C# Parameterized SQL Command - Parameters Not Working

Question

I was trying to prevent SQL Injections on my code and it is not updating the parameters. Here is my code.

private static void CheckTableColumns(SqlConnection sqlCon, SqlTransaction sqlTrans,
                    String tableName, List<TDBColumnInfo> columns)
        {
            StringBuilder sb = new StringBuilder();
            sb.Append("IF NOT EXISTS(SELECT COLUMN_NAME FROM INFORMATION_SCHEMA.COLUMNS ");
            sb.Append("WHERE TABLE_NAME = @tableName AND COLUMN_NAME = @columnName) ");
            sb.Append("ALTER TABLE @tableName ADD @columnName @dataType");
            String sqlFmt = sb.ToString();

            SqlCommand cmd = new SqlCommand(sqlFmt);
            cmd.Connection = sqlCon;
            cmd.Transaction = sqlTrans;

            foreach (TDBColumnInfo colInfo in columns)
            {
                if (colInfo.ColumnName == "RecID")
                    continue;

                SqlParameter tableNameParam = new SqlParameter("tableName", SqlDbType.Text);
                SqlParameter columnNameParam = new SqlParameter("columnName", SqlDbType.Text);
                SqlParameter dataTypeParam = new SqlParameter("dataType", SqlDbType.Text);

                tableNameParam.Value = tableName;
                columnNameParam.Value = colInfo.ColumnName;
                dataTypeParam.Value = colInfo.DataType;

                cmd.Parameters.Add(tableNameParam);
                cmd.Parameters.Add(columnNameParam);
                cmd.Parameters.Add(dataTypeParam);

                cmd.ExecuteNonQuery();
            }
        }

I also tried adding @'s at the beginning of the string here :

                SqlParameter tableNameParam = new SqlParameter("tableName", SqlDbType.Text);
                SqlParameter columnNameParam = new SqlParameter("columnName", SqlDbType.Text);
                SqlParameter dataTypeParam = new SqlParameter("dataType", SqlDbType.Text);

Still same.