Reflection 13

The focus of this course is on instructional strategies of teachers, but the concept of checking ones self, evaluating methods of instruction no matter what position is beneficial in any field whether working with students, parents, or professional team members.  Steven C. Reinharts, use of questions and explanations not only provided assessment of his students, but helped bring an awareness of his teaching methods and new techniques which benefited his students.

I completed middle school and high school answering many questions asking for only a yes or no answer.  In fact, most of my teachers were old school and students did not speak unless spoken to.  What a blessing, children now have increased opportunity to express their ability to use deeper thinking skills.  And if not skilled or yet ready to use critical analysis, children have the opportunity to practice and fine tune these skills. Not only are students given the opportunity to develop and improve thinking skills, teachers are able to use open ended questions to provide ongoing formative assessments of their students and themselves.

Letting students question, practice, and discuss answers are critical components of learning.  Part of learning also involves becoming confident in ones self and ones ability to provide answers.  I remember chosing to not answer or respond in class because I was worried my answers were wrong which lead to many unanswered questions and misunderstood steps.  It does seem advantageous to encourage students to answer in any case without drawing attention to those who are absolutely correct and those who are wrong.

I see using this technique or ideology for future classes I will teach.  Middle school is a difficult time for students. I believe it is the make them or break them point in education.  As teachers, we must desire to "catch" our students and give inspiration while teaching without discouraging thinking about thinking.  It should not be devistating to be wrong, it should be an opportunity to encourage research and review of information and material which instills learning.

Reflection 12

It seems using tools other than summative assessments and end of chapter or course test to assess student achievement is a valuable asset to any teacher. The ideas imposed by states which expect every student to perform and pass on levels and standards of equality are absurd.  Provisions to families are not distributed equally, time is not distributed equally, and disposable income is not distributed equally.  Depending on the socio economic status and class in which children are born ultimately has a significant impact on student performance.  Adding to the families focus for survival is the time involved to develop those pre literacy skills needed when entering kindergarten.  Speculating all children have equal cognitive abilities, parents and early childhood caregivers would need to teach all typically developing children at the same pace and level.  Sadly, most likely this will not happen and continues to put low income students at automatic disadvantages when compared to age equivalent peers.  Thus using alternative assessment tools such as formative assessments and portfolios give educators access to immediate feedback and knowledge of student understanding and performance hopefully helping to ensure improved outcomes for students with academic delays and or differences in learning styles.

Paul Black and Dylan Wilian discuss the negative impact current assessments have on students and the need to study more in depth the impact of these requirements on teachers and classrooms.  Systems need to take a chance on using different types of assessments for grading and comparing students to ascertain success or failure.  In a society which focuses so heavily on diversity and the individual uniqueness in personality, dress, and preferences there continues to be an unvarying idea of what is considered achievement and what is considered failure in education.  Since society allows for such diversity in individual style and choice, why does education continue to maintain a standardized formula for students?  Thus, using only summative assessments without assessing prior to and during instruction does not give teachers a good idea of individual student understanding of topics as various point during instruction. 

Furthermore, as imposed standards and achievement expectations increase with government driving reform and change, I ponder the initial intentions of those implementing state changes.  Do the intentions of lawmakers stem from wanting only to ensure all children have equal access to great teachers and great instruction?  Do, those who push the laws and rules consider or look into the micro, macro, and meso environments of those inside the classroom?  I worry lawmakers are too far removed from the group in which the standards are designed to supposedly benefit.  If you have never worried about where your child’s next meal is coming from or how the electric bill will get paid this month, the thought of families not being able to provide the early literacy skills and knowledge needed early in a child’s life would not occur thus putting additional responsibility on the classroom teacher for recognizing the home environments impact on students.  The academic burden of success is placed solely on classroom teachers.   Why not place more responsibility on student parents?  Placing some burden of success on the family for their children’s behavior, attendance, and performance in the classroom might improve our schools and overall outcomes.  It might bring awareness to government entities of the needs of families and cause some to consider how the child’s environment and socio economic status has significant impact on academic success alleviating some of the burden  and responsibility felt by teachers.

The use of portfolios is seen more often in classrooms with students receiving special education receiving special education services.   Vicki L. Maxwell and Marshall B. Lassak believe standard assessments are not the only way to assess student performance in classrooms.  I imagine portfolios being used across the curriculum in all classes with all students allowing teachers to see student weaknesses and strengths allowing for student differences.  Also, the authors shared the portfolios helped assess instruction allowing for changes and teacher improvement such as recognizing the need for more open ended questions used with activities in the portfolios giving students opportunities to think critically and involve the use of writing across the curriculum.  It is always beneficial to check instruction style and methods when it pertains to student learning.  It is essential to understand if the success or failure of an individual student is related to the way instruction is provided.  Not only is the use of portfolios beneficial for students and teachers but also for families. Portfolios give parents immediate, easily understood records of student performance.  For example, regarding norms imposed and levels of achievement given based on standardized test, families may or may not see an increase in their child’s academic understanding of specific concepts when reviewing summative test scores.  Portfolios seem to show where a student was at the beginning of the class and throughout the semester providing families a way to view growth in which summative test may not be able to show.   

Reflection 11

There is an element of collaboration needed when providing the most advantageous avenues for students to be academically successful to their fullest potential.  This element is dependent on parent engagement and involvement. Unfortunately, in my opinion and experiences, parents and teachers do not always respect each other.  But, parent involvement is a crucial piece of student success.  It seems, in the past, parents did not question teachers or school administration.  Parents, mothers in particular, allowed educators to decide the direction of students without question.  In recent years there has been a push for parent involvement and collaboration.  No longer does the teacher have all the knowledge.  Middle class mothers are taking charge of their children’s education ensuring every opportunity is available.  Those equipped with the right resources usually get what is desired.  In contrast, there continue to be parents struggling to understand the importance of their role in student success often taking a back seat, giving in and being labeled the parent who does not care.

In fact, some parents labeled as not caring and uninvolved had awful experiences in school.  Others are doing the best they can with the resources they have.  Parents, when focused on providing the basic physiological needs for their children may not have the internal drive or physical ability to add one more element of stress to their lives.  These families are doing just fine with life and adding any other elements is going to cause the dynamics of the family to significantly shift.   These are the parents to be reached.  Children of typical, middle class, duel income families are not going to fall between the cracks and go unnoticed.  It is the student whose family lacks adequate resources and support who will fail and give up. Struggling parents need teachers and teachers need these parents too.   It is my belief, family learning nights provide opportunities for teachers and parents to come together in a nonthreatening, fun, learning environment giving parents opportunity to be involved as well as provide teachers a chance to see parents in a different setting.

NCTM’s tips provide good quality information regarding contact and collaboration with parents.  Considering I believe parents are a key component in the academic success of students.  Essentially, teachers and parents have a duel role in working to keep students on task and on target.  And for this to be successful, teachers must be willing to build relationships and collaborate with their student’s parents and caregivers.  Most every suggestion given was appropriate with building relationships and helping students.  Although, I do not agree with giving an extra credit point to students whose parents email a response to the teacher.  There are many families who do not have adequate or consistent internet or email access and this is not a fair distribution of bonus points.   Additionally when looking at the dynamics of a student’s family, it is vital to know who is providing care or has custody.   For example, if the caregiver is a grandparent or great grandparent, the use of text and or email may not be their main method or mode of communicating with the outside world.  Believe it or not, there are families who chose to go without cable in order to provide better quality of care for their children. This is something to consider as the number of grandparents gaining custody of their grandchildren continues to rise.  Not only is the ability to stay up to date on frequently changing technology a disadvantage for older parents, but the lack of disposable income also contributes to involvement and resource support.

Working with students who are language delayed, my focus has always been on improving their limited vocabulary.  Family activities or events have always been designed with literacy and reading as the main focus. Yet, this article has given new insight to other important areas related and connected to literacy.  Andrea Lachance is right on target with her Family Math Nights.  Families are an integral part of student success and there must be a way to reach those who are not currently, actively working with their children at home.  Realizing the importance of not only reading literacy, but also math literacy is becoming quite apparent.  Families need to understand what to do to provide homework, after school, and summer activities for their children which are fun yet focusing on building and increasing the student’s knowledge and confidence in literacy and math.  Family math nights and event nights are great assets for families.

 In contrast, these kinds of activities take money, resources, and time.  Without the support of teachers, colleges, and other organizations, it can be difficult to pull these events off successfully.  Teachers and parents are overworked and underpaid often not wanting to give up precious time with their families to be involved.  For example, part of my job is to establish parent support meetings and family activity nights.  I am struggling with getting families to attend and become actively involved in their child’s education.  Furthermore, I do not have adequate funding to pay for large scale events.  In the past, events were scheduled monthly in 6 different locations across the state without childcare being provided.  Following this model is proving ineffective in the purpose of these meetings.  It is evident a change is needed and I am considering following a model very similar to the one provided in this article.  It is my hope to provide family learning opportunities which involve parents, children, and teachers.

Prior to reading any articles, I typically read titles, subtitles, and skim for basic information.  This technique is useful for any reader.  Of course the anxiety potential is heightened when seeing words such as polynomial, linear equation, and factoring trinomial.  My thoughts become twisted and stomach begins to knot up.  Immediately, thoughts go toward giving up and throwing the articles in the trash. There will be no reflection on this week.  None the less, I trudged on determined to connect and relate to the articles in some way reading again and again until there is some way found to connect and relate mathematics to language instruction and literacy.  Eventually a relation, a connection is realized regarding using concrete models to introduce concepts, increase and learn important vocabulary, and using alternative approaches to provide students access to mathematics understanding

Annette Leitze and Nancy Kitt believe learning algebra is possible for all persons by using concrete models such as the algebra tiles mentioned in the reading.  The authors suggest this technique gives students a series of levels to learning: concrete, pictorial and abstract or symbolic. This is true for all subjects and pertains to not only mathematics instruction but language based courses also.  Young children especially gain experience going through various levels and stages of learning beginning with concrete and progressing to the abstract.  When working with students who have various learning styles and special education services, concrete is a great first stage of presentation.  For example when working with a deaf student on vocabulary building, I can say the word cup, sign the word cup, show the printed letters for the word cup, but unless I show a picture of the cup or an actual cup the concept of cup may not be acquired or fully established.  Although a child may have been shown how to use the cup, without being able to relate the cup to everything, pictures, sign, print and tactile – full understanding of the concept or meaning is not established.  It would be interesting to do a study and collect data with deaf students implementing all steps or methods of language or vocabulary acquisition.

Next, Rhela N Rubenstein focuses on strategies for increasing and learning mathematics vocabulary.  Students with limited vocabulary as a result of language delays may easily become confused during instruction, for example when math words such as sum and some are used during instruction.  A deaf student relying on speech reading and lip reading skills may have difficulty understanding which word is being used if enough clarification is not provided.  Although students using sign language will understand the differences in meaning, students using speech reading and listening skills may become confused or misunderstand these two words since they both look exactly the same on the lips.  This article in particular states the importance and the need for early language and vocabulary work.  It is important for parents and teachers to show, explain, describe, print, and give details and concepts as early as possible with students having language delays.  This suggestion does not come from knowledge gained through research, but as a parent these are issues that popped up from time to time when my daughter was young. Children born with hearing loss or deafness are at an instant disadvantage. Without sound may of the ways early language is acquired such as environment, parents, radios, television, and other siblings are not available.  Language stimulation is acquired from one on one and face to face interactions.  This is but one challenge children with hearing loss face in the classroom.

Another challenge in language acquisition is having access to skilled interpreters.  Interpreters do not always have a good grasp on conceptual signing. Using the same sign for two words with different meanings such as some and sum could seriously impair a child’s understanding of mathematical concepts.  This unfortunately occurs more often than I care to discuss. Additionally, these authors asked “how do we help students recognize these nuanced differences of usage?”   The idea of the need for understanding the difference in meaning is enormous.  Students using speech reading and or sign language need to be exposed to all meanings.  Signs must be conceptually correct; Interpreters must have an understanding of mathematical concepts and meaning as well as parents.  These concepts must be expressed, signed, spoken, practices, and shown to ensure the correct meaning is acquired.

Last, John W. Coburn discusses using various approaches to teaching algebra.  This article seems similar to several of the earlier articles read this semester regarding students invented algorithms and teachers teaching from the same, old approach.  Although, I have solved inequalities, graphed quadratic equations and factored polynomials, my heart races and anxiety increases while reading this article.  I look at some of the text and feel as if I am reading a foreign language.   There are pieces of my mind wanting to shut down and give up.  Equally, the intrinsically motivated side of my mind is determined to give this another chance, to reread over and over until something stands out.   When Coburn discusses students using certain uncommon styles, I am intrigued and continue reading.  I absolutely agree with this discussion.  There is a lot of information which seems to support providing students multiple ways for solving mathematical equations.  It is essential  to use every available resource in an education setting and these resources should be used until the concept is acquired.

I am beginning to understand there is much more to being math literate than merely knowing math related vocabulary words.  When hearing the term, “math literate”  the association to this term has been to the meaning of words and not concepts.  After reading and studying ideas pertaining to math literacy, it appears becoming math literate follows a process similar to learning to read.  Students must acquire and understand specific components necessary when moving from the learning to read stage to the reading to learn stage.   Thus, if students begin to make decisions about being math smart or math dumb during early middle school years, classroom environments must be established allowing teachers to implement strategies and practices needed to build student confidence and knowledge of mathematics stages and provide opportunity to promote and excite students about doing math through effective discussions, good classroom management and building on student geometric concepts.

Smith et al., (2009) presents the Five Practices Model to promote student participation and effective discussions during mathematics instruction which assist with offering a more manageable group time.   Planning a lesson to the last detail including student anticipated responses and solutions is a key component in being able to offer the best mathematics instruction while reaching the most students.  According to Smith et al, having a variety of scenarios established and knowing which direction to focus student discussion based on purpose of the lesson makes wise use of instruction time.  I, as the teacher, must be able to think about and offer multiple solutions to problems and explanations of concepts students might come up with.  This creates some anxiety as I ponder my ability to understand multiple processes and be able to think about all the ways a student might consider solving a problem both correctly and incorrectly.  In order to adequately facilitate my students, I would consider it essential to collaborate and discuss lessons being planned with a more experiences math instructor.  I agree with and support the use of a constructivist approach in teaching mathematics.  A constructivist approach, I know is successful in reading instruction and feel this would be a great way to present math instructions.

Although this model is a great avenue for conducting student centered, whole-group discussions and instruction, I must be able to effectively manage my classroom and instruction time.  Students need to be able to talk and write about math.  Yet, as steps are being built to understand mathematical concepts it is equally important to build steps for appropriate discussion of math techniques.  Group discussion can easily move off task when a teacher is unable to effectively manage the class.  For instance, last week we talked about using hands on work and activities, and how without good classroom management these tasks can easily become chaotic.  The whole purpose of the lesson could be lost without a focused instruction plan and good management.  It is important to anticipate the direction student discussion may go and how to bring it back to the main focus should other ideas become the topic of discussion.   When discussions move off topic, it can use valuable instruction time and trying to get back to the main point becomes difficult.  For me, one way to keep instruction on point is to know specific levels and needs of all students in my classroom.  This knowledge can help with planning for possible scenarios and having responses and instruction geared toward keeping everyone on the lesson task.

Similar to reading concepts, math geometric concepts are built on in layers.  Middle school is a good time to build on students thoughts about geometric shapes and special sense.  Van de Walle suggest,  it is important as a teacher to be aware in grades 5-8 there will be students at varying levels and in order to move to the next level a student must be able to understand each layer presented in the van Hiele Theory of Geometric Thought.  Each level, content area, overlaps and builds on each other.  This seems very similar to the components needed to learn to read.   Considering the importance of parental involvement in student awareness of print and reading components in the early years, I think this same idea must apply to students learning math concepts.  Components necessary to build on one’s ability to understand and then apply knowledge to different concepts may not be focused on at home in the early years leading to difficulty obtaining basic information necessary when entering elementary and middle school math classes.   Yet, this is an area parents can work to provide developmentally appropriate practice for the student. I believe education and language level of parents do not necessarily impede learning of basic math sense.  Many parents recognize shapes and can talk about these in a variety of ways building on those lower levels of geometric sense which may have some benefit in the classroom.

Parents should be encouraged to provide early literacy opportunities in all subject areas including mathematics. I work to provide resources and support in reading literacy and focus on parent involvement in helping students to improve reading and writing ability.  However, it is becoming more apparent the need to work with families to provide support for their children in mathematics. Both articles present models which with some changes implemented to fit with the parent perspective might be useful when teaching how to work with and benefit students outside the classroom.

 Furthermore education has placed such a focus on reading and writing, I am concerned early learning moments for math concepts such as spatial sense are left out of the day’s instruction.  Also, more and more art programs are being cut from education budgets.  Early drawing in art classes gives students a sense of shape and space in a non threatening learning environment most children enjoy giving the child and opportunity for spatial sense and development of geometric thought an opportunity to grow. As education seeks to work toward improving the mathematics literacy in the United State, it would be interesting to study the implications of removing art programs because of budget restraints.

Reflection 5

September 25, 2012

There is an unspoken inequality which seems to silently hover over distinct groups of people, towns, and cities across America who are in some ways limited by their circumstances.  In fact, society has a way of blocking those who have limited resources from access to improving their situation.  Possibly, not intentional but none the less, a system whereby escape is difficult and can seem impossible.  Those living in poverty must deeply desire a change and be able to endure challenges and hardships while obtaining their ticket out.  I recently heard the comment, “They should go get a job and move to a different part of town.  They are there because they choose to be there.”   Yet I do not believe social class or poverty is a conscious choice any one would make.  In fact there are many individuals considered working poor living below the poverty threshold maintaining full-time employment with enough to barely live day to day, but never enough to get ahead.  I am curious if becoming math literate for this next generation is the key to make a change in a system of reoccurring poverty?   I believe, becoming math literate is a piece to the puzzle, but a teacher’s ability in the classroom as the only implemented change is not enough.  One can make all the necessary adjustment in education and teacher requirements it wants.  But, it is necessary to go beyond the teacher’s ability to reach the student to change the mindset of this county related to one’s ability to excel in math.  Change has to be across the whole system.

The Algebra Project, Cobb and Moses article resonated with many ideas I believe are true, specifically the statement, “Math illiteracy is not unique to Blacks the way the denial of the right to vote in Mississippi was.  But it affects Blacks and other minorities much, much more intensely, making them the designated serfs of the information age…”  Not everyone would agree with me, but I feel the United States has an unspoken class system which people refuse to acknowledge.  A system which is nearly impossible to change and to change it will take determination and a will which cannot be tackled by teachers only. Yes, math is a key component in education and with the advancement of technology in all fields the need for math and science literacy is here to stay.  Yet, becoming math literate is not going to change a system of generational poverty.  Perfecting one’s teaching technique, style and use of technology is not going to be enough.  I have spent fifteen years working with children from all socio economic levels.   There are always the few who can be reached, but I continue to see middle class and wealthy students doing much better than their peers living below the poverty threshold. 

And, teachers continue to work endlessly to plan and labor to generate lessons which provide better understanding of concepts in an attempt to give equal access for learning to all students using hands on and real world applications.  This is a great benefit to students yet on the other hand, schools can offer waivers and vouchers to cross zones and bus students to the so called better schools, provide the most up to date advance technology, and use best plus practices.  But the outside resources available to students living in poverty do not currently and will never equate to the resources of middle and upper class students.   Annette Lareau, (2003) author of unequal childhoods references Paul Kingstons, The Classless Society stating, parents’ social class position predicts children’s school success and thus their ultimate life chances.  In essence, where people live, parents education level, income earning potential all determine one’s social class which in turn is going to impact a child’s ability to get into the better school leading to the better college thus the better college determines the future income potential (2003) which in turn determines social class.    I believe Cobb and Moses are suggesting to truly change to an education system where everyone becomes math literate, there must be a whole system change such as a change within the community and family value of education.  In my opinion to make this switch of mindset, those in the classroom must make every effort to collaborate and build relationships with our students and their families.  This, I believe, is another crucial piece in the conquest of students becoming math literate.

Additionally, Drew Polly points out the importance of two teachers working together and preparing questions in advance of the lesson in order to more effectively present and instruct while using technology to improve student ability in mathematics.  Definitely, co-teaching is an effective and resourceful way to present a lesson.  However, to be successful, this style of teaching will work well only when being prepared.  Impromptu and poor planning will lead to organized chaos.  These two teachers must share the same goals and be able to work together in a flexible and respectful manner.  It can be difficult to place two adults in one classroom when teaching styles and perspective of education are different.  Using this style of instruction should be well thought out and when administration places teachers together it should be purposeful.    Also, the approach of the teachers and classroom diversity may determine which style of co-teaching is used.   I have worked in a middle school which used co-teaching across the curriculum in all grades.  And some of the best lessons presented were by two teachers who were using best practices and up to date technology.  I witnessed students able to work in small groups and receive more one on one instruction during the lesson.  These teachers used a drifting method.  While one teachers focused on the main instruction and presentation the other drifted from group to group ensuring each student understood and was able to move ahead in the lesson.  At varying times, both teachers would be interacting with the groups.  It seemed all children’s questions were answered and everyone had opportunity to present ideas and show progress.  If at any time a student found the work difficult or did not understand one teacher could focus on the specific needs of that child while the other teacher continued to move forward with instruction.  With two or more teachers in a classroom, students are monitored more closely, grouped heterogeneously, and student centered instruction is easier to conduct thus giving students more time and access to explore, think, and analyze solutions.  This setting would be my preference given a choice.

Van de Walle’s discussion of sequences and growing patterns in Chapter 9 is similar to learning the steps to read and write.  When learning to read and write there are essential building blocks necessary to learn before one can read to learn.  It seems this is similar to learning mathematics and becoming math literate with steps and sequences being introduced early in education to establish a strong foundation and build on a child’s existing knowledge.  Realizing the importance of students learning math in stages going from concrete to abstract, I am concerned about providing the appropriate math instruction to students in special education.  Often students with disabilities may need additional support and resources when learning math.   So I question, is it the disability inhibiting the learning of math or is there another delay such as language attributing to a student's ability to learn math? In my experience it is not the students with physical disabilities or even sensory loss who necessarily struggle with learning patterns and sequences.  I know of many deaf students who excel in mathematics.  But for every one who excels there is one who struggles.  Often, it is the student who is identified with a secondary disability and considered to have a language delay or language impairment.  When the language and vocabulary to understand instruction and concepts of any core subject is missing – language instruction can become the focus of education with little emphasis on mathematics instruction.  Apparently, this lack of emphasis is impacting the futures of many students.  As teachers we must find a way to introduce building blocks of language and the building blocks for mathematics equally.  I am suddenly realizing the apparent need for teachers in elementary and special education to understand the importance of mathematics to the future of our students.  And understanding I need to move away from the mindset of math ability being set as ither good or bad at math.  Although, I have not specifically participated in planning lessons or instruction practices focused on mathematics, I can now understand the need to become an effective math teacher who is able to introduce students with or without disabilities to mathematics concepts as well as work with their families to change family minsets about math ability.

If math literacy for all is this generation’s focus, and if American students are to keep up with other countries, teachers must be willing to grow and change using different approaches for real life application and up to date technology.  Teachers must also be willing to learn to teach subjects to students with a new mindset.  Realizing all students have the potential to learn.  Additionally, for students of all socio economic status to be successful in any area of instruction, parents, caregivers and guardians are vital to a child’s academic success.  Until we can change the cultural idea that it is the teacher’s full responsibility to teach children and everyone begin to recognize the role of parents as teachers, I am expecting reform to occur at a much slower pace than is needed.