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Learning First! Driven by Data! 1

TO: Related Servers

FROM: Related Service Administration

MEMO: Related Services Department Goal SY 2015-16

KEY PROVISION

Area of focus. In support of the Davis School District Vision and the DSD Special Education Department Mission, the Related Services Department has been asked to focus on helping students with disabilities to conceptualize, reason, and apply principles of higher-level thinking. To do this, we will focus on using the Math Practice Standards as a thinking framework including:

1) making sense of problems and persevere in solving them,

2) reasoning abstractly and quantitatively,

3) constructing viable arguments and critique the reasoning of others,

4) modeling with mathematics,

5) using appropriate tools strategically,

6) attending to precision,

7) looking for and make use of structure, and

8) looking for and express regularity in repeated reasoning.

Related Services Department Goal. Each related service or itinerant service provider is asked to engage in the following RS Department goal:

I (name), will systematically infuse a minimum of 1 of the 8 Math Practice Standards (MPS) in to my practice when working with students with disabilities by taking the following steps:

1. Preparation. Review the Math Practice Standards and engage in self-study and district-sponsored professional development to increase my knowledge and how the MPS apply to my discipline by September 11, 2015.

2. Plan. Determine how a Math Practice Standard(s) relates to my intervention and instruction (direct services, treatment) responsibilities and style by identifying

a. A student or students on my caseload who will benefit from increasing higher-level thinking skills,

b. A minimum of 1-2 math practice(s) and c. Developing an instruction unit including the student outcome and assessment

procedure for at least one student By October 9, 2015.


3. Collaborate with the student’s math teacher to better understand the student’s mathematics skills. Implement the intervention or instruction and document the impact of the intervention for a particular student by monitoring the students’ progress toward the math-related goals, or short-term objectives, or needs of students in at-risk groups between October 12, 2015 and the date of the professionals’ summative evaluation.

The goal will be achieved by 5/31/2016 and measured by providing a case study (as documented on the case study form) of at least one student to include:

a. Classroom and treatment pre-, during-, and post-data relating to one of the eight math practice standards,

b. A 2-3 sentence description of the plan as to how I will infuse the standard into my interactions with the student over the course of the school year, and

c. A 2-3 sentence reflection regarding the impact of my intervention and instruction (treatment, direct service) on the student’s progress and reported on the Math Practice Standard Case Study form.

EVALUATE DAVIS ALIGNMENT

The Evaluate Davis performance indicators that align with the goal include but are not limited to:

T.5 Learners have opportunities to engage in higher level thinking through questing, solving real-world problems, critically analyzing information, etc.

E.1 Students are willing to take risks in learning (ask and respond to questions, hypothesize, share alternative options and/or opposing opinions, etc.)

E.2 Each student is held to high expectations for learning and modifications to assignments are made as needed.

DISCUSSION

Math Practice Standards describe the concepts that are found in all facets of thinking and life and are applicable for all levels of learning and to all disciplines. For example, because we have high expectations of students with disabilities, during the provision of service we may work with students…

o to be able to learn to stay with a challenging problem for more than one attempt,

o to try several approaches in finding a solution, o to learn from previous solutions attempts and work over time to make a variety

of attempts (Mathematical Practice Standard 1).


DESK Standards alignment. The DESK Standards now include disciplinary literacy. This means that students are expected to learn how to read history, science, and math in addition to traditional story literature. As educators and particularly related servers, we are expected to know how to facilitate the development of literacy in all subject areas. One way to do this is to teach what is specialized about the vocabulary and how thinking and reasoning is different from one discipline cultures to the next. For example:

Mathematicians look for truth in the text, they read text carefully and engage in detailed reading and consideration of every word in the text. Every comma matters. The strategy for understanding is to re-read. Math text is dense, difficult, and every word holds weight and meaning. Mathematicians don’t add additional words, and they emphasize error detection. Precision of understanding is important. We don’t skim math text like we do a newspaper. Mathematicians rarely care who the author is because the information is not influenced by the perspective of the author.

Historians consider bias and perspective. Historians look for arguments with implicit claims that need to line up. They don’t want a text that is a central standard as many perspectives needed to fully understand history. Historians care about sources and who wrote the text and when it was written. Historians look at the text from the point of view of the time it was written. Historians corroborate and won’t read just one text as the gold standard because more than one perspective and context is needed. Historians view reading as a rich conversation.

Scientists look for a prediction of how the world works. They look for a close connection among prose, charts, and graphs. Word are not enough to describe the information adequately. Understanding depends on connecting to another way of describing. Charts and graphs are not ancillary, they are co-equal to text. Scientists need a text that is central to the profession, a gold standard. A ready strategy is to put the author out of your mind and focus on the text.

Educator Dispositions. When students with disabilities as well as educators embrace the idea that mathematics is more than calculating an addition or division problem then mathematical thinking becomes essential, doable, and exciting. Mathematical thinking becomes conceptualized and translates into higher-level thinking.

BEST PRACTICE

Educational best practice relates to using practices with high effect sizes. Related Servers can have a positive influence on student outcomes including the development of conceptual understanding. One way to engage students in higher level thinking is through questioning, solving real-world problems, and critically analyzing information.


Specifically, questioning has an effect size of .48 (Hattie, 2012) which falls within the zone of desired effects. This means well designed questions are a good use of a student’s instructional time. Low cognitive level questions that only elicit facts are not effective. Questions which promote active learning assists with the development of conceptual understanding and mental organization are ideal. Following are sample questions that may be used when helping students to use mathematical thinking.

Mathematical Practice Standard

Questions to Develop Mathematical Thinking

ON

E

Make sense of problems and persevere in solving them

How would you describe the problem in your own words?How would you describe what you are trying to find?What do you notice about…?What information is given in the problem?Describe the relationship between the quantities.Describe what you have already tried. What might you change?Talk me through the step you’ve used to this point.What steps in the process are you most confident about?What are some other strategies you might try?What are some other problems that are similar to this one?How might you use one of your previous problems to help you begin?How else might you organize…represent…show…?

TWO

Reason abstractly and quantitatively

What do the number used in the problem represent?What is the relationship of the quantities?How is ___ related to ___?What is the relationship between ___ and ___?What does ___ mean to you? (e.g. symbol, quantity, diagram)What properties might we use to find a solution?How did you decide in the task that you needed to use…?Could we have used another operation or property to solve this task? Why or why not?


THRE

EConstruct viable arguments and critique the reasoning of others

What mathematical evidence would support your solution? How can we be sure that…?How could you prove that…?Will it still work it…?What were you considering when…?How did you decide to try that strategy?How did you test whether your approach worked?How did you decide what the problem was asking you to find? (What was unknown?)Did you try a method that did not work? Why didn’t it work? Would it ever work? Why or why not?What is the same and what is different about…?How could you demonstrate a counter-example?

FOU

R

Model with mathematics

What number model could you construct to represent the problem?What are some ways to represent the quantities?What is an equation or expression that matches the diagram, number line…, chart…, table..? Where did you see one of the quantities in the task in your equation or expression?How would it help to create a diagram, graph, table…?What are some ways to visually represent…?What formula might apply in this situation?

FIVE

Use appropriate tools strategically

What mathematical tools could we use to visualize and represent the situation?What information do you have?What do you know that is not stated in the problem?What approach are you considering trying first?What estimate did you make for the solution?In this situation would it be helpful to use…a graph…, number line…, ruler…, diagram…, calculator…, manipulative?What was it helpful to use…?What can using a ___ show us that ___ may not?In what situations might it be more informative or helpful to use…?


SIX

Attend to precision What mathematical terms apply in this situation?How did you know your solution was reasonable?Explain how you might show that your solution answers the problem.What would be a more efficient strategy?How are you showing the meaning of the quantities?What symbols or mathematical notations are important in this problem?What mathematical language…, definition…, and properties can you use to explain…?How could you test your solution to see if it answers the problem?

SEVE

N

Look for and make use of structure

What observation do you make about…?What do you notice when…?What parts of the problem might you eliminate…, simplify…?What patterns do you find in…?How do you know if something is a pattern?What ideas that we have learned before were useful in solving this problem?What are some other problems that are similar to this one?How does this relate to…?In what ways does this problem connect to other mathematical concepts?

EIGH

T

Look for and express regularity in repeated reasoning

Explain how this strategy worked in other situations?Is this always true, something true or never true?How would we prove that…?What do you notice about…?What is happening in this situation?What would happen if…?Is there a mathematical rule for…?What predications or generalizations can this pattern support?What mathematical consistencies do you notice?


Helpful Sources

Scholastic Guide

http://www.scholastic.com/teachers/top-teaching/2013/03/guide-8-mathematical-practice-standards

San Francisco Unified School District

http://www.sfusdmath.org/standards-for-math-practice-in-child-friendly-language.html

Useful clips

Math Standards in the Core

https://www.youtube.com/watch?v=m1rxkW8ucAI&list=PLD7F4C7DE7CB3D2E6

Math Standards

https://www.youtube.com/watch?v=9pKcO9E4Flw&list=PLD7F4C7DE7CB3D2E6&index=6

https://www.youtube.com/watch?v=9pKcO9E4Flw&list=PLD7F4C7DE7CB3D2E6&index=6

https://www.youtube.com/watch?v=m1rxkW8ucAI&list=PLD7F4C7DE7CB3D2E6

http://www.sfusdmath.org/standards-for-math-practice-in-child-friendly-language.html




APPENDIX

DESCRIPTION OF MATH PRACTICE STANDARDS (Scholastic.com)


Math Practices Standard(s) Case Study Form

Related Server: Department:Student’s Name: Age: Grade: Classification: Collaborating Teacher:School:

Practice Standard(s) __________

IEP goal that aligns with math thinking need

Preparation. Self-Study Reflection

Description of the Plan, Student Outcome, Assessment

Outcome Data*

Pre-test Date

During-testDate

Post-test Date

Reflection

*see attached supporting data


EXAMPLE Math Practices Standard(s) Case Study Form

Related Server: Department: Speech-Language Pathology

Student’s Name: Age: Grade: Classification: Collaborating Teacher:School:

Practice Standard(s) ____8______


The student will describe 25 grade-level vocabulary words with 80% accuracy when provided with a picture prompt weekly over a 6-week time frame as measured by weekly expressive language opportunities.


9/11/2015I have attended the district-sponsored PD from UOU and have reviewed the materials. I already engage in many of the standards, I was pleasantly surprised. I am undergoing an attitude change about the role the math thinking in my practice. I am interested in #8 and how I can connect story grammar with regularity in repeated reasoning. I want my students to generalize their story grammar skills from one story to the next.


10/09/2015Plan. Math practice standard #8 Look for and Express Regularity in Repeated Reasoning will be used for my language instructional unit during direct service. I plan to use the Expanding Expression Tool to teach a systematic structure for describing an object including group, function, description, composition, component parts, location, and prior knowledge or fun facts. Understanding of each element of the structure will be pre-tested.

Student Outcome. The target student will learn a structure that will help the student to provide descriptions of novel objects thereby expanding expressive communication skills and regularity in repeated reasoning.

Assessment Procedure. The student’s use of expressing regularity in repeated reasoning will be measured weekly across a 12-week period using the Regularity in Repeated Reasoning Data Collection Tool.


Regularity in Repeated Reasoning Data Collection ToolItem Oral Written 1 category 1 function 1 physical

description1 physical composition

3 parts 1 where 2 other %

Outcome Data*

Pre-test 30%Date 10/09/2015

During-test 60%Date 11/6/2015

Post-test 80%Date 12/4/2015

Reflection

Spring 2016.I have developed a deeper understanding of the MPS and the relationship to my discipline and practice. I was able to effectively embed higher-level thinking opportunities into the student’s sessions using the MPS as an infrastructure. Collaboration with the math teacher was beneficial in that we both developed a better understanding of how to support the student from our different perspectives. I plan to continue using MPS when working with students. I anticipate that my Evaluate Davis scores will reflect this skill.




Related Server: Department: School PsychologyStudent’s Name: Age: Grade: Classification: Collaborating Teacher:School:

Practice Standard(s) _____1_____


The student will in a small group setting use the skill steps to break down a complex problem (for example but not limited to: 1. Take a deep breath, 2. Break down the problem into smaller steps, 3. Visualize completing those steps, 4. Attempt one step at a time) with 100% accuracy for three consecutive opportunities.

~OR~

Over one term, the student will independently complete an average of 80% of assignments with an accuracy of 85% by following skill steps for completing work (for example, but not limited to: completing daily assignment log, checking in with teacher at the end of the day and taking home necessary papers for homework) as measured by weekly missing assignment reports over one school term.


9/11/2015I have attended the district-sponsored PD from U of U and have reviewed the materials. I already engage in may of the standards, I was pleasantly surprised. I am undergoing an attitude change about the role of math thinking in my practice. I am interested in #1 and how I can teach children the skills to persevere in solving complex problems.


Plan. Math Practice Standard #1 Make sense of problems and persevere in solving them will be used for my instruction with the student during direct service time. I plan to use various social skills curriculum to teach a systematic way for breaking down a problem into smaller steps, while reinforcing relaxation techniques.


Student Outcome. The target student will learn a skill that will help the student to break down a complex problem into smaller steps, while successfully utilizing relaxation techniques o enhance mental clarity.

Assessment Procedure. The student’s use of these skills will be measured weekly across a 12-wek period using either structured role play scenarios, or classroom data regarding incidents of attempting the classroom task within the allotted time frame.

Outcome Data*

Pre-test Date

During-testDate

Post-test Date

Reflection





Related Server: Department: Occupational Therapy, Physical Therapy, Adapted Physical Education

Student’s Name: Age: Grade: Classification: Collaborating Teacher:School:

Practice Standard(s) ____4______


When given writing materials, the student will independently copy a give four to five word sentence using the correct letter size and formation with 90% accuracy across three consecutive data sessions as measured by work samples

~OR~

The student will be able to skip independently across the lunchroom floor demonstrating a rhythmic integrated movement, as measured by teacher observation and data collection for 2 out of 3 trials.


9/11/2015I have attended the district-sponsored PD from U of U and have reviewed the materials. I already engage in many of the standards, I was pleasantly surprised. I am undergoing an attitude change about the role of math thinking in my practice. I am interested in #4 Model with Mathematics and how I can teach children the skills to visualize math concepts during our sessions.


Plan. Math practice standard #4Model with Mathematics will be used for my instruction with my student during direct service time. I plan to have the child chart his progress and monitor it with me. Understanding if progress is being made or not will be discussed with the child after each graphing session. Student Outcome. The target student will learn a structure for charting his progress and


visualizing how mathematical concepts are applied in a real world situation.

Assessment Procedure. The student’s ability to chart his progress and verbalize information from the chart/graph will be measured weekly across a 12-week period using a checklist. This checklist will indicate whether the child correctly charted his progress and if the child was able to verbalize the information the information related to the chart/graph.

Outcome Data*

Pre-test Date

During-testDate

Post-test Date

Reflection





Related Server: Department: HearingStudent’s Name: Age: Grade: Classification: Collaborating Teacher:School:



The student will correctly use age-appropriate developmental language milestones, including, but not limited to, irregular plural and verbs, with 80% accuracy, in 4 out of 5 trials.

~OR~

The student will correctly define, and use in verbal and written sentences, target, and grade-appropriate vocabulary words, with 90% accuracy, in 2 out of 3 therapy sessions.



Outcome Data*

Pre-test Date

During-testDate

Post-test Date

Reflection




Related Server: Department: VisionStudent’s Name: Age: Grade: Classification: Collaborating Teacher:School:



The student will read and write complex sentences with 70% accuracy on 3 out of 5 given opportunities.

~OR~

The student will independently read and write the Braille alphabet with 85% accuracy on monthly assessments.



Outcome Data*

Pre-test Date

During-testDate

Post-test Date

Reflection


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