Wednesday, April 30, 2014

An 'App'etite for STEM Education

By Nate White, Guest Blogger, SMU Undergrad

Dr. Candace Walkington, math education professor at Southern Methodist University, teaches a course on STEM integration for pre-service elementary teachers. As part of the class, her students author a series of blogs where they discuss issues related to the integration of science, technology, engineering, and mathematics in elementary school. In this set of blogs, her students were discussing how they can use educational “apps” that are related to STEM in their classroom, focusing particularly on math. They were encouraged to take a critical stance towards the use of apps and to give clear guidelines for how teachers can find and evaluate high-quality apps for math learning.

There is a multitude of iPad applications, or "apps," out there for elementary education that can be utilized effectively in the classroom. There are nearly 100 new "education apps" added to the Apple App Store every day! Therefore, the number of educational applications is so broad that it encompasses both "good" and "bad" apps. When looking at science, engineering and mathematics, there is quite a variety in apps out there, even free ones! Let's look at some examples of free apps in the mentioned STEM subjects, with a focus on mathematics.

Engineering: Pettson's Inventions
This app balances fun and entertainment beautifully. Basically, there are numerous different scenarios (like the one in the photograph below) where the player must design and build some solution to an engineering problem. You are provided objects on the left side of the screen to drag over to the incomplete engineering design on the right, and each "part" is only used once in a specific manner (see the picture at left). It may not even seem like you are learning engineering problem solving skills when playing this game, but the game requires so much creativity, analysis and trial-and-error that you will develop engineering skills. This app seems appropriate for both younger and older elementary students. A couple plausible weaknesses of this app is the lack of engineering vocabulary, as well the lack of support or directions in difficult problems in particular, which could deter some students from persevering to solve the problem.

Science: Bill Nye The Science Guy
This science app is engaging and versatile. There are several different content areas within the app, which the user can choose to pursue. You can explore out solar system and learn about each planet (as seen in the picture below where you have missions to go to each planet and take pictures, place satellites and learn several interesting facts); you can learn about geology (layers of the Earth); or you can even learn about optical illusions. All of these topics are taught by interactive games with informative narration by Bill Nye himself! This app also includes video episodes (which you must purchase) and science experiments with elaborate directions. While this app is very engaging and informative, it could pose problems for English Language Learners because of the app's reliance on (English) narration.

Mathematics: Oh No Fractions! 
This app is composed of various fraction problems in which you must manipulate a visual representation in order to show the answer of the given problem (as seen in the picture at left). You can choose between addition, subtraction, multiplication, division and compare problems, all of which exclusively use fractions. This game is simple and explicitly educational without too much "fun and games," but I think it is a good tool for students in upper level elementary to practice manipulating fractions.

Math Champ
This app is categorized by grade and difficulty (grades 4-7 and five levels of difficulty). The app s free, however, it requires you to buy the uprated version to access the majority of its content. As for the elementary grades (4th and 5th) in the app, there are questions about geometry, fractions, decimals, multiplications etc. All of the questions are multiple choice (as you can see in the picture). The app does a good job of keeping it educational while adding a fun and engaging design. For example, you can unlock alien characters to play as.

Sushi Monster This is perhaps my personal favorite because of how challenging and fun the app is. This app assesses addition and multiplication of positive integers from zero up to the thousands place. First, you choose either addition or multiplication, and then pick a level of difficulty (1-5). In each level there is a different monster who is inside of a circular sushi bar. The sushi chef places several dishes of sushi, each with a number on it, and the monster will have a number on him. The goal is to add or multiply the correct sushi dishes to equal the number on the monster, and you do this by dragging the desired sushi from the outer sushi bar to the monster sitting at the center. You accumulate points and strive for a low time of finishing each stage. It is engaging because of the focus it requires due to the fast paced nature of the game, plus the fact that there is fun Japanese music playing while a monster is eating sushi you serve.

Lobster Diver The last math app I will discuss is a number line game where you play as a scuba diver who is fishing for lobsters. At the bottom of the screen there is a sea floor with a number line on it (which could be counting numbers, negative numbers, fractions, etc.). Each level is timed and you are told the point on the number line where you must dive to get the lobster, however, most of the number line is not marked, so the user must be able to count and decipher the number line in order to dive at the right place. In addition, there are eels constantly swimming by that you must avoid. I love this game because it provides the positives of a recreational game (e.g. eels and interactive scuba diver) yet challenges the player to understand a number line and thus correctly compare fractions and negative numbers. This could be a great app in the classroom.

Strengths and Weaknesses Because of the highly diverse array of apps in the STEM subjects, there are strength and weaknesses to different types of apps. Apps like Oh No Fractions! and Math Champ do not offer anything exclusive to technology, i.e., those problems can be done on the board or on a piece of paper in class, so you can definitely make a case for unnecessarily using technology in those examples. They do, however, enable students to test they knowledge of a wide variety and quantity of math problems efficiently. Games like Lobster Diver risk students doing poorly on the app, not because of their math skills/knowledge, but because of their lack of game playing skills, such as not avoiding the eel and losing all three of his/her lives thus having to start over. Math games like Sushi Monster are great for gifted students because you can always get faster and faster at the game and work with big numbers in the higher levels.

Criteria for Evaluating STEM Apps
As mentioned earlier, because of the quantity of education apps in existence currently as well as those being created everyday, there are plenty of STEM apps that are a waste of money and class time even if they are free. So how does an elementary school teacher evaluate whether or not he/she should purchase/download an app for STEM learning in the classroom? There are several variables that go into this, not to mention the context of the school (such as kids coming to school from impoverished homes where technology is a rarity). But generally speaking, there is certainly some criteria that should be used when evaluating apps.

Educational Technology and Mobile Learning offers some insight as well as rubrics and evaluation questionnaires for iPad educational apps. One example of a rubric I found to be quite effective is seen in the following figure:

I love how this rubric weighs things like engagement, levels of difficulty, various modes of play, and randomly presented content because it is important for students to want to play an app as well as be able to replay it without easily mastering it. As seen in this rubric, it is important to ask yourself if an app meets the students' needs and is aligned to your state standards. At the end of the day, your class time should be used to further your students knowledge to meet, if not exceed, state standards (TEKS, Common Core Standards e.g.). It is easy to find an extremely creative and engaging app with some educational ties and instinctively have your students play it, but careful analysis must take place where the teacher looks for concrete content in the app that assesses or instructs standards-based content. Other practical things should be considered as well, such as the availability of technology to use the app, the presence and extent of feedback given by the app to students. Cost is another factor, which is rather obvious in my opinion: A mediocre or even good app is not worth speeding money when there are so many great apps out there for free!

Another resource teachers can use to find ideas for free mathematics apps is found at TCEA.

More STEM apps for elementary are listed here at Imagination Soup.

Teachers should not rely on the Apple App Store ratings, or even comments, for evaluating and finding apps. It is wise to speak with other teachers, especially trying their apps out. Additionally, simply searching Google for Elementary iPad apps in whatever subject or specific content can provide good results as long as you carefully consider the given pros and cons.

Thursday, April 24, 2014

Subitizing and Decomposing Numbers for Early Math

By Dr. Deni Basaraba and Cassandra Hatfield, 
RME Assessment Coordinators

In 2013, the National Center for Education Evaluation and Regional Assistance (NCEE), in partnership with the Institute of Education Science (IES) released an educator’s practice guide focused on Teaching Math to Young Children. The intent of this Guide (and all similar Practice Guides) is to provide educators with evidence-based practices they can incorporate into their own instruction to support students in their classrooms. In this ongoing blog series we will focus on specific recommendations put forth in the Practice Guide Teaching Math to Young Children and provide practical suggestions for incorporating these recommendations into your classroom instruction.

Recommendation 1 in this Practice Guide is to teach number and operations using a developmental progression. Using and understanding a developmental progression for number serves as the foundation for later mathematics skill development. As noted in the work documenting the development of learning trajectories for mathematics (Clements & Sarama, 2004; Daro, Mosher, & Corcoran, 2011) as well as in our own work in the development of diagnostic assessments using learning progressions, developmental progressions can provide teachers with valuable information regarding students’ knowledge and skill development by providing a “road map for developmentally appropriate instruction for learning different skills” (Frye et al., 2013).

Specifically, the research recommends that teachers first provide students with multiple opportunities to practice subitizing, or recognizing the total number of objects in a small set and labeling them with a number name without needing to count them. According to Clements (1999), two types of subitizing exist:
  • Perceptual subitizing: The ability to recognize a number without using other mathematical processes (e.g., counting).
  • Conceptual subitizing: The ability to recognize numbers and number patterns as units of units (e.g., viewing the number eight as “two groups of four”).
The role of subitizing as it relates to numeracy (Kroesbergen et al., 2009) and procedural calculation (Fuchs et al., 2010) has been documented in the literature. Kroesbergen et al., (2009), for example, not only found that subitzing was moderately correlated to the early numeracy skills of kindergarten students, but that it also explained 22% of the overall variance observed n counting skills and 4% of the variance in early numeracy skills after controlling for language and intelligence. Moreover, research also indicates that instruction designed using a developmental progression can support students’ ability to subitize (Clements & Sarama, 2007), as evidenced by relatively large gains in the pretest to posttest gain scores observed for students receiving this type of instruction compared to a “business as usual” comparison condition.

To support students with subitizing and decomposing numbers, flash images of arrangements of dots visually for students for about 3 seconds. Then give students an opportunity to share what they saw. Over time, student’s verbal descriptions can transition to writing equations. For younger children, subitizing may be fast and efficient only when the number of objects is less than four (Sarama & Clements, 2009); numbers larger than this may require decomposition into smaller parts.. For students learning multiplication arrangements of multiple groups of dots can be shown to support visualizing equal groups.

How do you see this image?
5 and 5, minus 1 
4 and 4, plus 1 
2 and 2, doubled, plus 1 
2 groups of 4, plus 1

Print these dot cards or 10 frame cards on cardstock and put them on a ring. They can be used in various ways:
  1. Hang them in places throughout the hallway of your school. Working on subitizing is a great way to keep students engaged during transition times.
  2. Place them as a center for partners to flash the images and ask “How many?”
  3. Independent think time: Students can be given an arrangement and write all the different ways they see the arrangement.
  4. Warm-up activity to get students thinking prior to small group instruction
Hyperlink for dot cards:

Link for 10 frame cards:


Clements, D. H. (1999). Subitizing: What is it? Why teach it? Teaching Children Mathematics, 5, 400-405.

Clements, D. H., & Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical thinking and learning, 6, 81-89.

Clements, D. H., & Sarama, J. (2007). Effects of a preschool mathematics curriculum: Summative research on the Building Blocks project. Journal for Research in Mathematics Education, 38, 136-173.

Daro, P., Mosher, F. A., & Corcoran, T. (2011). Learning trajectories in mathematics: A foundation for standards, curriculum, assessment, and instruction. (CPRE RR-68). New York, NY: Center on Continuous Instructional Improvement.

Frye, D., Baroody, A. J., Burchinal, M., Carver, S. M., Jordan, N. C., & McDowell, J. (2013). Teaching mathematics to young children: A practice guide (NCEE 2014-4005). Washington, DC: National Center for Education Evaluation and Regional Assistance (NCEE), Institute of Education Sciences, U.S. Department of Education Sciences. Retrieved from the NCEE website:

Fuchs, L. S., Geary, D. C., Compton, D. L., Fuchs, D., Hamlett, C. L., Seethaler, P. M., Bryant, J. D., & Schatschneider, C. (2010). Do different types of school mathematics development depend on different constellations of numerical versus general cognitive abilities? Developmental Psychology, 46, 1731-1746.

Krosebergen, E. H., Van Luit, J. E. H., Van Lieshout, E. C. D. M, Van Loosbroek, E., & Van de Rijt, B. A. M. (2009). Individual differences in early numeracy: The role of executive functions and subitizing. Journal of Psychoeducational Assessment, 27, 226-236.

Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. New York, NY: Routledge.

Thursday, April 10, 2014

Math STAAR: Strategies for Success

By Dawn Woods, RME Elementary Mathematics Coordinator

As every math teacher across the state of Texas knows, the State of Texas Assessments of Academic Readiness (STAAR) testing window is upon us. You have worked diligently, teaching vocabulary, concepts & skills, through the lens of mathematical process standards thereby empowering your students to implement mathematics in everyday life, as well as perform on this assessment. The strategies listed in this blog are suggestions that could enhance your students’ success.
  1. Teach goal setting. Research suggests that when students are taught to set specific academic goals they make progress in learning skills and content, discover how to self-regulate learning, and improve their self-efficacy and interest in the task (Bandura & Schunk, 1981). Through this goal setting and self-assessment process, students are enabled to monitor and evaluate their performance during a lesson, unit of instruction, or review of course material thereby increasing student performance and instilling responsibility for their learning. An example of goal setting for STAAR could look like:
  2. Teach “timed” test strategies. A few strategies include:
    • Listen to the test proctor’s directions.
    • Budget time appropriately. Work quickly but do not rush.
    • Work the problems in the test book, not in your head!  Double check if you copied numbers correctly, if the units are similar, and if you applied the appropriate formulas. Use good handwriting so you do not misread your answer.
    • Do not be too happy to see your computed answer as one of the answer choices!  Test makers know what wrong choices could be made and include them in the answers. So check your answer before marking it on the answer sheet!
    • Do not panic. If the question is difficult, return to it later. Maybe another question will job your memory on how to answer the difficult question.
    • Position the answer sheet next to the test booklet so that you can mark answers quickly while checking that the number next to the circle on your answer sheet is the SAME as the number next to the question you are answering.
    • Before turning in your test, double-check your answers.
    • Make sure you bubbled in the answers correctly on your answer sheet.
    •  Don’t be disturbed by other students finishing before you. Extra points are not given for finishing early!
  3. Communicate with parents and students to encourage healthy pre-test behaviors. A few pre-test behaviors include:
    • Relaxing for a few hours before bedtime.
    • Getting enough sleep the night before a test.
    • Eating a healthy breakfast and avoiding foods that could make you groggy or hyper.
    • Don’t stress!  You’ve worked hard and are prepared for the test.
Works Cited:
Bandura, A., & Schunk, D.H. (1981). Cultivating competence, self-efficacy, and intrinsic interest through proximal self-motivation. Journal of Personality and Social Psychology, 41(3), 586-598.

Wednesday, April 2, 2014

Open Ended Assessments: Part 2 - Grade 8 Math

By Brea Ratliff, Secondary Mathematics Research Coordinator

 With the assessment season upon us, many teachers and administrators are looking for strategies to ensure their students are successful with all of the concepts being assessed. This blog describes a few ideas for open-ended assessments that build on this student expectation:

8.7(C) – The student is expected to use pictures or models to demonstrate the Pythagorean theorem.

Level 1 – Assessments designed to develop proficiency in 1 student expectation. Assessments build around one particular skill are often helpful after when introducing a concept, or providing targeted intervention.

Level 2 – Assessments designed to develop proficiency in 2 or more student expectations. The assessments for this level can vary in degree. While some may be designed to assess a combination of content knowledge, others may be written to include the process skills. This assessment addresses a wealth of knowledge and skills, and could possibly be used for several class periods.

8.2(D) - use multiplication by a given constant factor (including unit rate) to represent and solve problems involving proportional relationships including conversions between measurement systems. 

8.6(B) - graph dilations, reflections, and translations on a coordinate plane. 

8.7(C) – The student is expected to use pictures or models to demonstrate the Pythagorean Theorem. 

8.7(D) - The student is expected to locate and name points on a coordinate plane using ordered pairs of rational numbers. 

8.15(all) - The student communicates about Grade 8 mathematics through informal and mathematical language, representations, and models.