Case One: Marvin
Currently in the subject of Mathematics, Marvin is performing below grade level; he has also made less than average growth. Due to these findings as a result of the Universal Screener and a Response to Intervention (RtI) program, Marvin is being considered for Special Education services. As you can see in the graph provided below, Marvin scored below average on both Tests A (1) & B (2). On Test A, he scored a 1300 when the class average was 1330. Marvin’s test scores are depicted on the graph as the blue line, which is seen clearly below the class average exam scores depicted by the orange line. On Test B, he scored a 1380 while his same-aged peers scored an average of 1401. These scores clearly indicate that Marvin is below average, and this is the reasoning behind the potential Special Education services needed. Further illustrated on the graph is Marvin’s end of the year target score of 1499; we as teachers hope by the end of the year, Marvin is able to reach this goal. But as depicted by the graph, the class will reach the goal of 1499 well before Marvin who is not learning at the same rate. If the teacher is teaching to the average student in hopes that they reach the score of 1499 by the end of the year, Marvin will be left behind and not meet the goals set before him.
A subskill that should be included in Marvin’s intervention plan is 3.G.2 Fraction Models from Shapes (Geometry). After the test was completed, teachers received a graphic organizer of student results and understanding. Each question was presented with the number of people that got the answer correct and incorrect. From this, these questions were given a color either red, yellow, or green, that represented student understanding. If only 0-39% of the students got that question correct, the question would be colored red. If 40-60% got it correct, it would be indicated yellow, and 61-100% would be colored green. On Marvin’s individual test, he got question 46 wrong. Since this question was green, representing that 61-100% of his peers got this question correct, this would be a specific subskill that Marvin needs to work on.
Task 3: Pullout sessions of 30-60 minutes for individualized instruction
Monday: SMARTBoard app (Dreambox Teacher Tools)
This module contains 5 different SMARTBoard activities that start with a review of number sense with flashcards, and continue with the development of skills such as the combinations of 10, equivalencies for 20, addition on an open number line, and the introduction to fractions.
FOCUS: Development of number sense and addition practice.
PURPOSE: These specific activities are a great introduction to the week that lies ahead for Marvin. He gets a review of subjects he might have struggled with in the past, as well as an interactive introduction to the subject of fractions which can be difficult to grasp when first learned. Number sense lays a foundation for number use and comprehension for future lessons.
Tuesday: Internet Games
- “Magical Shape Hunt” by PBS Kids
Users search for designated shapes on the screen.
- “Shape Construction: Geometry & Symmetry Practice” by ABCya.com
Users create shapes from directions provided.
FOCUS: Recognizing shapes and being able to draw specific shapes after hearing them said orally or written.
PURPOSE: These specific website games will help Marvin recall shapes and their names. After he is able to successfully find the correct shapes in the first website, he will move on to constructing his own shapes or shapes from directions given to him. This lesson puts an emphasis on shapes and their specific features and characteristics. This will help Marvin the future when fractions are displayed with shapes.
Wednesday: iPad Technologies and Apps:
- “Match the Fraction” by Innovative Investments Limited
Match parts of a pizza to fractions, from 1/2 all the way up to 9/10ths of a pizza. Match parts of a pizza to other parts of a pizza representing the same quantity (e.g. 1/2 vs. 2/4, etc.). All fractions are grouped into individual groups so the teacher is able to decide when Marvin is ready for the next level.
- “Fractions” by Brainingcamp
Everything you need for teaching and learning: Narrated lesson, Practice questions, Virtual manipulative, Challenging game
TOPICS COVERED: Fractions Introduction, Equivalent Fractions, Comparing and Ordering Fractions
FEATURES: Lesson with visual models and audio narration to make abstract concepts concrete; Questions to practice what was learned; Virtual manipulative for hands-on discovery learning; Challenge game to interactively apply understanding; Alignment with state and Common Core standards; Suitable for ages 9-14
FOCUS: Being able to match pictures of fractions with their numeric representation
PURPOSE: To make sure that Marvin is able to correctly display the desired fraction for a given amount, and be able to identify equivalent fractions, both with numeric and pictorial representations. This will help him in future lessons when there is a need to analyze both fractions and shapes.
Thursday: QR Code Scavenger Hunt (Adapted)
Marvin must match the correct QR code for a specific fraction with the correct QR code of a pictorial representation of that same fraction, and vice versa.
FOCUS: Marvin must show that he is able to correctly match the numeric fraction with the correct pictorial representation of the correct geometric shape or shaded proportion.
PURPOSE: Connects previous lesson about both shapes as well as fractions in a fun and interactive way; Marvin is either given immediate feedback through the software (flash green for correct, red for incorrect), or they are given a comprehensive report of their success at the end of the scavenger hunt.
Friday: iPad Technologies and Apps: “Pizza Fractions 1” by Brian West
In chef’s pizzeria, the user masters the concept of naming simple fractions using pizza picture as examples. Pizza Fractions provides introductory practice with fractions in an approachable game-like environment.
Key features include: Players are presented with randomly generated fractions to identify by counting slices of pizza; simple fractions build confidence with denominators 1-12; the adjustable level of difficulty setting allows for beginners to start with easier fractions and progress as they learn; there is an option to advance questions by shaking the device or using a button if a questions is too difficult or too simple; score data and round timing allows for tracking to be done and informal assessing to take place (monitor progress using charts/graphs)
FOCUS: Connecting previous lessons by having Marvin see a pizza with a specific number of slices present, as well as missing, and then having him choose the correct numeric representation from a three options, two being incorrect.
PURPOSE: Marvin combines the week’s lessons and applies his knowledge to this game. This game is used to gain an understanding of his improvements throughout the week and overall throughout his intervention. Once all days are mastered, Marvin should exceed in the subskill of Fraction Models from Shapes.
After gathering data regarding Marvin’s performance after our intervention plan was implemented, it is seen that while he is gradually improving, he is still performing far behind expectations. When performing the probes, the expected scores were 80% and Marvin consistently scored far below that. At this point it is recommended that Marvin receives more intensive intervention than what he is receiving now. Although many of these lessons and activities are very good to use in a variety of situations and lay the groundwork for future math concepts, Marvin is still having trouble grasping much of the information. Moving forward, we recommend that Marvin is pulled out of his general education classroom for more than one hour a day to receive more intensive one-on-one intervention in a resource room within the school. The school should focus on strengthening the concepts that Marvin has already struggled with in the past so that once those are mastered, he can continue to move forward with the more grade-appropriate mathematics. Two months from the beginning of the new intervention, review Marvin to see if he should move forward in the same intervention, be reviewed for special education, or lessen the intervention and slowly move back into the general education classroom for more of the day. Throughout the two months, make sure that Marvin’s progress is closely monitored with probes and informal assessments so that everyone is aware of his progress and adjustments in curriculum can be made if necessary.