Presenting the Total PACKage
Context
As you open the door to my classroom, you will see approximately 22 six-year-olds engaged in learning activities. While this sounds like a typical first grade classroom, what sets this group of children apart is the diversity of the backgrounds the students come from. I teach first grade at a school that is minutes away from Michigan State University’s campus and international student housing. This location allows Red Cedar Elementary to be the school the majority of international students attend. Red Cedar represent approximately 45 countries and 36 languages and dialects other than English. Additionally, we are a Title I school. According to the US Department of Education, “Title I, Part A (Title I) of the Elementary and Secondary Education Act, as amended (ESEA) provides financial assistance to local educational agencies (LEAs) and schools with high numbers or high percentages of children from low-income families to help ensure that all children meet challenging state academic standards.”
In regards to technology, there are 2 desktop computers in the classroom. One is for the teacher and one for the students. Additionally, thanks to our Title I lable, we recently had the funds to purchase 1 iPad per classroom with the caveat that these iPads were for to be used solely by students who qualified for Title I services. I also bring in my personal iPad daily for the students to use. Our infrastructure was recently updated to include wireless internet in the classrooms.
Due to the varied backgrounds of my students, both socioeconomic and cultural, I have found there are certain areas in content where many students have gaps in knowledge. These gaps are especially prevalent in reading and math. Many parents who have children that do not speak English fluently have encouraged the students to focus on learning English rather than learning content. While this idea has merit, it causes some students to struggle in understanding the concepts that are presented in school.
In regards to technology, there are 2 desktop computers in the classroom. One is for the teacher and one for the students. Additionally, thanks to our Title I lable, we recently had the funds to purchase 1 iPad per classroom with the caveat that these iPads were for to be used solely by students who qualified for Title I services. I also bring in my personal iPad daily for the students to use. Our infrastructure was recently updated to include wireless internet in the classrooms.
Due to the varied backgrounds of my students, both socioeconomic and cultural, I have found there are certain areas in content where many students have gaps in knowledge. These gaps are especially prevalent in reading and math. Many parents who have children that do not speak English fluently have encouraged the students to focus on learning English rather than learning content. While this idea has merit, it causes some students to struggle in understanding the concepts that are presented in school.
Content
The first graders in East Lansing Public Schools are expected to master the Common Core State Standards set for students in grade one. In math, students should be able to “Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).” (CCSS.Math.Content.1.OA.C.5) This particular skill is a key building block for students in order to successfully move onto other, harder skills such as CCSS.Math.Content.1.OA.C.6 “Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).”
In my years of teaching, I have found that the students who have the most difficulty adding and subtracting within 20, are the students who have not yet grasped the idea that counting is directly related to adding and subtracting. There is a common misconception that children solely need to memorize math facts in order to succeed. I have students who have memorized 2+2=4, yet struggle to answer when given a word problem such as “Mike had 2 bananas. His mom gave him 2 more. How many bananas does Mike have?” This shows me that memorization is not enough. Students need to understand why 2+2=4 in order to be able to transfer this knowledge to different contexts. As Willingham suggests in Why Don’t Students Like School, students need to have a deeper understanding of (mathematical) concepts in order for this knowledge to be transferred. I think this is especially crucial for relating counting to addition and subtraction. Without this essential deep understanding, students will have a difficult time transferring numerical knowledge from the basic to the more complex.
In my years of teaching, I have found that the students who have the most difficulty adding and subtracting within 20, are the students who have not yet grasped the idea that counting is directly related to adding and subtracting. There is a common misconception that children solely need to memorize math facts in order to succeed. I have students who have memorized 2+2=4, yet struggle to answer when given a word problem such as “Mike had 2 bananas. His mom gave him 2 more. How many bananas does Mike have?” This shows me that memorization is not enough. Students need to understand why 2+2=4 in order to be able to transfer this knowledge to different contexts. As Willingham suggests in Why Don’t Students Like School, students need to have a deeper understanding of (mathematical) concepts in order for this knowledge to be transferred. I think this is especially crucial for relating counting to addition and subtraction. Without this essential deep understanding, students will have a difficult time transferring numerical knowledge from the basic to the more complex.
Technology
After taking into account my students’ needs, learning styles, and backgrounds, I decided the technology that seems best suited for my problem is iPads. I needed a technology that could be utilized by one student at a time in order for him/her to receive intensive support at the “just right” instructional level. Additionally, I wanted a technology that was hands-on and interactive in order to keep students engaged in the content and learning. It was also important to take into consideration the motivation of the students to engage in additional learning opportunities. iPads fit all of the criteria I had outlined.
While iPads are great tools, they do not serve much purpose without applications. My next step in this process was seeking out an app that met my goal of improving basic number sense in my struggling learners. I looked for an app that focused on number concepts (idea of number as a quantity), number relations (how numbers relate to each other), number ordering (ordering numbers in sequences), and counting (one-to-one, counting up, counting down, etc.). With these requirements in mind, I found “Native Numbers.” In addition to containing all of the concepts I was looking for, this app allows teachers/parents to set up multiple accounts for multiple students. It also allows the adult to monitor student progress through the Native Numbers dashboard. One of my favorite features is the ability of the app to teach to the student. Native Numbers can tell (thanks to responses and response time) if a piece of the content it too difficult or too easy. It then automatically adjusts the next question based on this feedback. The ability of the app to address the learning process of each individual learner is one that will keep students engaged since the material will not be too difficult nor too easy. This app has all of the features I was looking for in an app that would help improve number sense in students. It will allow learners to then be able to successfully move on to more complicated mathematical tasks.
My goal for implementation is to have 2-5 iPads in my classroom loaded with the Native Numbers app. I then plan to use these iPads as a center during math time each day. The students who have shown need in the area of number sense would be the students that would use Native Numbers when they have a turn at the iPad center. I will frequently check the teacher dashboard to monitor all students’ progress, and meet with students in order to discuss and check-in on learning.
While iPads are great tools, they do not serve much purpose without applications. My next step in this process was seeking out an app that met my goal of improving basic number sense in my struggling learners. I looked for an app that focused on number concepts (idea of number as a quantity), number relations (how numbers relate to each other), number ordering (ordering numbers in sequences), and counting (one-to-one, counting up, counting down, etc.). With these requirements in mind, I found “Native Numbers.” In addition to containing all of the concepts I was looking for, this app allows teachers/parents to set up multiple accounts for multiple students. It also allows the adult to monitor student progress through the Native Numbers dashboard. One of my favorite features is the ability of the app to teach to the student. Native Numbers can tell (thanks to responses and response time) if a piece of the content it too difficult or too easy. It then automatically adjusts the next question based on this feedback. The ability of the app to address the learning process of each individual learner is one that will keep students engaged since the material will not be too difficult nor too easy. This app has all of the features I was looking for in an app that would help improve number sense in students. It will allow learners to then be able to successfully move on to more complicated mathematical tasks.
My goal for implementation is to have 2-5 iPads in my classroom loaded with the Native Numbers app. I then plan to use these iPads as a center during math time each day. The students who have shown need in the area of number sense would be the students that would use Native Numbers when they have a turn at the iPad center. I will frequently check the teacher dashboard to monitor all students’ progress, and meet with students in order to discuss and check-in on learning.
Pedagogy
Addressing the issue of basic number sense is one that is challenging in many ways. Some students come in with no understanding of numbers, while others come in knowing what numbers are but not how they relate to one-another. Many students do not realize the importance of the relationships between numbers and how to transfer this knowledge once the value is recognized.
While thinking of these hurdles, I realized that the learning model that would best address my end goal was Cognitive Information Processing. As Leidner and Jarvenpaa state, “Learning involves processing instructional input to develop, test, and refine mental models in long-term memory until they are effective and reliable enough in problem-solving situations (Schuell, 1986).” My goal is for students to have a deeper understanding of numbers and relations between numbers. The way in which I plan on achieving this goal is to assist my students in processing and practicing information about numbers frequently. With enough practice integrated with higher-order thinking skills, I hope this foundational knowledge will become reliable enough for transfer to other situations where problem solving is involved.
Through encouraging students to practice foundational skills with feedback from both the program as well as the teacher, I believe that growth will be made. Differentiation based on learning needs and styles is also a major factor in addressing this problem. After using anecdotal evidence as well as assessments involving counting and ordering, I will be able to pinpoint the students that need additional support in number sense.
While thinking of these hurdles, I realized that the learning model that would best address my end goal was Cognitive Information Processing. As Leidner and Jarvenpaa state, “Learning involves processing instructional input to develop, test, and refine mental models in long-term memory until they are effective and reliable enough in problem-solving situations (Schuell, 1986).” My goal is for students to have a deeper understanding of numbers and relations between numbers. The way in which I plan on achieving this goal is to assist my students in processing and practicing information about numbers frequently. With enough practice integrated with higher-order thinking skills, I hope this foundational knowledge will become reliable enough for transfer to other situations where problem solving is involved.
Through encouraging students to practice foundational skills with feedback from both the program as well as the teacher, I believe that growth will be made. Differentiation based on learning needs and styles is also a major factor in addressing this problem. After using anecdotal evidence as well as assessments involving counting and ordering, I will be able to pinpoint the students that need additional support in number sense.
Total PACKage
When looking at the big picture, there are three main areas I am focusing on, technology (Native Numbers iPad application), pedagogy (Cognitive Information Processing learning model integrated with teacher and electronic feedback), and content (number sense). While each of these is important, it is critical for these three areas to work together to form the “Total PACKage." In order to best address the problem of practice that I have focused on, I took into account how technology, content, and pedagogy could be woven together to ensure student success in regards to improving number sense.
I began with thinking about the content. What was a problem of practice in my classroom that I felt was critical to address? After thinking of my students, the backgrounds of my students, and the needs of my students, I selected number sense. I chose this content because it is a foundational skill that is a large building block of mathematics. Without a strong foundation, mathematical knowledge can crumble, or may not even be built. This content area became my starting point.
Next, I had to decide if I wanted to find a technology that fit into a chosen pedagogy or a pedagogy that fit into a chosen technology. Since I am a relatively new teacher, I decided it would be good for me to be flexible with my pedagogy and potentially change the way I deliver content in some areas. Due to this, I decided to pick a technology that addressed my content. After evaluating many different technologies and weighing affordances and constraints of each, Native Numbers rose above the other options. This technology will allow students to gain a much deeper knowledge of numbers as well as differentiate learning for the student. At this point, I had my content and my technology which had a clear overlap.
The next step was thinking about the pedagogy that would overlap with both the content and the technology. I wanted learners to process the information taught to them through Native Numbers in order to develop these concepts in long-term memory. Through intensive lessons with practice and receiving feedback from multiple sources (teacher and technology), I think that the students will be able to build a strong knowledge base in number sense. This knowledge base will then be reliable enough to transfer knowledge to new and more challenging situations.
Using a backward design template, I was able to analyze my goals for the students and mesh three important areas of instruction together: technology, pedagogy and content. Bringing these areas together will create a “sweet spot” of learning that will enhance students’ ability to better grasp the content area.
I began with thinking about the content. What was a problem of practice in my classroom that I felt was critical to address? After thinking of my students, the backgrounds of my students, and the needs of my students, I selected number sense. I chose this content because it is a foundational skill that is a large building block of mathematics. Without a strong foundation, mathematical knowledge can crumble, or may not even be built. This content area became my starting point.
Next, I had to decide if I wanted to find a technology that fit into a chosen pedagogy or a pedagogy that fit into a chosen technology. Since I am a relatively new teacher, I decided it would be good for me to be flexible with my pedagogy and potentially change the way I deliver content in some areas. Due to this, I decided to pick a technology that addressed my content. After evaluating many different technologies and weighing affordances and constraints of each, Native Numbers rose above the other options. This technology will allow students to gain a much deeper knowledge of numbers as well as differentiate learning for the student. At this point, I had my content and my technology which had a clear overlap.
The next step was thinking about the pedagogy that would overlap with both the content and the technology. I wanted learners to process the information taught to them through Native Numbers in order to develop these concepts in long-term memory. Through intensive lessons with practice and receiving feedback from multiple sources (teacher and technology), I think that the students will be able to build a strong knowledge base in number sense. This knowledge base will then be reliable enough to transfer knowledge to new and more challenging situations.
Using a backward design template, I was able to analyze my goals for the students and mesh three important areas of instruction together: technology, pedagogy and content. Bringing these areas together will create a “sweet spot” of learning that will enhance students’ ability to better grasp the content area.
Resources
Leidner, D. E., & Jarvenpaa, S. L. (1995). The use of information technology to enhance management school education: A theoretical view. MIS QuarterlyMIS Quarterly, 19(3), 265-291. Retrieved from http://www.jstor.org/stable/249596?origin=JSTOR-pdf
National Governors Association Center for Best Practices, Council of Chief State School Officers. (2010). Common core state standards. In Washington D.C.: National Governors Association Center for Best Practices, Council of Chief State School Officers. Retrieved from http://www.corestandards.org/
U.S. Department of Education, (2011). Improving basic programs operated by local educational agencies (Title I, Part A) (84.010). Retrieved from Student Achievement and School Accountability Programs website: http://www2.ed.gov/programs/titleiparta/index.html
Willingham, D. T. (2009). Why don't students like school?. San Francisco, CA: Jossey-Bass.
National Governors Association Center for Best Practices, Council of Chief State School Officers. (2010). Common core state standards. In Washington D.C.: National Governors Association Center for Best Practices, Council of Chief State School Officers. Retrieved from http://www.corestandards.org/
U.S. Department of Education, (2011). Improving basic programs operated by local educational agencies (Title I, Part A) (84.010). Retrieved from Student Achievement and School Accountability Programs website: http://www2.ed.gov/programs/titleiparta/index.html
Willingham, D. T. (2009). Why don't students like school?. San Francisco, CA: Jossey-Bass.