Editor’s note: This is the second in a series of posts from guest blogger Jeff Hartman on the Common Mistakes made in Math Intervention
Mistake #2: Not Differentiating Enough
In an effort to deal with classes that have many students at varying functional grade levels, some instructors will choose to group students by level to better focus small group instruction. But grouping only by functional level doesn’t necessarily put students with the same needs together. Even if all the students in a group are operating at the same level, they very probably have different skill gaps and need a study plan that is precisely mapped to their individual needs, otherwise some of the students in the group will be spending time on lessons that do not correspond to their needs. For intervention to be most effective, instruction needs to be precisely tied to a student’s demonstrated skill gaps, and material that a student doesn’t need to learn should be removed from their study plan.
This is the first in a series of five posts on Common Mistakes Made in Math Intervention by Guest blogger Jeff Hartman
Mistake 1: Starting at the Top
A student who has major skill gaps from previous years is unlikely to fare well in grade level instruction. Unfortunately, too often educators start with just-below-grade-level instruction in hopes of bringing them quickly up to grade level. The temptation is to try to teach objectives that are just under grade level since they seem like the necessary prerequisites for grade-level learning, but often an intervention student is operating significantly behind grade level. It is far more efficient to begin instruction at the level of the student’s lowest skill gap. Not only does this fill in the deepest foundational cracks in their knowledge, it is also where their competency lies. It is where they are most likely to re-discover the sense of accomplishment that can lead to momentum and enthusiasm for learning math.
Too see just how common it is for students to have below grade level skill gaps download this report: Which Math Skills Students Are Missing.
Share these fund math problems with your students
1. Sweethearts candy hearts have been a popular Valentine’s Day treat for more than 100 years. NECCO, the maker of Sweethearts produces about 100,000 pounds of the candy hearts every day in order to meet the Valentine demand, when about 8 billion hearts are sold in six weeks. How many are sold on average each day during those six weeks?
2. Marcus found 32 candies in a box of candy hearts. He divided them up by what was written on them.
8 said Text Me
5 said U R A Star
6 said 4 Ever Fun
8 said Tweet Me
5 said Be Happy
What percent said either Text Me or Tweet Me?
3. The florist sells 150 bouquets of flowers. Each bouquet has a dozen roses. Five bouquets were returned because the flowers were wilted. How many flowers were sold in all?
4. At MathMart, packages of 20 Valentines are on sale for $4.00 each. How much does each card cost?
Share these fun Super Bowl math problems with your students!
1. A Super Bowl ring costs $10,000. There are 53 players on a winning team. How much will it cost to give them all Super Bowl rings?
2. The Panthers and Broncos have played each other four times. The Broncos have won three times and the Panthers once. Add up the scores for each below. Which team scored the most points? By how much?
2012 Carolina Panthers 14 Denver Broncos 36
2008 Carolina Panthers 30 Denver Broncos 10
2004 Carolina Panthers 17 Denver Broncos 20
1997 Carolina Panthers 0 Denver Broncos 34
3. If the final score of this year’s Super Bowl is Carolina 20 Denver 14 name all the different ways they could have earned those points.
Teachers: Some students may need to be told the meaning of a safety and have a brief review of the way football is scored. Here is a basic guide:
- Each touchdown is worth 6 points. After a touchdown, the scoring team can attempt to get an extra point.
- An extra point is worth 1 point. Right after a touchdown, the ball is placed at the opponent’s two-yard line and kicked. If the ball goes through the goal post, the extra point is earned.
- A field goal is 3 points. If the offense can not score a touchdown, they may choose to kick a field goal. A successful kick results in the ball passing through the goal post uprights and over the crossbar.
- A safety is worth two points and is earned when the offensive ball carrier is tackled behind his own goal line.
Check out this great logic puzzle from TedEd. Try to figure it out as a class or just by yourself.
No two students are exactly alike. In a perfect world, we would treat each as an individual, but it’s not a perfect world. Most often, one teacher must guide twenty or more young people to find the path to success and understanding. For many of us that’s okay. Since, with the teacher’s guidance, we often assist in finding our own unique path to learning.
However, the student who falls increasingly behind in math will remain lost and unable to find his way out of a foreboding wilderness. It becomes increasingly confusing and eventually frightening. The only way back into the clearing and back on level will require blazing an individual path out of the confusion. And that cannot be done without individual guidance each step of the way.
Imagine a map of a thick forest. Three students are lost in the forest.
First, we have to locate the student. How far back has this student fallen? At which functional grade level are the student’s math skills? Is he two grade levels back? Three? Four? Once, we know how far back they are, we can begin to plot a unique path to math success for that student. Let’s say our three students have all fallen three grade levels back. They may all have an equal distance to go but each is in their own location in the forest. Each will move in different directions and have different stopping points on their way out. Finding each student’s individual skill gaps is the only way to plot a reliable path out of the forest. If they go in any other direction or make any other stops along the way it will delay their journey back and even possibly put them deeper into the woods.
Teachers need two things to help students out of the forest: 1. An assessment that finds each student’s position and plots their individual paths forward (think of it as a GPS correlated to state standards). 2. The best instructional content providing students with the individual skills to make their way out.
Brian, Scott EdD, author of “The Effectiveness of Differentiated Instruction in the Elementary Mathematics Classroom.”
Wouldn’t it be great if all math students in a classroom came with the same experiences and same motivation to learn? It’s a nice thought, but the reality is that there is a wide range of skills and readiness in every classroom. Teachers are faced with the challenge of making sure that every student is at grade level or above by the end of the school year. Combined with growing class sizes and changing standards and curriculum, this expectation for teachers today is overwhelming. The believed solution is to simply differentiate instruction. To do this well requires teachers to have a deep understanding of the curriculum, strong classroom management skills, and use assessment well.
Teachers also need to access the scope and sequence of skills before and after each particular grade level. Allowing students to grow in their academic endeavors as seen in academic gains should be the goal for all students regardless of where they start at the beginning of a unit of study. Integration of technology to support the learning as well as classroom management procedures, are critical for optimized student learning. Having a tool available to communicate any skill gaps helps teachers to better understand and plan strategically. Individualized instruction can be very difficult to manage, especially with a large class and a wide range of mathematically ability.
The use of web-based support materials in a blended learning environment can be an effective way to better fill in the missing skills and extend the learning of those working below and above grade level. Avon Intermediate School East has implemented Ascend Math for several years for the primary purpose of extending the learning for those students at or above grade level. Further analysis of recent statewide testing indicates that not only the amount of time spent using the program, but the leveling up and teacher intervention based on the reports are crucial to attain this growth. This was true for students who are below or on grade level as well.
We have found that Ascend Math has multiple uses, and it can be a very helpful tool to reduce skill gaps if implemented well. There are multiple reports and resources. Its flexibility is its greatest attribute.
Dr. Brian Scott, Principal of Avon Intermediate School East
To learn more, read the white paper: Which Math Skills Are Students Missing?.
This is a fascinating video posted by Ted Ed and fun to watch. Whether discovered or invented, real or theoretical ideal, helping students to understand and appreciate mathematics is critical to our future.
Thank you to all math educators. Here’s wishing you a great new year!
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I wish you a wonderful and safe holiday break. Students have been progressing well in Ascend Math this year and are enjoying the reward of Base Camp. Ascend Math Base Camp is a virtual world with fun games and activities available to students as they progress through objectives and levels.
So, we created a special Holiday e-card featuring one of those math games just for you. To play, just scroll to bottom of card, adjust the angle and velocity and press launch. See if you can choose the best trajectory for your snowball toss in Holiday Bears. Share the game with your students and others.
View the e-card
I was recently asked for a good source on differentiated instruction. I replied that ASCD put out some exceptional publications. You can find them at: http://www.ascd.org/professional-development/differentiated-instruction-campaign.aspx
My concern with differentiated instruction has always been classroom management, simply put one teacher trying to see to the needs of numerous students. When each of these students has individual skill gaps, that challenge becomes even more daunting. No teacher can be expected to handle truly individualized instruction for more than a few students without help. And individualized instruction is so often needed when students fall behind in math.
In a recent article in Forbes Magazine, Jordan Shapiro explained that differentiation is easy when the teacher is working with an individual student because the teacher can adapt the teaching to fit the student.
“Great teachers adapt their teaching in this way thousands of times a day…for a few of their students. It just isn’t feasible to do it for everyone. No matter one’s intentions, teachers are human, they have limits. Therefore, for a variety of reasons, certain students in a traditional classroom reap the benefits of the instructor’s personalization skills and other students don’t.”
Our recent Math Skill Gaps Study shows conclusively that students identified for math intervention have skill gaps all different grade levels. In fact, the gaps are so diverse that in most cases individualized instruction is needed to fill gaps quickly and get them back up to grade level.