move forward in the subject material by deepening the understanding of math concepts.  

ADDITION AND SUBTRACTION
Students will work on computer programs and in small groups where they will begin focusing on representing and solving problems involving addition and subtraction with three numbers (into the 100's), to solve one and two step word problems as well learning about the relationship between addition and subtraction up to the number 20.  

ex activity: Represent And Solve Problems Involving Addition And Subtraction.

PLACE VALUE

Students will take what they have learned about place value and through the use of their knowledge of base 10, work to begin to understand concepts of greater than and less than by  Comparing Numbers.

Differentiated Assessment:

As these students move through each new element, they will be assessed at the end of each lesson on their understanding and comprehension of the newly learned skills through teacher led games and activities in the classroom and through computer based end of lesson assessments or "quizzes".  

Tier 2: At Grade Level

Differentiated Instruction:

The 12 students who demonstrated having some knowledge of Math Common Core Standards, but need to develop higher order thinking skills will continue with the established 1st grade math curriculum.  Students will go through a brief period of reviewing what they learned year before in kindergarten in order to further deepen and refresh their level of understanding and comprehension and then begin learning new related concepts.  

Through teacher led games and activities as well as through computer based assessment programs, students will review their understanding and comprehension of addition and subtraction and place value concepts and then demonstrate their learning by completing a computer based learning activity, worksheet or teacher led lesson or activity:

 PLACE VALUE
1. Students will begin to learn about place value and will use place value understanding and properties of operations to add and subtract.  Students will be taught that the two digits of a two-digit number represent amounts of tens and ones. First graders will learn the tens and ones place values through online learning games and classroom activities like Roll and Build and will learn correct mathematical terminology  (ie: Saying 67 as "6 tens, 7 ones" as well as "sixty-seven" ). 

ADDITION AND SUBTRACTION
 Students will work on addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing :Addition and Subtraction word problems

Differentiated Assessment

The assessments given to the students who are performing at grade level will directly reflect the concepts they have been working on.  They will participate in one on one activities with the teacher in addition, subtraction, and place value.

Tier 3: Below Grade Level

Differentiated Instruction

The remaining 5 students who appear to have limited knowledge of Math Common Core Standards will be grouped together, but the material that is presented to them will differ in context of materials and presentation, depending on student's specific needs: ELL and special needs.  

For these students, all 5 will be retaught what they were introduced to in kindergarten, but the information will be scaffolded in such a way that each student will move onto learning a new skill once an initial skill is mastered.

PLACE VALUE
1. Lessons for struggling students will be scaffolded beginning with material introduced to them in kindergarten.  Students will work on using manipulatives to compose and decompose numbers from 11-19, in order to understand what sum 11-19 represent ( For example, a number such as 15 looks like the numbers "one" and "five", not 1 ten and 6 ones).  An example of some activities using manipulatives to make groups of tens and ones could be as follows: 

ADDITION AND SUBTRACTION

1.  Students will revisit and practice Choral counting from 1-120 forwards and backwards starting with sequence counting from 1-30 and then over time increasing from 1-50 and then 1-100.  Students will also solve simple addition and subtraction problems either through teacher led mental math imagery stories with the aide of manipulatives or using computer based math games or worksheets with the aide of objects or drawings to represent the problem.

Mental math activity using maipulatives (students count out gems and take them away according to the story):

"Chatter the red squirrel was out collecting acorns for the winter and as he was scurrying about he picked up three acorns and put them into his pouch.  (students take 3 gems and put them in front of them).  As he was hopping up the tree one gems fell out of his pouch.  How many gems did Chatter have now?......."

Example activity of learning numbers past 10: 
Students revisit what "teens' are using the following activity Grouping Numbers into teens

ELL and Special Ed Modifications: 

The following modifications will be implemented into the instruction given to students who are ELL or have special needs: the language used to describe tasks will be simplified, there will be periodic check-ins with students to track their understanding and comprehension of material taught, pictorial representations will be provided to students along with words when possible in order to provide a clearer understanding of material presented.  

Differentiated Assessment

Students will be assessed based on the material they were taught using the following assessment: Kinder addition and subtraction assessment tool. Students will be allowed the same ELL and special ed modifications that were mentioned above will be provided to students during assessments as well.

Here is a visual representation of process of differentiating the math lesson for first graders:First Grade Math 

References:

California Department of Education.  (n.d.) Common Core State Standards
 https://www.cde.ca.gov/be/st/ss/documents/ccssmathstandardaug2013.pdf

Differentiation & LR Information for SAS Teachers.Differentiation. Pre-Assessment ideas.  Retrieved from the internet on December 5th, 2019.  https://sites.google.com/site/lrtsas/differentiation/5-preassessment-ideas

Illustrative Mathematics.  Retrieved from the internet on Dec 5, 2019.  1.OA At the Park
https://s3.amazonaws.com/illustrativemathematics/attachments/000/008/571/original/public_task_160.pdf?1462387606

Illustrative Mathematics.  Retrieved from the internet on Dec 5, 2019.   1.NBT Roll & Build.
https://s3.amazonaws.com/illustrativemathematics/attachments/000/009/053/original/public_task_987.pdf?1462394355

Illustrative Mathematcis.  Retrieved from the internet on Dec 3, 2019.  2.OA A Pencil and a Sticker https://s3.amazonaws.com/illustrativemathematics/attachments/000/008/463/original/public_task_1.pdf?1462386937

Teacher Pay Teachers.  Retrieved from the internet on Dec 2, 2019.  Kindergarten Addition & Subtraction Assessment.  https://www.teacherspayteachers.com/Product/Kindergarten-Addition-Subtraction-Assessment-1176272

g and building upon the student’s current knowledge. Use the resources provided on the next slide to help with differentiating instruction, tasks, and assessments. Consider prerequisite skills that are missing for some students and differentiate the learning for them.  Consider addressing misunderstandings that students have. Consider extending and building upon the student’s current knowledge. Use the resources provided on the next slide to help with differentiating instruction, tasks, and assessments.

Making Space for Change

 

🌲 Project Based Learning 🌲

Over our four-week science block the first grade students worked with community members and planning officials to help to create an environmentally sustainable redesign of a vacant community space in a local neighborhood.  The objective was to answer the following question: How can we redesign a public space to make it more environmentally sustainable?  What aspects do we need to consider when designing a space?  Some questions to take into consideration are:  Who will this space be used by? Who uses it now?  How will it affect the plants, animals and current habitat?  What are the needs of the community?  How will it be funded?

The students will spend 4 weeks on this project.  During that time they will visit the space and then meet with local planners and residents who will provide them with the context, needs, resources, and constraints of transforming the space into a useable, accessible open space, multi-use area for the community.  The students will then engage in discussions, asked informative questions, and finally provide feedback and offer up ideas to the community for the spaces new use.   They will present their hand drawn picture ideas to community members and local planners, parents, and the school as their final project submission.  

First Graders will meet the following Science and Engineering Practices standards according to the CA state standards in the science curriculum.   The following is taken from the Next Generation Science Standards for California Department of Education(2013).

Constructing Explanations and Designing Solutions

Constructing explanations and designing solutions in K–2 builds on prior experiences and progresses to the use of evidence and ideas in constructing evidence-based accounts of natural phenomena and designing solutions. 

• Make observations (firsthand or from media) to construct an evidence-based account for natural phenomena. (1-LS3-1)
• Use materials to design a device that solves a specific problem or a solution to a specific problem. (1-LS1-1)

Obtaining, Evaluating, and Communicating Information

Obtaining, evaluating, and communicating information in K–2 builds on prior experiences and uses observations and texts to communicate new information.

• Read grade-appropriate texts and use media to obtain scientific information to determine patterns in the natural world. (1-LS1-2)

⤃⤃⤃⤃⤃⤃⤃⤃⤃⤃⤃⤃⤂⤂⤂⤂⤂⤂⤂⤂⤂⤂⤂⤂

🌲 Monitoring Student Projects 🌲

The students will be evaluated based off the following rubric and criteria:

Making Space for Change: First Grade Rubric

⤃⤃⤃⤃⤃⤃⤃⤃⤃⤃⤃⤃⤂⤂⤂⤂⤂⤂⤂⤂⤂⤂⤂⤂

🌲 Creating A Strategy for Feedback 🌲

This project is meant to take place over the course of a four-week science block.  I will provide feedback to students on a bi-weekly basis; each Monday and Friday throughout the block period (8 check-in times total), I will meet one on one with each student and look over their journals to make sure the students are demonstrating their learning and recording their work in their journals.  I will also use formative assessments to check in daily to see of students are understanding what they have learned.   I will record their progress on a spreadsheet.  Each week the students will also draw a picture of what they have worked on that week:

Week 1:  surveying the site

Week 2: community meeting and input

Week 3: researching and designing a plan

Week 4: presenting their work

I will give students feedback through a checklist that will be posted in the front of the classroom.  As students complete tasks, they will check off each task as they go.  We will review the chart each day as a whole class each morning as a part of our schedule review and morning routine.  Students will receive a red, yellow, or green sticker to indicate where they are in their weekly project submissions, color will correspond with the rubric.  I will also use the app Remind to communicate with parents on a weekly basis to make sure they are aware of their child's progress and progression with their work and help keep their child stay on task.

⤃⤃⤃⤃⤃⤃⤃⤃⤃⤃⤃⤃⤂⤂⤂⤂⤂⤂⤂⤂⤂⤂⤂⤂

References:

PBLWorks. (gleaned from the internet on November 16, 2019).  Buck Institute for Education.   Making Space for Change.  https://my.pblworks.org/project/making-space-change

Stenger, Marianne.  (2014).  Edutopia.  5 Research-Based Tips for Providing Students with Meaningful Feedback.  https://www.edutopia.org/blog/tips-providing-students-meaningful-feedback-marianne-stenger

California Department of Education.  (2013).  Next Generation Science Standards for California Public Schools.  https://www.cde.ca.gov/pd/ca/sc/ngssstandards.asp

Pictures from google or from my photo album.

Caron Kotalik's Formative Assessment for First Grade

Formative assessments are "a wide variety of methods that teachers use to conduct in-process evaluations of student comprehension, learning needs, and academic progress during a lesson, unit, or course (Great Schools Partnership 2014).  Based on the feedback I received from Kelly and from my own experience of using these Formative Assessments in my classroom, I believe that my assessments have been successful.  The process of design and revision I found to be pretty intuitive.  For example, during our first grade Main Lesson time each morning, we as a class have an entire block of time carved out for reviewing the material that was brought the day before.  This is the time when I use formative assessments to get a read on what information students were able to retain, what elements of the lesson were unclear, and how to differentiate learning for the remainder of the lesson.  

I honestly had no idea that what I was doing was labeled Formative Assessment, and so I really enjoyed learning what exactly formative assessments were and other ways of assessing students performance and my teaching from cohort members and from the resources provided by our instructor.  I appreciate being exposed to and learning about so many other ways to assess student learning, aside from the tools and activities I already use.   I specifically wrote about using Story timelines, chalkboards, and alphabet cards as formative assessment tools in my classroom.

Using an Exit ticket is another assessment tool I use regularly, but I never heard of it before nor had ever I called it that.  For example, every Monday, after the students have their outdoor Ecoliteracy day on the Friday before, I have the children draw a picture of what they did and what they learned during Ecoliteracy.  The students may illustrate a fun experience, something they didn’t understand, or something funny that happened; usually we have a theme.   It’s a great review and recall activity for my students and often times I don’t go with them on these field trips, so it’s also a great way for me to hear about what they did.  I have then been giving these pictures to their eco lit teacher and she absolutely loves it.  She and I check in once a week and go over what the students created.  It’s great process for all of us.   We also use this reflective tool as a review for the stories we hear in Main Lesson that pertain to either Language Arts, Math, or Form Drawing, depending on the block.

From our most recent Math block, learning about the quality of numbers 

 "Chatterer, Grey Squirrel, Finn, and Wynn trying to figure out the riddle told by the wise old woman."

 

"Finn, Wynn, Chatterer, and Grey Squirrel sitting in front of the fire, listening to the wise woman." 

(The number and roman numeral 5).

As far as how my research, cohort discussions, and/or feedback I received from peers and my instructor helped me to develop and improve my formative assessments, I honestly could’ve used more help and greater access to information regarding ELL and special education alternatives to formative assessments seeing as how we, as a cohort through TeachNow, have not yet addressed ELL or special education before.  I did find a few resources online for ELL and sped students, but to get them to fit with the specifics of my assessments was difficult. On a separate note,  I very much appreciated Kelly's comment, that by incorporating the use of this data I could complete another formative assessment for the students to assess whether the are visual or auditory learners, was a terrific recommendation and will do so in my upcoming assessments.

                                              

I love using chalkboards as a formative assessment tool.  I use them in form drawing class, math, and language arts.  I can immediately gauge where the students are as I ask them to write a letter, number or form and hold it up as they are finished.  I then record the students level of understanding and comprehension in a notebook that I then transfer over into an excel spreadsheet.  In Todd Finley’s web article, Dipsticks: Efficient Ways to Check for Understanding, he agrees that “by methodically watching and recording student performance with a focused observation form, you can learn a lot about students’ levels of understanding in just a few moments” (2014).  

I feel the assessments I use in my classroom are accurate in gauging student learning and that the real-time data I collect tis accurate and informative.  Each time I perform an assessment I record results of student performance and confidence level in a spreadsheet that helps me keep track of where the students are in their learning.  I then use that data to modify my daily lessons and review and revisit any material that students may need revisited. In the online article by Lisa Greenstein, she states that, “ Formative assessment is purposefully directed toward the student. It does not emphasize how teachers deliver information but, rather, how students receive that information, how well they understand it, and how they can apply it”.  I only partially agree with this statement because I strongly believe these assessment tools can provide teachers with the opportunity to reflect on whether or not the information they are delivering is being done so in a way that is effective and clear.  When the students are not excelling, are not grasping concepts, or seem confused or lost by the directions, these are all great indicators my delivery of information needs to be more effective and I am able to gauge this through the use of the formative assessment tool.  

My students are pretty young still, and where I would refrain from sharing the results directly with them in a formal matter, I would instead congratulate them on their learning and let them know that because of their progress and job well done, we as a class are able to move on to the next challenge.  The students would become aware of their progress as I change the activity to become more complicated and challenging for them. I  have also differentiated the activity based on how particular students are progressing through the activity/assessment.  I will either add additional challenges or maintain the same level of difficulty until a student shows the ability to grasp the concept. and move forward.  As my students are 6 and 7 years old and while they are actively involved in participating in the assessment process itself, I would refrain from inviting them to help keep a record of their progress.  This can really encourage a competitive atmosphere in the classroom and that is the complete opposite of what I have been working so hard to develop and foster amongst my students this year.   We encourage each other and lift each other up.  Learning is not a competition, but instead,  I explain to my students that we all excel when everyone does well, we work together to help each other and record keeping is not something I feel these children are ready for.  Maybe in the third or fourth or fifth grade, but not at this age. 

I really appreciated reading other peoples use of formative assessments in the classroom as well as the plethora of information and resources out there on the web.  Edutopia is usually my go to and they have multiple fantastic websites and links that I’ve been looking at for quite a bit over the past few days: Edutopia !o Fun-Filled Formative Assessments, This too is a great video example fo a teacher using formative assessments with her class: 5 Types of Formative Assessments Overall, this assignment has been helpful in finding ways to make formative assessments fun and interactive.

References: 

Finley, Todd.  (2014).  Dipsticks: Efficient Ways to Check for Understanding.  https://www.edutopia.org/blog/dipsticks-to-check-for-understanding-todd-finley

Great Schools Partnership.  (2014).  Formative Assessment.  https://www.edglossary.org/formative-assessment/

Greenstein. Laura.  retrieved from the internet on November 9, 2019. What Teachers Really Need to Know About Formative Assessment.  http://www.ascd.org/publications/books/110017/chapters/The-Fundamentals-of-Formative-Assessment.aspx

Hill, Hillary.  (2013).  10 Fun-Filled formative Assessment Ideas. https://www.edutopia.org/discussion/10-fun-filled-formative-assessment-ideas

Youtube video.  (2017).  5 Types of Formative Assessments.  https://www.youtube.com/watch?v=NUhFwvHIdxw