This document summarizes a presentation on recent advances in math interventions. It discusses key concepts like math proficiency, foundational math skills, and common math myths. It also outlines a multi-tiered system of supports including strategies for Tier 1 core instruction, Tier 2 small group interventions, and Tier 3 individualized supports. Specific evidence-based practices are recommended, such as explicit instruction, strategic use of math vocabulary, and targeting foundational skills like whole number knowledge before rational numbers.
Highlights From Future of Education - mSchool + DreamBox LearningDreamBox Learning
In the edWeb.net Blended Learning community’s latest webinar, Elliot Sanchez joined Dr. Tim Hudson, Senior Director of Curriculum Design for DreamBox Learning, Inc., and discussed the future of math education. Elliot, Founder & CEO of mSchool, and one of the 2014 Forbes 30 Under 30, is a leading education innovator with 14 state-funded classrooms that successfully leverage blended learning. Elliot and Tim discussed mSchool’s approach and successes, blended learning, formative assessment, meeting the diverse needs of all students, Common Core State Standards, and digital learning technologies. They provided a recap of insights from the January 22, 2014 The Future of Math Education: A Panel Discussion of Promising Practices webinar, with a focus on blended learning. That panel included NCSM President Valerie Mills, renowned math educator; author Dr. Cathy Fosnot, and past NCTM and AMTE President Dr. Francis (Skip) Fennell. Everyone interested in the success of all students in learning mathematics—educators, parents, and community members— can appreciate the valuable insights and approach to innovation from these education thought leaders.
EDUU 512 RTI Case Study Rubric Criteria Exemplary (.docxtoltonkendal
EDUU 512 RTI Case Study Rubric
Criteria Exemplary
(5 pts.)
Proficient
( 4 pts.)
Emerging
(3 pts.)
Needs Improvement
(2 pts.)
Summary
Clearly and concisely
summarizes the problem,
how the problem was
determined, interventions
used and the effectiveness of
the interventions
Adequately summarizes
the problem, how the
problem was
determined,
interventions used and
the effectiveness of the
interventions
Partially summarizes the
problem, how the
problem was
determined,
interventions used and
the effectiveness of the
interventions
Little or no summary
provided that includes
the problem, how the
problem was
determined,
interventions used and
the effectiveness of the
interventions
Analysis & Reflection
Clearly and concisely
describes insights gained
about the RTI process, the
role of data collection and
analysis, the ways in which
teachers collaborate, and the
relationship between RTI and
differentiated instruction.
Adequately describes
insights gained about the
RTI process, the role of
data collection and
analysis, the ways in
which teachers
collaborate, and the
relationship between RTI
and differentiated
instruction.
Partially describes
insights gained about
the RTI process, the role
of data collection and
analysis, the ways in
which teachers
collaborate, and the
relationship between
RTI and differentiated
instruction but analysis
is minimal.
Little or no description
of insights gained about
the RTI process, the role
of data collection and
analysis, the ways in
which teachers
collaborate, and/or the
relationship between
RTI and differentiated
instruction.
Writing Style/Mechanics
• Writing is clear and
concise
• Varied sentence
structure
• Academic writing
conventions (grammar,
spelling, punctuation
etc.)
Writing is clear and concise.
Sentence structure is varied.
Fully adheres to academic
writing conventions
(grammar, spelling
punctuation etc.)
Writing is clear and
sentence structure is
somewhat varied.
Adequately adheres to
academic writing
conventions (grammar,
spelling, punctuation
etc.) There are a few
grammar, spelling and/or
punctuation errors.
Writing is unclear and
wordy. There is minimal
variation in sentence
structure. Partially
adheres to academic
writing conventions
(grammar, spelling,
punctuation etc.) There
are several grammar,
spelling and/or
punctuation errors.
Writing is unclear.
Sentence structure is
the same throughout
the paper. Writer does
not adhere to academic
writing conventions
(grammar, spelling,
punctuation etc.)
2nd Grade Case Study
Making Sense of the Problem-Solving RtI Process in Mathematics
Miss Concepcion, a second grade teacher in Algorithm Elementary School, was a veteran
teacher, both in the profession and at this elementary school. She felt fortunate to work
with three other second grade teachers who were veter.
EDU 573 Instructional MethodsDaily Math Lesson Plan- DeveEvonCanales257
EDU 573: Instructional Methods
Daily Math Lesson Plan- Development Part I
Taya Hervey-McNutt
Dr. Hau Nguyen – Course Instructor
Strayer University
January 26, 2022
Lesson Plan-Daily Math Lesson
Teacher’s Name Professor Allen
Date of Lesson 14-02-2022
Time of Lesson 10:05 a.m.
Subject The concept is Single subjected; Observation.
Factors that can affect
what you can teach
The first factor is class size. The classroom is small, which
makes it very convenient to teach the subject. The small class
size will help increase student engagement and make them
have a higher ability to adapt to educational and intellectual
challenges that they will likely face.
The next factor is time. Over the years, it has been deduced
that the time of the day significantly impacts students'
achievement. The selected time is suitable as it matches their
scores and learning style preferences.
The other factor is space. Students will be placed at a safe
distance from one another to ensure they are in a tidy and
clean environment, which will make them more focused and
have motivation towards the lesson.
Class Demographics
There are 402 students. Their average age is six years. There
are a total of 218 girls and 184 boys. On average, the
economic status of the students in the middle.
The ability levels of the students are as follows: visual
learners, auditory learners, writing learners, and kinesthetic
learners.
The school setting is learner-centered. This is the case since
the learning institution assesses students' needs, for instance,
allowing students to create their own meaning according to
the previous knowledge.
A brief summary of the schedule is 8:20-9:00 as arrival time,
9:25 clean up, 10:00 – 10:45 math talk, and 10:45 to 11:00,
individual/partner work, 11:15 dismissal.
The teachers' qualities include love for their work, creativity,
flexibility, patience, sense of humor, and compassion.
Three potential
advantages to teaching
this mix of students.
In this environment, teachers mix students with mixed
abilities, which allows them to learn and accept their
differences.
A teacher will have an easy time placing the students into
discussion groups or engaging the class in the discussion
because each student has their own perspective on things.
The high-level students can assist lower-level learners by
encouraging and modeling them.
Two potential challenges
to teaching this mix of
students.
Teachers face the challenge of teaching effectively because
they will be required to know every student's ability and
identify a suitable way of teaching them.
It is possible that teachers may feel out of touch with the
learners when they post negatively unintended outcomes.
Scope
● The time to teach
this lesson.
● Classroom
resources
● How this lesson
plan fits into either
a single-subject
curriculum or
connects as an
interdisciplinary
plan
1. The lesson will be taught at 10:05 a.m. Usually, students
tend to be better focused on learning at this time ...
The power of learning analytics to unpack learning and teaching: a critical p...Bart Rienties
Across the globe many educational institutions are collecting vast amounts of small and big data about students and their learning behaviour, such as their class attendance, online activities, or assessment scores. As a result, the emerging field of Learning Analytics (LA) is exploring how data can be used to empower teachers and institutions to effectively support learners. In the recent Innovative Pedagogy Report Ferguson et al. (2017) encourage researchers and practitioners to move towards a new form of learning analytics called student-led learning analytics, which enable learners to specify their own goals and ambitions. They also support learners to reach these goals. This is particularly helpful for individuals who have little time to spare for study. In this ESRC session, based upon 6 years of experience with LA data and large-scale implementations amongst 450000+ students at a range of context, I will use an interactive format to discuss and debate three major questions: 1) To what extent is learning analytics the new holy grail of learning and teaching? 2) How can instructional design be optimised using the principles of learning analytics?; 3) With the introduction of student-led analytics, to what extent can learning analytics promote ‘personalisation’ or ‘generalisation’ for diverse populations of students?
Highlights From Future of Education - mSchool + DreamBox LearningDreamBox Learning
In the edWeb.net Blended Learning community’s latest webinar, Elliot Sanchez joined Dr. Tim Hudson, Senior Director of Curriculum Design for DreamBox Learning, Inc., and discussed the future of math education. Elliot, Founder & CEO of mSchool, and one of the 2014 Forbes 30 Under 30, is a leading education innovator with 14 state-funded classrooms that successfully leverage blended learning. Elliot and Tim discussed mSchool’s approach and successes, blended learning, formative assessment, meeting the diverse needs of all students, Common Core State Standards, and digital learning technologies. They provided a recap of insights from the January 22, 2014 The Future of Math Education: A Panel Discussion of Promising Practices webinar, with a focus on blended learning. That panel included NCSM President Valerie Mills, renowned math educator; author Dr. Cathy Fosnot, and past NCTM and AMTE President Dr. Francis (Skip) Fennell. Everyone interested in the success of all students in learning mathematics—educators, parents, and community members— can appreciate the valuable insights and approach to innovation from these education thought leaders.
EDUU 512 RTI Case Study Rubric Criteria Exemplary (.docxtoltonkendal
EDUU 512 RTI Case Study Rubric
Criteria Exemplary
(5 pts.)
Proficient
( 4 pts.)
Emerging
(3 pts.)
Needs Improvement
(2 pts.)
Summary
Clearly and concisely
summarizes the problem,
how the problem was
determined, interventions
used and the effectiveness of
the interventions
Adequately summarizes
the problem, how the
problem was
determined,
interventions used and
the effectiveness of the
interventions
Partially summarizes the
problem, how the
problem was
determined,
interventions used and
the effectiveness of the
interventions
Little or no summary
provided that includes
the problem, how the
problem was
determined,
interventions used and
the effectiveness of the
interventions
Analysis & Reflection
Clearly and concisely
describes insights gained
about the RTI process, the
role of data collection and
analysis, the ways in which
teachers collaborate, and the
relationship between RTI and
differentiated instruction.
Adequately describes
insights gained about the
RTI process, the role of
data collection and
analysis, the ways in
which teachers
collaborate, and the
relationship between RTI
and differentiated
instruction.
Partially describes
insights gained about
the RTI process, the role
of data collection and
analysis, the ways in
which teachers
collaborate, and the
relationship between
RTI and differentiated
instruction but analysis
is minimal.
Little or no description
of insights gained about
the RTI process, the role
of data collection and
analysis, the ways in
which teachers
collaborate, and/or the
relationship between
RTI and differentiated
instruction.
Writing Style/Mechanics
• Writing is clear and
concise
• Varied sentence
structure
• Academic writing
conventions (grammar,
spelling, punctuation
etc.)
Writing is clear and concise.
Sentence structure is varied.
Fully adheres to academic
writing conventions
(grammar, spelling
punctuation etc.)
Writing is clear and
sentence structure is
somewhat varied.
Adequately adheres to
academic writing
conventions (grammar,
spelling, punctuation
etc.) There are a few
grammar, spelling and/or
punctuation errors.
Writing is unclear and
wordy. There is minimal
variation in sentence
structure. Partially
adheres to academic
writing conventions
(grammar, spelling,
punctuation etc.) There
are several grammar,
spelling and/or
punctuation errors.
Writing is unclear.
Sentence structure is
the same throughout
the paper. Writer does
not adhere to academic
writing conventions
(grammar, spelling,
punctuation etc.)
2nd Grade Case Study
Making Sense of the Problem-Solving RtI Process in Mathematics
Miss Concepcion, a second grade teacher in Algorithm Elementary School, was a veteran
teacher, both in the profession and at this elementary school. She felt fortunate to work
with three other second grade teachers who were veter.
EDU 573 Instructional MethodsDaily Math Lesson Plan- DeveEvonCanales257
EDU 573: Instructional Methods
Daily Math Lesson Plan- Development Part I
Taya Hervey-McNutt
Dr. Hau Nguyen – Course Instructor
Strayer University
January 26, 2022
Lesson Plan-Daily Math Lesson
Teacher’s Name Professor Allen
Date of Lesson 14-02-2022
Time of Lesson 10:05 a.m.
Subject The concept is Single subjected; Observation.
Factors that can affect
what you can teach
The first factor is class size. The classroom is small, which
makes it very convenient to teach the subject. The small class
size will help increase student engagement and make them
have a higher ability to adapt to educational and intellectual
challenges that they will likely face.
The next factor is time. Over the years, it has been deduced
that the time of the day significantly impacts students'
achievement. The selected time is suitable as it matches their
scores and learning style preferences.
The other factor is space. Students will be placed at a safe
distance from one another to ensure they are in a tidy and
clean environment, which will make them more focused and
have motivation towards the lesson.
Class Demographics
There are 402 students. Their average age is six years. There
are a total of 218 girls and 184 boys. On average, the
economic status of the students in the middle.
The ability levels of the students are as follows: visual
learners, auditory learners, writing learners, and kinesthetic
learners.
The school setting is learner-centered. This is the case since
the learning institution assesses students' needs, for instance,
allowing students to create their own meaning according to
the previous knowledge.
A brief summary of the schedule is 8:20-9:00 as arrival time,
9:25 clean up, 10:00 – 10:45 math talk, and 10:45 to 11:00,
individual/partner work, 11:15 dismissal.
The teachers' qualities include love for their work, creativity,
flexibility, patience, sense of humor, and compassion.
Three potential
advantages to teaching
this mix of students.
In this environment, teachers mix students with mixed
abilities, which allows them to learn and accept their
differences.
A teacher will have an easy time placing the students into
discussion groups or engaging the class in the discussion
because each student has their own perspective on things.
The high-level students can assist lower-level learners by
encouraging and modeling them.
Two potential challenges
to teaching this mix of
students.
Teachers face the challenge of teaching effectively because
they will be required to know every student's ability and
identify a suitable way of teaching them.
It is possible that teachers may feel out of touch with the
learners when they post negatively unintended outcomes.
Scope
● The time to teach
this lesson.
● Classroom
resources
● How this lesson
plan fits into either
a single-subject
curriculum or
connects as an
interdisciplinary
plan
1. The lesson will be taught at 10:05 a.m. Usually, students
tend to be better focused on learning at this time ...
The power of learning analytics to unpack learning and teaching: a critical p...Bart Rienties
Across the globe many educational institutions are collecting vast amounts of small and big data about students and their learning behaviour, such as their class attendance, online activities, or assessment scores. As a result, the emerging field of Learning Analytics (LA) is exploring how data can be used to empower teachers and institutions to effectively support learners. In the recent Innovative Pedagogy Report Ferguson et al. (2017) encourage researchers and practitioners to move towards a new form of learning analytics called student-led learning analytics, which enable learners to specify their own goals and ambitions. They also support learners to reach these goals. This is particularly helpful for individuals who have little time to spare for study. In this ESRC session, based upon 6 years of experience with LA data and large-scale implementations amongst 450000+ students at a range of context, I will use an interactive format to discuss and debate three major questions: 1) To what extent is learning analytics the new holy grail of learning and teaching? 2) How can instructional design be optimised using the principles of learning analytics?; 3) With the introduction of student-led analytics, to what extent can learning analytics promote ‘personalisation’ or ‘generalisation’ for diverse populations of students?
Investigating learning strategies in a dispositional learning analytics conte...Bart Rienties
This study aims to contribute to recent developments in empirical studies on students’ learning strategies, whereby the use of trace data is combined with self-report data to distinguish profiles of learning strategy use [3, 4, 5]. We do so in the context of an application of dispositional learning analytics in a large introductory course mathematics and statistics, based on blended learning. Building on our previous work which showed marked differences in how students used worked examples as a learning strategy [7, 11], this study compares different profiles of learning strategies with learning approaches, learning outcomes, and learning dispositions. One of our key findings is that deep learners were less dependent on worked examples as a resource for learning, and that students who only sporadically used worked examples achieved higher test scores.
Metacognitive Strategies: Instructional Approaches in Teaching and Learning o...IJAEMSJORNAL
The purpose of the study is to determine the effectiveness of the metacognitive strategies as instructional approaches in teaching and learning of Basic Calculus. A number of 48 students consisting of 24 boys and 24 girls were purposively sampled in this study. Pretest-posttest quasi experimental research design was used which applied t-test and descriptive statistics. Both groups were subject to two instruments that were comprised of problem-solving test (pretest and posttest) and observation guide. Experimental group was taught Basic Calculus using metacognitive strategies while the control group was taught Basic Calculus using traditional teaching strategies. Both groups were subject to a pretest. Class observation was done while the two teaching strategies were applied. In the end, the posttest was administered to both groups to identify the effectiveness of the two teaching strategies. The data gathered were treated using paired sample t-test and independent sample t-test. The results of the study showed that the experimental group had significantly higher posttest scores as compared to control group which proved that metacognitive teaching strategies were more effective in improving the performance and problem-solving skills of the students than the traditional teaching strategies. It was also observed that students who taught using metacognitive strategies helped the students to be extremely engaged in Basic Calculus lessons cognitively, behaviorally, and affectively. The study reveals that the significant increase of the students’ learning engagement in Basic Calculus lessons led the students to a corresponding increase in their posttest scores.
Empowering Pre-Service & New Math Teachers to Use the Common Core Practice St...DreamBox Learning
How prepared are the K-12 teachers of tomorrow to inspire the next generation of young mathematicians? In this webinar for the edWeb.net Adaptive Math Learning community, attendees learned how essential it is for pre-service teachers to learn, develop, and model the Standards for Mathematical Practice to improve learning for their future students. Ben Braun, Associate Professor of Mathematics at the University of Kentucky, and Tim Hudson, Senior Director of Curriculum Design at DreamBox Learning, discussed ways to ensure that pre-service teachers start their careers understanding how mathematical proficiency requires more than simply content knowledge. Tim and Ben shared ideas for K-12 school leaders and mentor teachers who are responsible for new teacher induction, as well as, implications for college and university faculty teaching both math methods and content courses. They also discussed potential disconnects between pre-service content and methods courses and also eventual in-service expectations, while providing examples of math problems to engage pre-service and new teachers. View the webinar to better understand how to use the Standards for Mathematical Practice.
Investigating learning strategies in a dispositional learning analytics conte...Bart Rienties
This study aims to contribute to recent developments in empirical studies on students’ learning strategies, whereby the use of trace data is combined with self-report data to distinguish profiles of learning strategy use [3, 4, 5]. We do so in the context of an application of dispositional learning analytics in a large introductory course mathematics and statistics, based on blended learning. Building on our previous work which showed marked differences in how students used worked examples as a learning strategy [7, 11], this study compares different profiles of learning strategies with learning approaches, learning outcomes, and learning dispositions. One of our key findings is that deep learners were less dependent on worked examples as a resource for learning, and that students who only sporadically used worked examples achieved higher test scores.
Metacognitive Strategies: Instructional Approaches in Teaching and Learning o...IJAEMSJORNAL
The purpose of the study is to determine the effectiveness of the metacognitive strategies as instructional approaches in teaching and learning of Basic Calculus. A number of 48 students consisting of 24 boys and 24 girls were purposively sampled in this study. Pretest-posttest quasi experimental research design was used which applied t-test and descriptive statistics. Both groups were subject to two instruments that were comprised of problem-solving test (pretest and posttest) and observation guide. Experimental group was taught Basic Calculus using metacognitive strategies while the control group was taught Basic Calculus using traditional teaching strategies. Both groups were subject to a pretest. Class observation was done while the two teaching strategies were applied. In the end, the posttest was administered to both groups to identify the effectiveness of the two teaching strategies. The data gathered were treated using paired sample t-test and independent sample t-test. The results of the study showed that the experimental group had significantly higher posttest scores as compared to control group which proved that metacognitive teaching strategies were more effective in improving the performance and problem-solving skills of the students than the traditional teaching strategies. It was also observed that students who taught using metacognitive strategies helped the students to be extremely engaged in Basic Calculus lessons cognitively, behaviorally, and affectively. The study reveals that the significant increase of the students’ learning engagement in Basic Calculus lessons led the students to a corresponding increase in their posttest scores.
Empowering Pre-Service & New Math Teachers to Use the Common Core Practice St...DreamBox Learning
How prepared are the K-12 teachers of tomorrow to inspire the next generation of young mathematicians? In this webinar for the edWeb.net Adaptive Math Learning community, attendees learned how essential it is for pre-service teachers to learn, develop, and model the Standards for Mathematical Practice to improve learning for their future students. Ben Braun, Associate Professor of Mathematics at the University of Kentucky, and Tim Hudson, Senior Director of Curriculum Design at DreamBox Learning, discussed ways to ensure that pre-service teachers start their careers understanding how mathematical proficiency requires more than simply content knowledge. Tim and Ben shared ideas for K-12 school leaders and mentor teachers who are responsible for new teacher induction, as well as, implications for college and university faculty teaching both math methods and content courses. They also discussed potential disconnects between pre-service content and methods courses and also eventual in-service expectations, while providing examples of math problems to engage pre-service and new teachers. View the webinar to better understand how to use the Standards for Mathematical Practice.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Recent Advances in Math Interventions. Programs Tactics Strategies.Handouts.pdf
1. Recent Advances in
Math Interventions:
Programs, Tactics, &
Strategies
Minnesota State
University
August 14, 2023
Robin S. Codding, Ph.D.
r.codding@northeastern.edu
7. • understanding math concepts, laws,
principles, and relations.
Concepts
• algorithms, mnemonics, mental math,
and automatic recall of basic facts.
Procedures
• formulating, representing, and solving
math problems.
Strategies
• explaining, reflecting, and justifying
math problems and their solutions.
Reasoning
• beliefs about the value of math as
useful, sensible, and worthwhile.
Disposition
8. What the Science
Says…
Pitting procedural fluency against conceptual
understanding creates a FALSE DICHOTOMY (NCR,
2001, p. 100)
Conceptual understanding and procedural fluency
(including quick & effortless recall of facts) are
MUTUALLY BENEFICIAL (NMAP, 2008, p. 11)
Empirical studies have shown a bidirectional
relationship between concepts and procedures
(Canobi, 2009; Hectht & Vagi, 2010; Rittle-Johnson & Koedinger, 2009; Rittle-Johnson et al., 2001, 2015; Schneider et
al., 2011)
9. CRITICAL
FOUNDATIONS
FOR
(Gersten et al., 2009; National Mathematics Advisory Panel [NMAP], 2008; USDOE, 2008)
Algebra
Whole Number
Proficiency
Fluency with
Fractions
Key Aspects of
Geometry
Key Aspects of
Measurement
10. KEY IDEA
Students’ math success can
be promoted by ensuring
that students have the
foundational skills
necessary to engage in
advanced math topics as
they progress through
schooling
12. WHAT MYTHS OPERATE IN
YOUR SCHOOL/DISTRICT?
1. Teach Conceptual Knowledge 1st
2. Standard Algorithms are Harmful
3. Productive Struggle Leads to Deeper Learning
4. Explicit Instruction is Only Helpful for Some
Students
5. All Standards Are Created Equal
6. Executive Functioning Training Matters
7. Growth Mindset Increases Math Achievement
8. Timed tests & Tasks Cause Math Anxiety
9. Fact Fluency Doesn’t Matter
13. • Interleave conceptual understanding & procedural knowledge in
every lesson
1
• Teach the standard algorithm
2
• Challenge students with novel problems ONLY AFTER they are accurate and fluent with key
skills & concepts
3
• Use explicit & systematic instruction everyday & at all tiers
(including core instruction)
4
• For mastery of key foundational skills required for students to
engage in advanced math
5
• Remediate learning challenges by improving students’
accuracy, fluency, and generalization of critical MATH skills
6
• Show students how to engage in their own learning
7
• Once of the most effective practices for building fluency is timed
practice activities
8
• Facts are the building blocks in math
9
14. How Did We Get Here?
Pseudoscience is
Seductive
Reform Efforts Left
Behind Proven Practices
Limited tSOM Examples
Included in Textbooks
Overload of information
on the internet and via
social media
Implementation
Challenges
15. TIER 1: ALL STUDENTS
PARTICIPATE IN AND CAN
ACCESS THE CORE CURRICULUM
75-Minute Block (45 Core + 30 Min of Tiered Supports)
17. Strengthening Core Instructional
Practices…
• the number of students who will require
additional supports to be successful
Reduces
• resources to provide those students with or at-
risk for learning disabilities the services and
supports that they need
Frees
• the accuracy with which we identify students
that need specialized intervention supports
Increases
• in BETTER OUTCOMES for students receiving
specialized intervention supports
Results
Targeted
Interventions
Individualized
Interventions
High-quality Core
Instruction Provided In
The General Education
Classroom
(Barrett & VanDerHeyden, 2020; Fuchs et al., 2008; VanDerHeyden et al., 2021)
18. Procedural vs.
Conceptual Debate
seems only to apply
to U.S.
Other countries
recognize practice
with procedures as
a route to
understanding
U.S. students cannot solve basic facts
as quickly or efficiently as their
international peers
Neither textbooks nor instruction
provide enough opportunities for
practice with procedural knowledge
U.S. Curricula
Gaps in BOTH
Conceptual &
Procedural
Knowledge
(Codding et al., 2017; NCR, 2001;NMAP, 2008 )
19. Access Problem
Nearly 30% of surveyed 4th and 8th
grade math teachers reported that a lack
of adequate math instructional materials
and supplies was a moderate or serious
problem (NAEP, 2019)
20.
21. Review of Elementary Level Curricula
Inconsistent Use
of Explicit &
Systematic
Instruction
Lack of Dedicated
Time for
Opportunities to
Practice
Limited Iterative
Sequencing of
Conceptual
Understanding &
Procedural
Knowledge
Little Guidance to
Teachers for
Providing Student
Feedback
Minimal Guidance
on Using
Assessment for
Instructional
Decision Making
(Bryant et al., 2008; Doabler et al., 2012; Jitendra et al., 2005; Sood & Jitendra, 2007)
23. Evaluating
Curricula:
8 Instructional
Practices to
Look For
(Doabler et al., 2012; Hughes et al., 2016;
Riccomini et al., 2015)
Prerequisite Skills
Teach Key Math
Vocabulary
Explicit &
Systematic
Instruction
Instructional
Examples
Use of Math
Models
Opportunities to
Practice &
Cumulative Review
Procedures for
Providing Student
Feedback
Formative
Assessment
26. Tertiary
• Smaller Group & Individualized Supports
• Monitor Weekly
Secondary
• Small Group Intervention (homogeneous skills)
• Monitor Bi-Weekly/Weekly
Class-Wide Supplements
• Address Foundational Skill Gaps with Whole Class
• Monitor Weekly
Core Instruction
• Universal Grade Level Instruction to All Students
• Monitor 2-3 times Per Year
Tier 1.5
27. Classwide
Intervention
• Fluency with
Foundational Skills
Build
• Average Classroom
Performance
• Beliefs & Attitudes
@ Math
Improve
• Into Naturally
Occurring Routines
Embed
(Codding et al., 2009; Kilpatrick et al., 2001; NMAP, 2008; Slavin & Lake, 2008; 2009)
28. Class-Wide
Intervention
Class Median < 25th
Percentile on
Universal Screener
Address Critical
Skill Gaps (50%+
of the class are
missing)
Provide
Brief
(10- to 15-Min)
Interventions
Increase
Opportunities to
Practice Skills &
Concepts
Increase
Amount & Type of
Feedback Provided
29. Focus on Math Facts & Complex
Computation
390 Math Facts
109 +62 | 317 – 25
25 x 50 | 6,598/18
Determine Equivalent
Fractions | Compare &
Order Fractions | Estimate
Sums of 2 Fractions
(Dehaene, 2011; DeSmedt et al., 2011; Gersten et al., 2009; Hasselbring et al., 1988; Jordan et al., 2009; O’Connell & SanGiovanni, 2011; Powell & Fuchs 2013; Price et al., 2013; Stickney et al., 2012)
30. ADD ACHIEVE THE CORE SKILL SEQUENCE
Achievethecore.org :: Instructional Content Nav -
Mathematics: Focus by Grade Level
Identify A Skill
Sequence
31. Benefits of
Peer-Assisted
Learning
Students working in PAIRS or SMALL GROUPS daily
scored higher on the NAEP (2017) than their peers
Benefits students from low income, minoritized
backgrounds in urban schools as well as English
learners
Better when students monitor own outcomes, set
goals, & evaluate own performance
More evidence supporting benefits for whole-
number concepts
(Bowman-Perrott et al., 2013; Ginsburg-Block et al., 2006; Greenwood et al. 1993; Kunsch et al., 2007; NCES, 2018; Robinson et al., 2005)
32. Peer-Assisted Learning Steps
1. Select Activity &
Set Time (10-15 min)
2. Pair Students 3. Provide background +
review key concepts &
procedures
4. Identify Rules
for Working
Together
5. Create Team Score
Card
6. Have Pairs
Select Daily or
Weekly Goals
7. Assign Student
to Begin as
Tutor/Coach
8. Use Timer to
Signal Role
Switching
9. Wrap-Up: Evaluate
Teamwork & Goals
33. Cover-Copy-Compare
• Model to ensure accurate
responding
• Easy to use when
differentiating skills or different
set sizes among students
Pros
• Number of opportunities to
respond are slowed by the
study-cover-copy-compare
process
Cons
34. Detect-Practice-Repair
DETECT:
Powerpoint slide
with basic facts
scheduled to change
every 3 seconds (1-
min). Students have
worksheet to write
answers & later
score.
PRACTICE:
Select 5 incorrect
problems from the
detect phase &
build own Cover-
Copy-Compare
worksheet
REPAIR:
Redo Detect Phase
with second
worksheet
(e.g., Poncy et al. 2010)
35. Explicit Timing
Timed Practice Activity
• Students need to accurately &
independently complete the activity
• Teacher provides finite time for task (1-min,
2-min, 4-min)
• Student either works problems for the time
allocated or stops at 30 second intervals
Pros and Cons
• PROS: Easy to incorporate in classroom
routines, low cost, efficient & effective
• CONS: Need to match the student to the
appropriate skill & know when to move to a
new skill
37. Logistics of Math Intervention Delivery
Daily (@ least 4 days per week)
Small Groups of
• 2 (higher quality teacher-student interactions & more OTPs)
• 5 (more opportunities for peer discourse)
30-Minutes Per Session (minimum)
Progress Monitor Outcomes 2 Ways
• Grade Level CBM
• Subskill Mastery Measures
38. Behaviors
of Students
with
Math
Problems
Poor Recall of Number Combinations (Facts)
Not Understanding Commutative Property
Ineffective Counting Strategies
Regrouping Errors
Misaligns Numbers
Trouble with Meaning of Symbols (+, -, <, %)
Difficulty Solving Word Problems
Problems Implementing a Plan to Solve Word Problems
Trouble Identifying Tangential Information
Not Understanding the ? Asked
Math Language
Failing to Check Work
(Bryant, Bryant, & Hammill, 2000)
39. Key Content Areas to Target
Kindergarten to Grade 5
• Strategic Counting
• Magnitude Comparison
• Number Composition &
Decomposition
• Basic Whole Number Operations
• Place Value
• Explicit Teaching of Word Problems
Grades 4-8
• Operations (fractions, decimals,
ratios, percentages)
• Complex Operations (e.g., long
division)
• Explicit Teaching of Word
Problems
(Gersten et al., 2009)
In Depth Knowledge of Rational
Numbers
In Depth Knowledge of Whole
Numbers
40. Key Content Targets for Mastery (K-5)
Algebra
Whole Number
Proficiency
Fluency with
Fractions
Key Aspects of
Geometry
Strategic
Counting
Magnitude
Comparison
Composition
Decomposition
Fluency w/ Simple
Number
Operations
Fluency w/
Complex
Number
Operations
Word
Problems
(Gersten et al., 2009; National Mathematics Advisory Panel [NMAP], 2008; USDOE, 2008)
41. Bucket 1
Whole Number Knowledge
Word
Problems
Number
Operations
Numeracy
National Mathematics Advisory Panel (2008)
42. Key Content Targets for Mastery (4-8)
Algebra
Whole Number
Proficiency
Fluency with
Fractions
Key Aspects of
Geometry
Magnitude
Comparison
Operations
Word
Problems
(Gersten et al., 2009; National Mathematics Advisory Panel [NMAP], 2008; USDOE, 2008)
44. Relationship
Between Whole
& Rational #
Knowledge
Whole Number
Magnitude
Representations
Calculation
Fluency
Fraction
Knowledge
(Hansen, et al., 2017; Numkung et al., 2018;Resnick et al 2018; Ye et al., 2016)
Students without whole number proficiency wereMORE LIKELY to have TROUBLE with fraction
understanding than students with whole number proficiency
46. Establishing Proficiency with Foundation Skills within Common Core
Standards: Climbing a Mountain
3.OAA: REPRESENT AND SOLVE PROBLEMS INVOLVING
MULTIPLICATION & DIVISION
Interpret 5 x7 as 5
groups of 7 objects
Interpret 35/7
35 objects
partitioned
into equal
shares of 7
objects each
Use x and / within
100 to solve word
problems
Determine
unknown
number in 5 x ?
= 35
•A Common Core cluster is
at the top of the
mountain.
•Standards fall below the
cluster, when these
foundational skills are
integrated they lead to
mastery of the cluster.
Powell et al. (2013, p. 43)
47.
48. 1. EXPLICIT INSTRUCTION…
(ROSENSHINE, 2010)
Sets the Stage For Learning
Presents clear explanation of what to do
Modeling & Demonstration
Guided Practice
Independent Practice
Lesson Closure & Assessment
49. Evidence
Students with math
difficulties & disabilities
BENEFIT MORE from
explicit instruction than
discovery-oriented
methods
(Kroesbergen & Van Luit, 2003)
0
0.25
0.5
0.75
1
1.25
Gresham et al.
(2009)
Swanson
(2009)
Baker et al.
(2002)
Effect Size
Moderate
Large
50. 2. Include Precise Math Language
105 Novel Math
Terms by the End
of 1st Grade
325+ Novel Math
Terms by the End
of 5th Grade
Teaching language that is
mathematically correct can
help children generalize
across concepts and is
necessary for
understanding math in oral
and written forms
(Ernst-Slavit & Mason, 2011; Hughes et al., 2016; Riccomini et al., 2015)
51. Say This Not That
• “Let’s start counting with 1”
• “Three hundred twenty-four”
• “Compose” or “Decompose”
• “Greater than” or “Less than”
• “regroup”
• “Numerator” and “Denominator”
• “Equivalent fraction in simplest
form”
• 5.4 is “five and four tenths”
• “Cube has 6 faces”
• Transformations: “Reflection,
translation, rotation”
• “1 is the first number”
• “Three hundred and twenty-four”
• “Make” or “Break Apart”
• “Bigger” or “Smaller”
• “borrow”
• “Top Number” and “Bottom Number”
• “Reduce”
• 5.4 is “five point four”
• “Cube has 6 sides”
• Transformations: “flips, slides, turns”
52. Vocabulary Pre-View
Provide Examples and Non-
Examples
Illustrate with a Visual or
Picture
Use Simple, Direct Language
Pre-teach Key Vocabulary
Terms for Unit/Lesson
54. 4. Use Number Lines (& Other Math Models)
• Students who use
accurate visual
representations are 6
times more likely to
correctly solve
mathematics problems
than are students who
do not.
• Students with math
disabilities and
difficulties often DO
NOT USE or CREATE
accurate visual
representations
(Boonen et al., 2014; Chard, Gellar, & Powell, 2017; van Garderen et al., 2012; van Garderen et al., 2014)
Number Lines
Strip Diagrams
Pictures
Graphs/Charts
Graphic Organizers
55. 5. Explicitly Teach
Word Problems
• Organize problems on structural
features (e.g., additive total,
difference, change) using
diagrams
• Use explicit modeling of problem-
solving steps
• Teach attack strategies
57. CULTURALLY RESPONSIVE
ADAPTATIONS
Include Culturally
Relevant Teaching
Examples
Encourage
Students to Create
their Own Examples
& Word Problems
based on Their
Lived Experiences
Encourage Bilingual
& Multilingual
Students to Use
Their Preferred
Language When
Using “Math Talk”
Preview & Review
Math Vocabulary in
Students’ Preferred
Language
(Driver & Powell, 2017; Freeman-Green et al., 2021; Luevano & Collins, 2021)
58. 6. Use Timed Practice To Build Fluency
(Codding et al., 2019; Doabler et al., 2019, Fuchs et al., 2021)
Deliberate, Productive Opportunities To Practice Are Required
For All Types Of Learning (e.g., sports, music, math)
Promote Active Engagement with Math Content
Provide High Levels of Feedback & Support
Timed Practice Opportunities that Promote Efficient &
Accurate Performance Improve Student Outcomes
59. Guided
Practice
Timed
Practice
Cumulative
Review
Teacher-Led (Accuracy)
• Demonstration & Modeling
• Think Aloud While Solving
• Worked & Partially Worked Examples
Student-Led (Fluency)
• Flash Cards
• Worksheets
• Peer-Mediated or Team Based
• Technology
Integrate Previously Learned Skills
& Concepts (Generalization)
• Games
• Challenge Problems
• Interleaved Practice
Establishing
Retaining &
Maintaining
Enduring &
Applying
60. BEGIN WITH STANDARD PROTOCOL
INTERVENTIONS
Effective Interventions
Interventions that
Work
Interventions with
Known Evidence
Based Practices
61. Standard
Protocol
Interventions
(Gresham, 2007)
Goal: Provide research
validated treatment protocols
Includes: Materials, protocols,
assessment tools, treatment
adherence forms
Advantages: Better quality
control of treatment delivery,
more feasible and usable
64. Individualize Instruction by
(Gresham, 2007)
Clearly DEFINE the Learning Challenge
Collecting DATA
Generating REASONS for the Learning
Challenge
Linking Reasons to Instructional
Intervention PLANS
66. Students in
Need of
Intensive
Individualized
Support
Require…
Changes in frequency and
duration of instruction
Increased motivation &
sustained engagement
Smaller slices of the curricula
(More focused and specific
goals)
Consider cognitive load, working
memory, and retention of
learners
(e.g., Fuchs et al., 2012; Lemons et al., 2018; Mellard et al., , 2010;Vaughn et al., 2010)
67. REASONS FOR STUDENTS’ ACADEMIC
DIFFICULTIES
Academic
Challenges
Don’t
Want To
Not
Enough
Practice
Need
More
Help
Its Too
Hard
Haven’t
Done it
That Way
(Daly et al., 1997)
Motivation
Increase
Support
Evaluate
Pre-
Requisite
Skills
More
OTPs
Generalization
Daly et al. (1996)
68. Instructional
Hierarchy
Adaptation
APPLYING: Skills & Concepts are Integrated and Applied to
Novel Problems
Generalization
ENDURING: Skills & Concepts Transfer Across Academic
Tasks & Situations
Fluency
REMEMBERING & RETAINING Skills & Concepts: Building
Efficiency | Automaticity| Fluency + Accuracy
Acquisition
ESTABLISHING Skills & Concepts: Building Accuracy
(Burns et al., 2010; Codding et al., 2017; Haring et al., 1978)
69. Instructional Hierarchy
(Burns et al., 2010; Peltier, 2021)
Find Students’ Stage
of Skill Development
& Match it to
Corresponding
Instructional
Strategies
70. Using the IH for Diagnosis & Intervention
Slow + Inaccurate
• Implement explicit
instruction with
modeling, guided
practice, immediate
and corrective
feedback
Slow + Accurate
• Develop fluency
with opportunities
for productive
practice
Fast + Accurate;
No Transfer
• Help student
generalize their
skills across time
and tasks
Fast + Accurate +
Transfer
• Provide novel and
challenging
problems that
require skill
integration
ADAPTATION
FLUENCY
ACQUISITION
GENERALIZATION
71. Instructional Goal
Build Accuracy
Establish Skill/Concept
Deliver Small Slices of Curriculum
Make Learning Errorless &
Concrete
Instructional Strategies
Modeling
Present example of a skill (e.g., look at this…)
Demonstration
Active performance of a skill (e.g., watch me, I will show you
how to…)
Prompting & Cueing
Providing a cue to perform a response (e.g., remember to…)
Immediate Feedback
Provide praise for correct responses & correct
misconceptions
Acquisition
A student is in the ACQUISITION
STAGE when:
They perform a skill slowly &
inaccurately
72. Best Forms of Practice For Acquisition
Guided
Practice
Drill
Worked
Examples
Teacher-Led
• Demonstration & Modeling
• Think Aloud While Solving
Skill in Isolation
• Flash Cards
• Incremental Rehearsal
Worked Examples
• Completed
• Partially Completed
73. Instructional Goal
Build Efficiency/Fluency
Retain Skill/Concept
Provide Lots of Opportunities for
Brief & Frequent Practice
Instructional Strategies
Timed & Peer Practice
Delayed Feedback
Feedback on Fluent Performance
Self-Monitoring, Reflection & Graphing Progress
Fluency
A student is in the FLUENCY
STAGE when:
They perform a skill slowly &
accurately
74. Best Forms of Practice for Fluency-Building
Drill
Practice
Skill in Isolation
• Flash Cards
• Incremental
Rehearsal
Combine Sets of
Problems
75. Instructional Goals
Transfer Across Tasks, Activities, Problems
Consistency Across Time & Settings
Application of Skills
Combine Previous & Recently Learned
Skills and Concepts
Instructional Strategies
Solve Problems Multiple Ways
Team-based Activities
Math Games
Generalization
A student is in the
GENERALIZATION STAGE when:
They perform a skill fast &
accurate but without transfer
76. Best Forms of Practice for Generalization
Interleaved
Practice
Cumulative
Review
Interleaved Practice
• Tasks & Activities that
Integrate Skills
Integrate Previously
Learned Skills &
Concepts
• Games, Advanced Problems
77. Interleaving
Problems
• Interleaving is the process of mixing up the
skills practiced rather than focusing on a
single topic or skill
• Consecutive problems cannot be solved
with the same strategy
• Students need to learn to choose the most
efficient strategy
• Cognitive psychologists believe that
interleaving improves the brain’s ability to
differentiate, or discriminate, between
concepts and strengthens memory
associations.
(Rohrer, Dedrick, & Agarwal, 2017, pp. 3-4)
(Rohrer, Dedrick, & Agarwal, 2017, p. 8)
78. Instructional Goals
Application of Skills and Concepts
Integration of a Variety of Skills & Concepts
Instructional Strategies
Simulations
Novel & Challenging Problem
Solving
Adaptation
A student is in the ADAPTATION
STAGE when a skill or concept is
mastered:
They perform a skill quickly,
accurately with transfer
80. LONGER TOTAL DURATION
Tendency to
hold onto the
idea we can
address student
learning needs
in a fixed period
of time (8-12
weeks)
Total
Duration
Initial Scores Matter
• Met criterion after 10, 20, 30 weeks
(Vaughn & Linan-Thompson, 2003)
More Total Weeks
• Secondary students = 2 years of Support
(Vaughn et al., 2011)
Fading 100 min/day to 50-min
• 40% of students could transition out of
special education (Torgersen et al., 2001)
81. MOTIVATION & ENGAGEMENT
Students with math learning difficulties have
trouble beginning and persisting with problem
solving tasks
Student attention is one of the most persistent
child-level predictors of responsiveness to whole
number interventions
(Gersten, Beckmann et al., 2009; NMAP, 2008; Powell et al., 2015, 2017)
82. Improve Student Beliefs &
Attitudes About Math
Teamwork & Motivation
• Facilitate teamwork, mutual
assistance, encouragement,
and commitment to pro-
social goals.
• Math achievement is
improved by enhancing
motivation and making
students active learners.
Token Economy Group
Contingency
Behavior
Contract
Mystery
Motivator
(Gersten et al., 2009; NMAP, 2008; Powell et al., 2015, 2017, Pellegrini et al, 2021)
83. ADD AMOUNT & SALIENCE OF
FEEDBACK
Praise Self-Scoring Self-Charting Choice
Goal
Reflection
Ticket Out: 3
Things I Learned
84. Layer Self-Regulation &
Motivation Components Into
Skill-building
• Praise Effort & Persistence
• Establish Short-Term Learning Goals
• Offer Opportunities for Reflection
• Teach Students to Monitor Their Own
Progress Toward Individualized
Learning Goals
• Show Students How to Record Learning
Accomplishments
• Encourage Students to Check their
Work
(Park et al., 2016)
85. SELF-
REGULATION
Help students become aware of
how they think when problem
solving
Use of Heuristics & Mnemonics &
Verbalization to teach students how
to PLAN, MONITOR, & MODIFY their
work
Metacognitive strategies IMPROVE
math problem solving of students
with mathematics learning
difficulties and disabilities (Montague, Enders, & Dietz, 2011; Pfannenstiel, Bryant, Bryant, & Porterfield, 2015)
87. Teaching Heuristics
(Zrebiec Uberti,, Mastropieri & Scruggs, 2004)
Understand the
Problem
Restate In Own Words;
Break It Down Into
Smaller Parts; Draw A
Picture; Act It Out; Use
Manipulatives Or
Visuals
Devise a Plan
Make a table
Draw a diagram
Translate into an
equation
Carry out the Plan
Look Back (check
results)
Put Results In Words
Does The Answer
Address The Question?
88. REDUCE SET SIZE
Set Size
Number
of Items
Targeted
As SET SIZE increases,
magnitude of intervention
effect decreases
Example: Set Size
2 Facts ~50% Retention
4 Facts ~75% Retention
8 Facts ~33% Retention
( Burns et al., 2016; Poncy et al., 2015 )
89. What about Individual
Differences?
Fraction intervention with either fluency or conceptual
practice activities
Students with very poor working memory
scores did better with the conceptual
practice version
Students with better working memory
scores did better with fluency practice
version
Number knowledge intervention with fluency building
or conceptual knowledge activities
Regardless of cognitive reasoning skills
(weak or strong) improvement occurred
with fluency building version
For students with weak reasoning ability, the
conceptual activity version led to poorer
outcomes than students with stronger
reasoning ability
Bottom Line: the way the
math activities were
constructed was altered
to address individual
cognitive differences
(Fuchs et al., 2013; Fuchs et al, 2014)
90. Best Practices
To Individualize Math Interventions
• Minimize cognitive load on working memory and
reasoning by
• including explicit instruction & breaking down
problems into smaller more manageable parts
• Minimize excessive language load by
• using visual and concrete representations and
providing fluency practice
• Increase repetition and opportunities to practice
(especially if carryover from one day to next
doesn’t happen)
The most effective way to
address math skill deficits is
to DIRECTLY remediate
math skills
91. Preview for Next Time
Linking Assessment to
Intervention
Creating Systems to Support
Data-Based Decision Making