Friday, April 26, 2013

Focus on Research: A Discussion on Learning Progressions for Instruction and Assessent

By Dr. Deni Basaraba, RME Assessment Coordinator

The need for differentiated instruction to meet the needs of all learners is one source of evidence that students’ learning is not linear and that not all students follow the same learning pathway to mastering content. Learning progressions can be used to describe the successively more sophisticated ways student think about an idea as a student learns, providing a description in words and using examples of what it means to move over time toward a more “expert” understanding of a given topic or content area (Duschl, Schweingruber, & Shouse, 2007).

In addition to including descriptions of students’ understanding as they move from novice to expert understanding, learning progressions also often include descriptions of common misconceptions students may have about the content of interest that may hinder or impede their understanding; these misconceptions can then provide the focus for targeted instruction (Alonzo & Gearhart, 2006).

The complexity associated with learning new content, because it is not linear or the same for every student, is best represented graphically as a complex map or network of connections and interactions rather than a linear path; this complex map allows for the fact that there is no “best” pathway and that some students may take one path in their learning than others to attain proficiency with the same content. A map of a sample learning progression will show not only the development and sophistication of students’ thinking as they move in the learning progression (i.e., increasing in sophistication of their skills and understanding) but will also represents an interaction and integration of knowledge.

In addition to relatedness among constructs in the learning progression, there are also connections of the knowledge and skills between one skill and the next. For example, if the target strategy for a level of a learning progression is the ability to recall multiple
strategies for single-digit addition (e.g., making tens, doubles), the perquisite skill might be a count on strategy whereby students can count on from an initial term (e.g., 5) to make a larger number (e.g., 5, 6, 7, 8). Finally, the most foundational skill in this hypothesized learning progression might be the ability to count all, that is, start from counting at 1 all the way to the desired sum (e.g., When asked what 5 + 3 equals the student starts counting from one – 1, 2, 3, 4, 5, 6, 7, 8).

How can learning progressions inform instruction and assessment?
Learning progressions can be a critical cog in the machinery of instruction and assessment. If, for example, we know that learning progressions provide ordered descriptions’ of students’ understanding, we can then use that information to help identify the “landmarks” or essential knowledge and skills students will need to learn as part of the math content, which can be used to help with instructional planning (e.g., what content to teach and when to teach it).

In addition, because learning progressions often include descriptions of the target knowledge and skills as well as common misconceptions or errors in students’ thinking we hypothesize may be interfering with students’ acquisition of a particular skill or mastery with specific content, learning progressions can provide valuable insights to how students think about the content of the learning progression. Together, these pieces of information can be used to help determine an appropriate sequence for the content of instruction (e.g., focusing first on foundational, prerequisite skills that gradually increase in complexity) as well as to develop classroom-based assessment items that focus on knowledge and skills that have been taught during instruction.

Alonzo, A. C., & Gearhart, M. (2006). Considering learning progressions from a classroom assessment perspective. Measurement: Interdisciplinary Research & Practice, 14(1-2), 99-104.

Duschl, R. A., Schweingruber, H. A., & Shouse, A. W. (Eds.) (2007). Taking science to school: Learning and teaching science in grades K-8. Washington, DC: National Academies Press.

Monday, April 15, 2013

RTI in a Middle School Mathematics Classroom

By Lindsey Perry, RME Research Assistant

Are you looking for tools and resources to help you reach all students, including those who are struggling in mathematics? Are you seeking out professional development to help you grow in your teaching? The Middle-school Students in Texas: Algebra Ready (MSTAR) initiative can help you learn instructional strategies to assist students struggling with mathematics, assess student understanding, and meet the needs of all learners.

The MSTAR initiative, funded by the Texas Legislature and developed by the Texas Education Agency, is a comprehensive project that provides teachers and administrators with assessments, professional development, and intervention lessons to improve grades 5–8 mathematics achievement in Texas and to sustain the implementation of Response to Intervention (RTI).

An important step in the RTI process is assessing student understanding. To do just that, the MSTAR initiative provides teachers with screening and diagnostic instruments, the MSTAR Universal Screener and the MSTAR Diagnostic. The MSTAR Universal Screener assists teachers in determining if a student is at-risk or on-track for meeting grade level algebra-readiness expectations and the level of support the student may need in order to be successful. The MSTAR Universal Screener is administered three times per year in order to monitor student progress and is administered online at The spring administration window is April 8 – May 10, 2013. To find out more, visit or email

The MSTAR Diagnostic Assessment is currently in development. The MSTAR Diagnostic should be administered to students who have been identified by the MSTAR Universal Screener as at-risk for meeting algebra-readiness expectations. This instrument provides teachers with information about why students are struggling and the misconceptions students may have. We are currently seeking a small set of classrooms to participate in the MSTAR Diagnostic Beta test. These classes must have already taken MSTAR Universal Screener at least once this year. While this is a beta test, teachers will receive data on how their students performed. If you are interested, please email us at

The MSTAR Initiative also includes numerous online and face-to-face professional development opportunities. Trainings are available that focus on providing all students with quality Tier I instruction (MSTAR Academy I), strategies for Tier II instruction (Academy II), and data-driven decision making (Implementation Tools). Trainings on topics such as addressing the needs of English language learners, addressing the College and Career Readiness Standards, and teaching fraction/decimal relationships are also available, among many others. Many of the trainings are now available online at For more information, contact your Education Service Center or search the Project Share course catalog at

The MSTAR Initiative can help you improve your teaching and help you better understand your students’ needs and how to meet those needs. We encourage you to check out the MSTAR assessments and professional development offerings!

For detailed information about the initiative and the Response to Intervention framework, we invite you to click the link for a copy of “Supporting Students’ Algebra Readiness: A Response to Intervention Approach” in Texas Mathematics Teacher.

Wednesday, April 10, 2013

"Repeat after me: I'm a math person."

By Marilea Jungman, RME Project Specialist

“I’m not a math person”. It’s a comment you hear, usually said with chagrin and a shake of the head. It’s a phrase that creates a divisive line. There are those who are math people, and those who aren’t. Not being a math person is a perfectly acceptable label. Or is it? Do we ever hear people say, “I’m not a reading person?” No!

At our research-to-practice conference in February we heard from a panel of experts on STEM, the role of mathematics, and the critical state of the current pipeline. Ken Fenoglio, President of AT&T University represented the needs of the workforce and the demand for advanced skills – AT&T employs 40,000 advanced math professionals.

Dr. Fred Olness, SMU Physics professor, highlighted the numerous advantages that a STEM education can provide:

  1. get a job 
  2. keep a job 
  3. keep a life

For every 2.5 STEM jobs available, there is 1 qualified candidate. Conversely, for every 1 non-STEM position, there are 3.3 unemployed candidates competing for that job. And, the average annual compensation for STEM occupations is three times the per capita income in Texas. Dr. Olness provided real-life examples of the importance of mathematics to everyday life, but he also pointed out what he called, “million dollar mistakes.” From an error in a calculation for an architectural design to inaccurately measuring the length of a cord for a bungee jump, Dr. Olness showed us that lack of proficiency in STEM can lead to very costly mistakes. STEM is all around us.

So, very clearly we know it pays to be a “math person”. Where do we start? Who is responsible? I’ll be the first to admit, the dreaded phrase has fallen from my own mouth. But as a parent, and as a member of a research in mathematics education team, I realize the mindset has to change at a very individual level – it’s a phrase I certainly don’t want my young daughter or son to hear, much less say.

Our unit recently hosted a group of parents at SMU and we challenged them to think of simple ways to integrate mathematics into daily life. From plotting a garden, mathematics in art, measurements in baking, as well as board games such as Chutes and Ladders, the opportunities to explore and connect to mathematics is considerable. RME researcher Dr. Candace Walkington has performed studies aimed at the personalization of algebra. In other words, for students, especially struggling learners, having word problems in a context that interests them increases their likelihood of not only attempting, but correctly answering a problem they normally would have simply avoided. You can read the full text of the article here.

What steps will you take to be a math person?

Friday, April 5, 2013

Rounding vs. Estimating: Is there really a difference?

By Sharri Zachary, RME Mathematics Coordinator

Rounding is a familiar estimation strategy because the numbers in a given problem are changed to make computation easier for the problem solver. For rounding “to be useful in estimation, [it] should be flexible and well understood conceptually” (Van De Walle, Karp, Bay-Williams, 2013). For problems that involve the operations, students can generally round as a strategy for estimating their answer. However, when presented with a problem that involves measurement, perhaps, there is in fact a difference in rounding and estimating.

Consider this example:
     What is the approximate length of this line segment in inches?
By inspection, a student may try to visualize an inch ruler or use the tip of their pointer finger to estimate the length of the line segment to be about 3 inches long.

When given an inch ruler, a student may measure the length of the line segment and find that the precise length is 2 ¾ inches but recognize that they are not required to provide an exact answer. Knowing this, they can take their exact measure and round their answer to the nearest inch, providing an answer of about 3 inches long.

A solution to this question can be offered using estimation that is based on prior knowledge (and experience) or rounding the precise answer to the nearest inch.

There are other forms of estimation, such as compatible numbers, that can be used to solve problems. Often, it has been observed that students are told that rounding and estimating are one in the same. However, a measurement example sheds some light on this situation. Perhaps, there is a difference.

Van De Walle, J.A., Karp, K.S., & Bay-Williams, J.M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Upper Saddle River, NJ: Pearson Education, Inc.

Tuesday, April 2, 2013

So, your students hate math...?

By Savannah Hill, RME Professional Development Coordinator and Erica Simon, RME Project Specialist

Maybe I am the only math teacher that ever had at least three students (times a lot) tell me they hated math. I like to believe that one reason is that they had never had anyone put math into context for them. I did everything I could to be a resource for my students and to put math into context, but sometimes, it is difficult. So, where do you look to find resources for the resource?

These days, it seems to be YouTube, Twitter, and Google to name a few.

I found a great website on Twitter that many teachers would find very helpful to introduce to their students. Its called Numberphile.
As one of the first original series funded by YouTube, Numberphile presents "videos about numbers and stuff." The videos present mathematical concepts in a captivating and well explained way using intelligent questioning and editing.

For example, take this video, "Calculating Pi with Pies." The measuring unit is an actual pie. They determine how many pies it takes to calculate the circumference and diameter of a large circle drawn on the ground. Through modeling the formula circumference divided by diameter (C/d), the quotient is approximately 3.14 or pi! This visual representation is a great way of putting math into context.

Many students hate math because they don't see how it is used in the real world, don't like how it is taught, or just don't get it. Numberphile can be a fantastic resource for bell ringers, test problems, or a math project-based learning activity in a classroom. Parents can also introduce it to their children as a fun way to explore mathematical concepts!

Monday, April 1, 2013

Math is Everywhere!

By Savannah Hill, RME Professional Development Coordinator

Last week, at an event hosted by RME, we discussed the importance of making mathematics relevant to children in their everyday lives. Many students may lack motivation in mathematics.

Students think math is not relevant.
Math is meaningless.
Math is boring.

In addition, as mathematics gets more difficult, students are even more unmotivated to persist.

We challenged our participants to come up with some ways that they could involve mathematics during activities they encounter everyday! Take a look!

During story time
  • Looking at the page numbers
  • Telling a story about planning how many people can share a picnic using leftover fruits, etc.
  • Calculating the percentage of a book completed and counting the characters in a story.
  • Finding mathematics in art.
  • Adding ages of people, pets, etc.
  • Reading mathematics related children's literature.
When outdoors
  • Planting a garden with your child. Make sure you measure the space and figure out how many rows and columns of veggies can fit in your garden. You could also find the area and perimeter!
  • Finding numbers on road signs
  • “Pick up 20 acorns, subtract 8. How many are left?”
  • Counting the number of white cars, blue cars, red cars.
  • Tracking sports statistics.
  • Discussing geometry and angles of playground activities such as swing sets and teeter-totters.
In the car or on the bus
  • Counting the floor tiles
  • How many miles to go? How much longer is a bus pass valid?
  • The bus holds how many? Costs how much?
  • Talking about speed limits and time. If the car is going at 60 mph then it’s a mile a minute and how far would it go…
  • Reading/following a map – distances and destinations.
  • Measuring car dimensions and ratios. Count items in view when in motion (driving).
At meal time
  • Baking a pie or cake for dessert. Become familiar with measurements. After, dividing the pie or cake into
  • pieces and illustrating fractions.
  • Counting your green beans. If you eat 5, how many are left?
  • What is the cost of different foods?
  • Figuring out how many pizzas to order – size needed – to feed a group of friends.
  • Discussing fractions (Ex. ½ or ¼ apple, 3/8 peas.)
Doing household chores
  • Finding 6 pairs of shoes and placing them in their proper places.
  • Calculating the square footage of a room vs. how long it takes to vacuum.
  • How long would it take to complete specific tasks? (Ex. make bed, hang clothes, pick up toys.)
  • Discussing the most efficient ways to clean the house and dilute cleaning products using fractions.
At the grocery store
  • Comparing prices - Calculate the cost per ounce and the price difference between products.
  • Weighing the produce.
  • Helping out by keeping an account of how much the grocery bill will be with the use of a calculator.
  • Listing the ingredients you will need to make a recipe (ex. a cake, a pizza, cookies) and calculating how much money you would need to buy ingredients on the list.
  • Reading weights and volume on packages. Convert between pounds and grams; package dimension and its content versus price. Ask your child to determine how much could be bought with his or her allowance?
Around the house
  • Encouraging your child to figure out how to make an allowance last 7 days.
  • Opportunities to earn money from performing special tasks/projects.
Math is all around us. There are numerous daily opportunities for you to share new math words and concepts with children. The more we talk about it, the better chance we have at changing their attitudes towards math and increasing their motivation! Do you have some other ways that you could engage the children in your life to make math relevant daily?