My research has helped answer my essential question. I read about a positive math mindset, a growth mindset, inquiry in mathematics, the benefits of student collaboration, and other topics aligned with my essential question. I am currently finishing my research project in my classroom, and will have my results in a week and a half. The most beneficial research has been on the benefits of inquiry in mathematics. It gave me a better understanding of the importance of inquiry in math instruction. By embedding inquiry into math, students develop lifelong skills that lead to the development of 21st century skills (i.e. critical thinking and collaboration). The results I have for my pre-test, along with the research articles I have been reading, have made me wonder if there is a more effective way to measure inquiry. Currently, I have a survey the students took on inquiry/questioning in mathematics. In the future, I will also record student conversations based around inquiry into my data collection for inquiry. I saw that this was done in some of the research articles I read, and thought it helped support the other data in a meaningful way. I look forward to completing this research project in my classroom, and comparing the pre-test and post-test data.
1 Comment
My Essential Question: How can I use inquiry based instruction to develop a positive math mindset and increase student performance on Bridges assessments in the area of mathematics?
I will be relying on qualitative methods of research for data analysis for the growth mindset/inquiry portions of my research. I have individualized these assessments for my classroom. I created a Math Mindset quiz and an Inquiry quiz to give at the beginning of this study, and at the end. These quizzes will help to measure each child’s math mindset principle in relation to math, as well as their ability to understand and identify inquiry in mathematics in relation to Costa’s Levels of Questioning. The quantitative portion of my data analysis is done through the student performance portion. My students will be taking a pre-test and post-test from our Bridges math curriculum. These results will give me a clear cut picture of whether or not the standards were met. I am planning on displaying this data as a bar chart to provide the percentages. Multiple methods of assessment will help me gain a holistic understanding of how my students are progressing in relation to my driving question. I chose these data analysis methods because the use of multiple data ensures the trustworthiness of my data. What perspectives did the 3 new research articles offer?
One theme that stood out among all three articles is how, at its core, Inquiry-based teaching (IBT) encourages students to develop thoughtful questions where they can make sense of things. It requires that students generate questions and use materials to help develop their problem-solving skills. Students should be encouraged to share their ideas in a safe environment. They should read the works of others and connect their own ideas and try out new ideas Another big theme was the necessity of students engaging in communication and collaborating within small group activities centered around open-ended activities where students respond to meaningful prompts. Another common them in these articles is that teachers were initially uncomfortable teaching with inquiry-based instruction, and required support to implement IBT into their classrooms. There needs to be a shift where teachers feel capable of effectively managing classrooms where this type of learning takes place. This is the shift I am working to make! How do they inform your study and methodology? One article stated that teachers should be conscientious facilitators who value the work of students, and should see students as important and necessary collaborators (Magee, Paula & Flessner, Ryan, 2012). This shapes part of my methodology in relation to inquiry and a positive math mindset. I will be facilitating opportunities to cultivate a positive math mindset and to have student-centered, inquiry-based methodologies during math instruction. Another important aspect of my study will be providing reflection and feedback for my students. These powerful tools will help my students grow in inquiry and math mindset. This could be both formal and informal. For example, having a student identify what level a question is, and then providing feedback to that student will be a quick and meaningful way to grow them in the area of questioning. I liked the idea from one research article where discussion takes place before the actual math lesson begins in the classroom. This would include discussing what math mindset we will begin the lesson with, and questions to begin the inquiry process once the lesson begins. How do they relate to your driving question? One statement stood out that clearly relates to my driving question: “In high-quality teaching, the process of inquiry, not merely "giving instruction," is the very heart of what teachers do. Inquiry not only tests what students know, it presses students to put what they know to the test. It uses "hands on" approaches to learning, in which students participate in activities, exercises, and real-life situations to both learn and apply lesson content. It teaches students not only what to learn but how to learn.” (Stonewater, J.K., 2005) This statement clearly defines what I am seeking to do with inquiry and cultivating a positive math mindset in the classroom. It will be important to model both inquiry and a positive math mindset. This means engaging the class in exploring, deciding on appropriate questions, and modeling ways to answer those questions. It will also require me to be a facilitator where I help students connect the mathematical content and their steps in inquiry. Magee, P. A., & Flessner, R. (2012). Collaborating to Improve Inquiry-Based Teaching in Elementary Science and Mathematics Methods Courses. Science Education International, 23(4), 353–365. Retrieved from http://0-search.ebscohost.com.library.touro.edu/login.aspx?direct=true&db=eric&AN=EJ1001629&site=ehost-live Stonewater, J. K. (2005). Inquiry teaching and learning: the best math class study. School Science and Mathematics, 105(1), 36+. Retrieved from http://0-link.galegroup.com.library.touro.edu/apps/doc/A126932535/PROF?u=nysl_me_touro&sid=PROF&xid=c2e099f4 Why should educators care about cultivating a positive math mindset through inquiry in mathematics? There are many reasons. Having a positive math mindset not only helps student become more confident in math, it also allows them to prime their brains to think more effectively (Sparks, Sarah D., 2015). Increasing each child’s math mindset will make my entire unit of study more effective. Inquiry will lead to greater student understanding, and prepare students to successfully engage in the “4 Cs”: Creativity, Collaboration, Communication, and Critical Thinking. When students have a deeper level of discussion, they can make discoveries while talking about their thought process in solving problems which increases their understanding for how to solve problems ( James, Lorie, 2016). This is why it is important study how inquiry based instruction will help develop a positive math mindset and increase student performance on Bridges math assessments.
I will be doing this study with the students in my fourth grade classroom. I anticipate that my students will develop deeper inquiry skills when taught questioning strategies in mathematics. I predict that each child's math mindset will increase through teaching with positive math mindset principles, verbiage, and strategies. I anticipate that focusing on inquiry and a positive math mindset will increase student performance levels in the math curriculum Bridges, which is used by my school district (Napa Valley Unified). I intend to give my students a series of formal and informal assessments over a five week period. I will give different assessments at the beginning and end of this study. I will administer a math mindset survey, an inquiry assessment on levels of questioning, and a student performance pre-test and post-test from the Bridges math curriculum. I will compare the pre-tests and post-tests scores to evaluate if these methods of instruction were effective. One of the seminal people researching in the area of my driving question is Jo Boaler. Boaler discusses the importance of a positive math mindset in her book, “Mathematical Mindsets: Unleashing Students’ Potential Through Creative Math, Inspiring Messages, and Innovative Teaching.” Jo Boaler has incredible insights into how a positive math mindset empowers students for deeper learning. She discusses equitable strategies which include encouraging students to think deeply about mathematics through hands-on experiences, project-based curriculum, curriculum with real-life applications, and providing opportunities for students to work together. Jo Boaler’s insights support what Carol Dweck says about mindsets.
Carol Dweck is a Stanford psychologist who coined the terms “Growth” and “Fixed” mindsets. She discusses how students with a growth mindset are more willing to work on challenging problems, and stick with that challenge, despite setbacks. This is especially important in math. Sarah Sparks discusses the power of a growth mindset in mathematics. She states how having a positive math mindset not only helps student become more confident in math, it also allows them to prime their brains to think more effectively A positive math mindset is necessary for effective inquiry instruction to take place. Providing students with meaningful questions will give them the opportunities to have deeper levels of discussion. During discussions students can use their positive math mindsets to make discoveries and increase understanding. Increasing each child’s math mindset will make my entire unit of study more effective. Inquiry will lead to greater student understanding, and prepare students to successfully engage in the “4 Cs”: Creativity, Collaboration, Communication, and Critical Thinking. My Direct Question is: How can I use technology, inquiry, and focused intervention groups to develop a positive math mindset and increase student understanding in the area of mathematics?
The educational context for my Direct Question for our nation, state, district, and school is as follows: National: As a nation, Common Core Standards are leading students to have a deeper understanding of what they are learning through 21st century thinking skills. We are moving away from memorizing information, and moving towards teaching students how to access information and think critically about what they are learning. We are currently preparing our students for jobs that do not yet exist! A research article I am reading is entitled, “Mathematics Awareness through Technology, Teamwork, Engagement, and Rigor” by Lori James. One line that resonated with me was, “Teachers need to be creative through a combination of integrated technology and intervention groups while providing a positive classroom atmosphere where students learn from each other.” This portion of the article holds many goals I hope to achieve throughout the process of answering my Direct Question. I want to integrate technology in a meaningful way that will support student learning and to help develop their critical thinking skills. Intervention groups will be necessary so that I can help individualize instruction. All of this will take place in a positive classroom atmosphere where students can thrive. Lori James goes on to say, “Students can expand on their understanding through productive struggle. When students make mistakes experiencing productive struggle, their brain activity grows because synapse fires making new connections. “ This supports my desire to implement positive math mindset principles into my Driving Question. In order for my students to succeed at developing their inquiry skills in math and raise their test scores, they will need to be able to have productive struggle in an environment where they are comfortable making mistakes in order to continue growing, learning, and developing. All of these 21st century skills, combined with the goal to close the achievement gap, fall in line with where our nation is moving in education. State: The mission statement for the California Department of Education is: “California will provide a world-class education for all students, from early childhood to adulthood. The Department of Education serves our state by innovating and collaborating with educators, schools, parents, and community partners. Together, as a team, we prepare students to live, work, and thrive in a multicultural, multilingual, and highly connected world.” I believe that my Driving Question is in line with California’s goal for education. Focusing on developing a positive math mindset, and increasing student understanding in the area of mathematics, will require my students to collaborate with one another and use 21st century thinking skills. Integrating technology, inquiry, and intervention groups will cause students to use their communication skills, along with critical thinking, which will prepare them for a successful future in our highly connected world. District: Our district would like teachers to focus on implementing 21st century skills in the classroom. This means that students should be answering important questions and mastering important skills in order to have students be able to articulate what they are learning. NVUSD focuses on the “6 Cs”, and how we should be providing plentiful and meaningful opportunities for students to engage in critical thinking, collaboration, communication, creativity, character, and citizenship. The use of technology is a instructional asset and a learning and productivity tool. A research article I am reading is entitled, “In math, Positive Mindset May Prime Students’ Brains” by Sarah Sparks. This article discusses the impact a positive mindset in math has on student understanding. This belief that intelligence or other skills can be continually improved with practice causes students to feel more confident. This mindset ties in to what our district wants us to do as teachers in regard to teaching 21st century skills and increasing student’s abilities to persevere and become lifelong learners. This also ties into the growth mindset principles of AVID, a program that many schools in Napa have implemented. Our school has been trained in AVID Elementary, and I have seen the powerful results of implementing growth mindset principles in the classroom and the impact of intertwining growth mindset principles with academics. Jo Boaler wrote a book entitled, “Mathematical Mindsets: Unleashing Students’ Potential Through Creative Math, Inspiring Messages, and Innovative Teaching.” One chapter is entitled, “Assessment for a Growth Mindset”. In this chapter she discusses the concept of assessment for learning and the importance of helping students know where they are now, where they need to be, and how they can close the gap. This type of assessment is a powerful way to increase student understanding and inquiry skills. School: Currently our school is in an Accelerate Math Partnership with NapaLearns. Through this partnership, we have the opportunity to be coached by experts in the field of Math through Bridges (our core math curriculum). Our site is specifically focusing on the power of inquiry in math. Having students be able to identify different level questions is also a key focus. This school-wide goals clearly aligns with my Driving Question. My essential question currently is: How will I strategically use differentiated instruction and growth mindset principles in order to effectively engage students in the area of mathematics?
After reviewing the IRB I see that there are many steps I need to take to implement my essential question in my classroom. In order to address my essential question, I will need to gather evidence to effectively measure how I can meet all of my student’s individual needs. I need to set a timeline. In addition, I need to make each method of assessment (formal and informal) clear and measurable so that I can compare my data from the beginning of this study to the end. My “Need to Knows” are: 1. Identifying number 17 on the IRB: What are the documents I need to create for my study (consent letters, survey questions, focus group questions, etc.)? Our Falk book had a sample consent letter on pg. 72 that I may consider editing this one to fit what I am going to do with my students in this study. 2. Identifying 16d: Will there be a follow-up? I want to know what is required in order to do a follow-up. 3. Identifying Number 14 on the IRB: What are the potential risks and benefits to your human subjects? I need to further investigate the risks in this study. I will focus on gathering more information on these questions. 1) Question 1: “What problems in your classroom might point you to your driving question?” One immediate problem that affects me on a daily basis as I plan my instruction is being able to reach my students individually in an effective way. Or, in question form, “How will I reach all of my students individually in the most effective way?” This question is too broad to effectively analyze and keep my framework strong throughout this process. This leads me to ask, “How can I refine this question into a more measurable subject area? How can I make this question more particular, not universal?”
Currently our school is in an Accelerate Math Partnership with NapaLearns. Through this partnership, we have the opportunity to be coached by experts in the field of Math and Bridges (our core math curriculum). I believe this would be the best subject area to focus on for this essential question. In addition to researching how to best enhance my teaching methods and strategies in this subject area, I would also like to add the necessity of growth mindset principles in relation to math. I am trained in AVID Elementary, and I have seen the powerful results of implementing growth mindset principles in the classroom. I have also seen the impact of intertwining growth mindset principles with academics. I want this element to be included in my driving question because it will be a powerful tool to get the best results possible. Currently I am seeing my driving question look like this: How will I use differentiated instruction and growth mindset principles in order to reach all of my students in the most effective ways in the area of mathematics? There are the four subquestions that I plan to explore to help me with this project: 1. What will my small group sessions look like through a unit of study for math? 2. How will I differentiate my teaching for intervention, core, English Learners, and advanced leaners? 3. How will observational data of my students help me assess growth mindset and inquiry growth? 4. How will data drive my curriculum? What I plan to do: I plan on studying about differentiated teaching in mathematics and growth mindset principles, and then applying it to my classroom. I will benefit from the coaching support we are receiving from math specialists in our Accelerate Math Partnership. I plan on using data from pre-tests, mid-point assessments, post-tests, and observations to document student growth. Context/Background for my question: I am choosing this topic because I daily think about it while planning instruction. I want to be the most effective teacher I can be, and that requires helping each individual child reach his/her greatest potential. Math is a focus area for our school, and for me personally. I will continue to refine this driving question to make it more concise and clear as I delve into action research in this area. I currently have thirty-four fourth graders during math with diversely different needs. My English Learners require intensive interventions, building of background knowledge, visuals, hands-on learning, and specific language development instruction. My students who require intervention support, require heavy scaffolding, teacher modeling, hands-on learning, and plenty of repetition of the key concepts so they can continue building on those concepts. My students on and above grade-level require teacher modeling, scaffolding, and interactive lessons that push them to engage with the material at a higher level while using their critical thinking skills. Enrichment includes helping children developing their critical thinking and inquiry skills. I will keep all of this in mind as I work to answer my driving question. 2) Question 2: “What will you need to know to answer that question?” For this step I must gather evidence to effectively measure how I can meet all of my student’s individual needs. I must have a baseline assessment to start. After clearly identifying where I want my students to achieve after completing a unit of study, I will administer a baseline assessment. I will use two forms of a baseline assessment: a standards based test, and also a verbal baseline test to assess inquiry and growth mindset principles in relation to math. Next, I will administer midpoint and post assessments. Other forms of assessment will be observation and record keeping. Since inquiry is a central focus for my school this year in relation to math, I will gather data from student conversations about math individually, and with their peers. One place to easily gather this information would be at our Number Corner (a component of our math program that focuses almost exclusively on using math academic vocabulary, questioning, and inquiry). This would also tie into measuring the growth mindset principle in relation to math. Gathering data from my students verbally in this area will show where their personal mindset is with math. This will allow me to watch their growth mindset and academic progress. I will compare the baseline and midpoint assessments before administering the post test. This will allow me to evaluate what areas the students need more work in before the final post test. These modes of assessment will be done through a naturalistic approach, because this kind of research is field-focused and will take place in my classroom. I will be relying on qualitative methods of research, especially for the growth mindset/inquiry portions. This will be derived from observations, videography to review and compare, open-ended questions, and document collection. Multiple methods of assessment will help me gain a holistic understanding of how my students are progressing in relation to my driving question. The growth mindset is part of my driving question, so I could observe and record how my students speak about approaching a new math concept in relation to those growth mindset principles (i.e. “I can do this”/ “I can’t do this”, etc.). Then I will compare these conversations from the beginning to the end of this inquiry. 3) The last question I am addressing is, “What do you already know (from your own experience and from reading about)?” I will identify what I already know works from my own experience, and from reading The Power of Questions, to reflect, analyze and draw conclusions. It is important to have a combination of direct instruction, peer collaboration, independent work time, and small groups/individual conferencing, in order to reach as many students as possible. I have found that “Call and Response” techniques and “Whole Brain Teaching” methods work well for engagement. For example, I use the phrase, “Mirror with words.” My students repeat what I am saying, and the movements I am making. This allows students reinforce the concept kinesthetically and orally. Additional auditory tools I use are teaching with music, song, or a chant. Kinesthetic learning can be demonstrated through using manipulatives. For example, students can physically build an array with tiles to represent an multiplication problem so students can “see” “7x5=35” by physically building that problem with math tiles. My interpersonal learners benefit from speaking with their peers in pairs or small groups. Repeating/reteaching the standard being taught with peers reinforces what is being taught. This strategy helps linguistic learners clearly formulate their thoughts to express their learning verbally. Giving my students the opportunity to talk to one another in pairs or small groups about the new concept being introduced during direct instruction. Direct instruction followed by independent work and reflection helps auditory learners and intrapersonal learners. Intrapersonal leaners benefit from individual reflection time in order to organize their thoughts and understandings of concepts before sharing out thoughts with others. Other helpful methods of teaching include videos and visuals to build background knowledge. A collaborating activity such as students working in small groups to create posters representing new concepts can include many learning styles in a powerful way. For example, students collaborate, make a visual picture, write a definition, and share with the class. Small group sessions give me the opportunity to work with one group at a time to further enhance student understanding of new concepts. To best address my driving question I will need to be objective, precise, and have results that are able to be verified by others. I will need to use evidence gained by systematic methodologies to effectively answer my driving question. |
AuthorWrite something about yourself. No need to be fancy, just an overview. Archives
December 2018
Categories |