Common Learning Characteristics

Common Learning Characteristics

that make

Mathematics Difficult

for Struggling Learners

Adapted from Allsopp, Davi H., Maggie M. Kyger and LouAnn H. Loving. Teaching Mathematics Meaningfully: Solutions for Reaching Struggling Learners.Baltimore, London, Sydney: Paul Brookes Publishing Co. 2007.

1.  LEARNED HELPLESSNESS

Defined:

Students who experience continuous failure in mathematics expect to fail, resulting both in reticence to try something new and reliance on others to help them.

Why:

When mathematics instruction has been solely focused on right and wrong answers, even students as young as 5 years can quickly become intimidated when their answers and methods do not match the teacher’s (adult’s) way of thinking about the problem, especially when the teacher’s method does not make sense to them.

What to do:

Examples of instructional strategies that can assist students in overcoming learned helplessness include breaking down tasks into more manageable segments, proving visual organizers that cue students to important aspects of a concept, and continuously monitoring student progress so that instruction can be changed quickly if it is not successful. It is important to note here that these instructional strategies are not “doing the thinking” for the students, but are a way to provide structure to the task so that it is manageable for the students in their current state of learned helplessness.

2.  PASSIVE LEARNING

Defined:

Struggling learners often are not active learners. They do not actively look for and make connections between what they already know and what they are presently learning. When presented with a problem-solving situation, they do not implement strategies or activate previous knowledge to solve the problem.

Why:

Afraid to engage actively in activities that might lead to more failure, students shy away from exploration and experimentation. They do not want to “discover” the answer because given their past experiences; they do not believe that they can. Students who are passive learners will have difficulty making connections between concepts of number and operation concepts and algorithmic procedures.

What to do:

Embedding mathematical instruction in relevant authentic contexts and encouraging students to develop and consider several strategies to complete a task will help these students make important connections and develop flexibility in their thinking. It also will be helpful to provide an explicit way (e.g., a strategy journal for mathematics) for students to actually see their progress in developing and using alternative strategies for mathematical problem solving.

3.  MEMORY DIFFICULTIES

Defined:

Students with memory difficulties have difficulty retaining and retrieving information, particularly related to basic addition, subtraction, multiplication, and division facts and multistep sequencing and problem solving.

Why:

“Here today and gone tomorrow!” It is important to differentiate between students who have difficulty remembering because they have trouble acquiring an understanding of a concept and those who acquire understanding but have difficulty retrieving the information from memory.

Difficulty with acquiring understanding most likely is related to ineffective use of learning strategies (e.g., rehearsal and retention strategies, meta-cognitive strategies such as self-talk, connecting to existing knowledge) or ineffective instruction (e.g., lack of context, limited use of multi-sensory instruction). For these students, remembering what they learned is difficult because they have never really learned it

Difficulty with retrieval is more closely linked to problems with organization and association (i.e., linking to existing knowledge). Students who have difficulty with retrieval may not have developed efficient memory retrieval strategies.

What to do:

Providing students with visual organizers and multiple opportunities to represent problems and regularly integrating mnemonics into instruction can help ameliorate the effects of memory deficits. In particular, strategy instruction that incorporates mnemonics is described as an instructional practice that helps students with memory difficulties.

4.  ATTENTION DIFFICULTIES

Defined:

Learning and doing mathematics requires a great deal of attention, especially when multiple steps are involved in the problem-solving process. During instruction, students who have attention difficulties often miss important pieces of information. When doing mathematics, students may also miss a step due to distractibility, thereby reaching an incorrect solution.

Why:

They are less likely to accomplish comprehensive comparisons between and among similar and dissimilar concepts, inhibiting their ability to build mathematical connections. Students with attention difficulties often miss important mathematical information as it is being discussed or as they engage in problem solving. They have trouble filtering out all of the information that their senses and brain are processing. Rather than not focusing on anything, these students are focusing on everything.

What to do:

Using visual, auditory, tactile (touch), and kinesthetic (movement) cues to highlight the relevant features of a concept is a helpful teaching technique for addressing attention difficulties. In addition, teaching students to use self-cuing strategies (i.e., strategies that prompt students to use a relevant cuing device to highlight important aspects of a problem) can be helpful.

5.  COGNITIVE/META-COGNITIVE THINKING DEFICITS

Defined:

Meta-cognition has to do with students’ abilities to monitor their learning, which involves 1) evaluating whether they are learning, 2) implementing strategies when needed 3) knowing whether a strategy is successful, and 4) making changes when needed. These are essential skills for any problem-solving situation.

Why:

Students with meta-cognitive deficits do not use these essential meta-cognitive thinking skills. Because problem solving is an integral part of mathematics, students who are not meta-cognitively adept will have great difficulty being successful with mathematics. When students with meta-cognitive deficits use strategies to problem solve, they often use them inefficiently.

To communicate effectively, one has to be aware of the audience, develop and deliver the message, and then monitor the communication to ascertain whether the message has been received as it was meant to be. Students must

What to do:

Meta-cognitive strategy instruction involves teaching strategies to 1) recognize big ideas among details. 2) Identify how information is structured, 3) see relationships between different sets of information, and 4) self-monitor learning.

Students must be able to decide what is being said with mathematical numbers, symbols, and shapes and whether they understand the message; and, on the basis of their understanding, develop a response. They need to be aware of their use of problem solving, reasoning, and representation processes to monitor their understanding of the mathematics that they are communicating and fix misunderstandings when they occur.

Students must be provided with opportunities to learn about strategies. They must be provided with multiple opportunities to use them and to generalize their use across a variety of contexts. Teachers who model using metacognition, who teach students problem solving strategies, who reinforce students’ use of these strategies, and who teach students to organize themselves so that they can access strategies will help students who have meta-cognitive deficits to become meta-cognitive learners.

6.  PROCESSING DEFICITS

Defined:

Students with processing deficits have difficulty accurately perceiving what they see, hear, and/or feel. Many students with learning disabilities possess processing deficits. Their vision and hearing are intact, but their central nervous system processes information differently, leading to misperceptions regarding what they learn.

Why:

A student with a visual processing deficit may see a mathematics equation accurately, but the visual information that he or she inputs may get distorted when the brain processes it; therefore, what the student sees is not actually what he or she perceives. Other students may require more time to process information that they hear. To them, the teacher seems to talk too fast, when, in actuality, their central nervous system processes at a slower rate.

Students with processing deficits are likely to misperceive information that is presented to their primary processing deficit.

Processing deficits can involve multiple input and output pathways (e.g., visual-motor, auditory-motor, visual-speech, auditory speech). Often, the student will be able to represent accurately what he or she saw or heard when asked to say it rather than write it.

What to do:

Providing multimodal instruction (both teacher input and student response) can help alleviate the effects of a processing deficit. Hands-on, kinesthetic learning will provide students with opportunities to integrate information across modalities, thereby engaging multiple senses. Providing wait time for students is another effective approach when students are to respond to questions. Teachers provide wait time by letting a student know that they are going to ask him or her a question (cuing), asking the question (auditory input), then providing the student time to process the question before expecting an answer or moving to the next part of the question (allowing extended processing time). In addition, when teachers are able to discuss tasks with students and how the student reasoned about completing the task, the teachers can prompt student thinking with purposeful questions. When teachers are explicit with student about using this process to make sense of how they are thinking, students can begin to realize that mathematics is more than just right and wrong answers. Also, students’ responses provide the teacher a framework for pinpointing each student’s understanding and possible misconceptions.

7.  LOW LEVEL OF ACADEMIC ACHIEVEMENT

Defined:

Students who experience failure in mathematics often have holes in their knowledge base. Struggling learners have these holes for a variety of reasons. For example, students with a visual or auditory processing deficit require a longer time to process visual and auditory information than typical learners. Because of this they often do not have enough time or opportunity to master the foundational concepts and skills that make learning more complex mathematics possible.

Why:

Reading is another area of low level academic achievement. This limits mathematical vocabulary development. Teaching students to solve work problems using cue words is not an effective strategy, even when students do not have limited vocabulary. Cue words do not always work. Consequently, teaching students to use cue words to solve word problems can actually continue the vicious circle in which students meet failure in mathematics.

Gaps inevitably occur in mathematical understanding. Sometimes teachers identify these “holes” in knowledge as a lack of “basic skills.” Teachers will often say that students need to know their basic facts before they can do any higher level problems and so the instructional focus becomes having students “learn” these “skills” via drill and memorization (i.e., the traditional method of reaching number facts). In actuality, the holes may be there because students’ only exposure to these ideas was through drill and memorization, not through concept development. Mathematics builds on ideas, and when the foundation consists of isolated bits of information, holes will be present.

What to do:

Using multiple representations for mathematical concepts and combining concrete experiences with authentic contexts that engage students to use their own language to describe what they are learning is also important. Providing students with multiple opportunities to use their developing understanding of mathematical concepts in meaningful ways (what we call practice), so that proficiency and mastery of new concepts and skills are attained is essential, as is planning periodic review and practice of concepts and skills that students have mastered previously so that students maintain what they have learned.

8.  MATH ANXIETY

Defined:

Struggling learners often approach mathematics with trepidation. Because learning and doing mathematics are difficult for them, “math time” often is an anxiety-ridden experience predisposing them to “shut down” when confronted with learning something new. The best cure for math anxiety is success.

Why:

The distress comes from the student's own awareness that his or her own knowledge or learning is not what that student feels is adequate (for his or her own purposes. which might be wanting to satisfy others). The level of distress is heightened when the student actually tries to learnitems which are not yet known or fails to learn what now is being encountered. The subconscious mind compiles an internal personal mathematical history, which can follow a child into adulthood.

Weaknesses in knowledge at lower levels undermine learning at higher levels. When each step is only partial learned, the learned portions become progressively smaller. So, scholastic success becomes increasingly difficult to achieve or sustain.

The further the students go along a developmentally discontinuous curriculum, the more they must rely on merely memorizing things that do not make sense to them. Along the way, their mathematical comprehension gap progressively widens. So, their abilities to learn mathematically progressively deteriorate -- whether or not they are aware that it is happening.

What to do:

The attitude with which teachers approach these students can be a crucial first step in rectifying the mathematical difficulties that they are having.

Providing these students with non-threatening, risk-free opportunities to learn and practice mathematical skills lays a critical foundation.

Working with Low Achieving Students Page 2/9